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## Big Ideas Math Book 5th Grade Answer Key Chapter 7 Divide Decimals

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**Lesson: 1 Division Pattern with Decimals**

**Lesson: 2 Estimate Decimals Quotients**

**Lesson: 3 Use Models to Divide Decimals by Whole Numbers**

- Lesson 7.3 Use Models to Divide Decimals by Whole Numbers
- Use Models to Divide Decimals by Whole Numbers Homework & Practice 7.3

**Lesson: 4 Divide Decimals by One-Digit Numbers**

- Lesson 7.4 Divide Decimals by One-Digit Numbers
- Divide Decimals by One-Digit Numbers Homework & Practice 7.4

**Lesson: 5 Divide Decimals by Two-Digit Numbers**

- Lesson 7.5 Divide Decimals by Two-Digit Numbers
- Divide Decimals by Two-Digit Numbers Homework & Practice 7.5

**Lesson: 6 Use Models to Divide Decimals**

**Lesson: 7 Divide Decimals**

**Lesson: 8 Insert Zeros in the Dividend**

**Lesson: 9 Problem Solving: Decimal Operations**

- Lesson 7.9 Problem Solving: Decimal Operations
- Problem Solving: Decimal Operations Homework & Practice 7.9

**Chapter: 7 – Divide Decimals**

### Lesson 7.1 Division Pattern with Decimals

**Explore and Grow**

Use the relationship between positions in a place value chart to find each quotient.

What patterns do you notice?

Answer:

**Structure**

Describe the placement of the decimal point when dividing a decimal by 10, 100, 0.1, and 0.01.

Answer:

**Think and Grow: Division Pattern with Decimals**

**Example**

Find 74 ÷ 10^{3}.

Use place value concepts. Every time you multiply a number by \(\frac{1}{10}\) or divide a number by 10, each digit in the number shifts one position to the right in a place value chart.

Notice the pattern: In each quotient, the number of places the decimal point moves to the left is the same as the exponent.

**Example**

Find 5.8 ÷ 0.01.

Use place value concepts. Every time you multiply a number by 10 or divide a number by 0.1, each digit in the number shifts one position to the left in a place value chart.

Notice the pattern: When you divide by 0.1, the decimal point moves one place to the right. When you divide by 0.01, the decimal point moves two places to the right.

**Show and Grow**

**Find the quotient.**

Question 1.

62.5 ÷ 10^{2} = ______

Answer: 0.625

Explanation: First Simplify the 10^{2} which means 10X10 =100 then we need to calculate the fraction to a decimal just divide the numerator(62.5) by the denominator (100): 62.5 ÷ 100 =0.625 so, 62.5/100 =0.625

Question 2.

1.84 ÷ 0.1 = ______

Answer: 18.4

Explanation: To convert this simple fraction to a decimal just divide the numerator (1.84) by the denominator (0.1): 1.84 ÷ 0.1 = 18.4 so, 1.84/0.1 = 18.4

**Apply and Grow: Practice**

**Find the quotient.**

Question 3.

76 ÷ 10 = ______

Answer: 7.6

Explanation: To convert this simple fraction to a decimal just divide the numerator (76) by the denominator (10): 76 ÷ 10 = 7.6 so, 76/10 = 7.6

Question 4.

3.65 ÷ 0.1 = _______

Answer: 36.5

Explanation: To convert this simple fraction to a decimal just divide the numerator (3.65) by the denominator (0.1): 3.65 ÷ 0.1 = 36.5. so, 3.65/0.1 = 36.5

Question 5.

2.9 ÷ 0.01 = ______

Answer: 290

Explanation: To convert this simple fraction to a decimal just divide the numerator (2.9) by the denominator (0.01): 2.9 ÷ 0.01 = 290. so, 2.9/0.01 = 290

Question 6.

18.7 ÷ 10^{2} = ______

Answer: 0.187

Explanation: First Simplify the 10^{2} which means 10X10 =100 then we need to calculate the fraction to a decimal just divide the numerator(18.7) by the denominator (100): 18.7 ÷ 100 =0.187 so, 18.7/100 =0.187

**Find the value of k.**

Question 7.

95.8 ÷ k = 958

Answer: K = 0.1

Explanation: Lets solve your equation step by step 95.8/k = 958

Multiply both side by side K.

95.8 = 958K

958k = 95.8 (Flip the equation)

958k/958 = 95.8/958(Divide both sides by 958)

K=0.1

Question 8.

k ÷ 10^{3} = 0.35

Answer: K =350

Explanation: K÷10^{3 }=0.35

Step 1: calculate the value of the power which means 10^{3} = 10x10x10=1000

k/1000=0.35

step 2: multiply both side by 1000

1000X K/1000 = 1000X0.35

Step 3: simplify

1000 X K/1000 = 1000X0.35

K = 350

Question 9.

245 ÷ k = 24,500

Answer: K =0.01

Explanation: variable K cannot be equal to 0 since division by zero is not defined. Multiply both side of equation by K

245 = 24500K

swap sides so that all variables terms are on the left hand side

24500K = 245

Divide both sides by 24500.

K =245/24500

Reduces the fraction 245/24500 to lowest terms by extracting and cancelling out 245

K = 1/100 ,Therefore K = 0.01

Question 10.

Newton goes on a 10-day road trip. He takes $435 with him. He spends all of his money and spends the same amount each day. How much money does he spend each day?

Answer: $43.5/per day

Explanation: Newton takes $435 for 10 days road trip.

435/10 = 43.5

Newton Spend the money per day is = $43.5/day

Question 11.

**Number Sense**

For which equations does b = 100?

49 ÷ b = 0.49

247 ÷ b = 0.247

1.3 ÷ b = 0.013

0.5 ÷ b = 0.05

Answer:

49 ÷ b = 0.49

1.3 ÷ b = 0.013

For these two equations b value should be 100.

Question 12.

**YOU BE THE TEACHER**

Your friend says 8,705 ÷ 10^{3} is equivalent 8,705 × 0.001. Is your friend correct? Explain.

Answer:

First simplify the 10^{3 }which means 10 10 10 = 1000

8,705 ÷ 10^{3 }

= 8,705 ÷ 1000

= 8,705

= 8,705 0.001

8,705 ÷ 10^{3} is equivalent 8,705 × 0.001

So, my friend answer is correct.

**Think and Grow: Modeling Real Life**

**Example**

A contractor buys 2 adjacent lots of land. One lot is 0.55 acre and the other is 1.65 acres. The contractor divides the land equally for 10 new homes. How much land does each home have?

To find how much land each home has, divide the sum of the lot sizes by 10.

Add the sizes of the lots.

Divide the total number of acres by 10. Dividing 2.20 by 10, or 10^{1}, shifts the digits ______ position to the right in a place value chart. So, the decimal point moves ______ place to the left.

2.20 ÷ 10 = 2.20 ÷ 10^{1} = ______

Each home has ________ acre.

**Show and Grow**

Question 13.

An art teacher has 68.5 pounds of clay and orders 56.5 more pounds. The teacher equally divides the clay among 100 students. How much clay does each student get?

Answer:

To find how much clay each student get, divide the sum of the clay by 100.

Add the quantities of the clay.

68.5 + 56.5 = 125

Divide the total clay by 100. Dividing 125 by 100, or 10^{2
}125 ÷ 100 = 125 ÷ 10^{2 }= 1.25

Each student gets 1.25 pounds clay.

Question 14.

A museum has a replica of the Space Needle that is 6.05 feet tall. It is one-hundredth of the height of the actual Space Needle. How tall is the actual Space Needle?

Answer:

Replica of the Space Needle height = 6.05 feet

Let actual Space Needle height = h

(h) = 6.05

h = 6.05 100 = 605

So actual Space Needle height is 605 feet.

Question 15.

**DIG DEEPER!**

A pile of 10^{2} loonies weighs 627 grams and a pile of 10^{2} toonies weighs 730 grams. How much more does a toonie weigh than a loonie? Is there more than one way to solve the problem? Explain.

Answer:

A pile of 10^{2} loonies weight = 627 grams

A pile of 10^{2} toonies weight = 730 grams

730 – 627 = 103

Toonie weighs 103 grams more than a loonie.

Method – 2

1 loonie weight = = 6.27

1 toonie weight = = 7.30

7.30 – 6.27 = 1.03

For 10^{2} toonies and loonies = 1.03 x 10^{2} = 103

Toonie weighs 103 grams more than a loonie.

### Division Pattern with Decimals Homework & Practice 7.1

**Find the quotient.**

Question 1.

810 ÷ 10 = ______

Answer: 81

Explanation:

To convert this simple fraction to a decimal just divide the numerator (810) by the denominator (10):

When we divide by 10, the decimal point moves one place to the left.

810 ÷ 10 = 81.

Question 2.

7.4 ÷ 0.01 = ______

Answer: 740

Explanation: To convert this simple fraction to a decimal just divide the numerator (7.4) by the denominator (0.01). When we divide by 0.01, the decimal point moves two places to the right. : 7.4 ÷ 0.01 = 740.

Question 3.

903 ÷ 10^{3} = ______

Answer: 0.903

First Simplify the 10^{3} which means 10 x 10 x 10 =1000, then we need to calculate the fraction to a decimal just divide the numerator (903) by the denominator (1000).

When we divide by 1000, the decimal point moves three places to the left.

Question 4.

267.1 ÷ 0.01 = ______

Answer: 26710

Explanation: To convert this simple fraction to a decimal just divide the numerator (267.1) by the denominator (0.01).

When we divide by 0.01, the decimal point moves two places to the right :

267.1 ÷ 0.01 = 26710

Question 5.

5.6 ÷ 0.1 = ______

Answer: 56

Explanation: To convert this simple fraction to a decimal just divide the numerator (5.6) by the denominator (0.1).

When we divide by 0.1, the decimal point moves one place to the right :

5.6 ÷ 0.1 = 56

Question 6.

0.4 ÷ 10^{2} = ______

Answer: 0.004

First Simplify the 10^{2} which means 10 x 10 = 100, then we need to calculate the fraction to a decimal just divide the numerator (0.4) by the denominator (100).

When we divide by 100, the decimal point moves two places to the left :

0.4 ÷ 100 = 0.004

**Find the value of k.**

Question 7.

89 ÷ k = 8.9

Answer: k = 10

Explanation: Lets solve your equation step by step 89 ÷ k = 8.9

Multiply both sides by K.

89 = 8.9 K

8.9 K = 89 (Flip the equation)

= (Divide both sides by 8.9)

k = 10

Question 8.

k ÷ 0.01 = 36

Answer: k = 0.36

= 36

Multiply both sides by 0.01

x 0.01 = 36 x 0.01

k = 0.36

Question 9.

72.4 ÷ 0.724

Answer: 100

To convert this simple fraction to a decimal just divide the numerator (72.4) by the denominator (0.724).

Question 10.

A box of 100 sanitizing wipes costs $12. How much does one wipe cost?

Answer:

100 sanitizing wipes = $12

one wipe cost = = $0.12

When we divide by 100, the decimal point moves two places to the left.

Question 11.

**Patterns**

How does the value of a number change when you divide by 10? 100? 1,000?

Answer:

When we divide by 10, the decimal point moves one place to the left.

When we divide by 100, the decimal point moves two places to the left.

When we divide by 1000, the decimal point moves three places to the left.

Question 12.

**Writing**

How can you determine where to place the decimal point when dividing 61 by 1,000?

Answer:

When we divide by 1000, the decimal point moves three places to the left.

so, = 0.061

Question 13.

**DIG DEEPER!**

What is Newton’s number?

Answer:

3.4 is the number.

57 – 23 = 34

34 x 0.1 = 3.4

Question 14.

**Modeling Real Life**

A family buys 2 personal watercrafts for $3,495 each. The family makes 10 equal payments for the watercrafts. What is the amount of each payment?

Answer:

To find amount of each payment, divide the sum of the personal watercrafts by 10.

Add 2 personal watercrafts.

3,495 + 3,495 = 6990

Divide the total sum by 10. Dividing 6990 by 10, or 10^{1
}6990 ÷ 10 = 6990 ÷ 10^{1 }= 699

So, the amount of each payment = $699.

Question 15.

**Modeling Real Life**

A group of people attempts to bake the largest vegan cake. They use 17 kilograms of cocoa powder, which is one-tenth the amount of kilograms of dates they use. How many kilograms of cocoa power and dates do they use altogether?

Answer:

Cocoa powder = 17 kilograms

Let dates amount = d

(1/10)d = 17

dates(d) = 17 x 10 = 170 kilograms

Sum of cocoa power and dates = 17 + 170 = 187 kilograms

**Review & Refresh**

**Find the sum or difference.**

Question 16.

0.75 – 0.23 = ______

Answer: 0.52

Question 17.

1.46 + 1.97 = ______

Answer: 3.43

### Lesson 7.2 Estimate Decimals Quotients

**Explore and Grow**

Choose an expression to estimate each quotient. Write the expression. You may use an expression more than once.

Compare your answers with a partner. Did you choose the same expressions?

Answer:

**Construct Arguments**

Which estimated quotient do you think will be closer to the quotient 8.3 ÷ 2.1? Explain your reasoning.

Answer:

**Think and Grow: Estimate Decimals Quotients**

**Key Idea**

You can use compatible numbers to estimate quotients involving decimals. When the divisor is greater than the dividend, rename the dividend as tenths or hundredths, then divide.

**Example**

Estimate 146.26 ÷ 41.2.

Round the divisor 41.2 to 40.

Think: What numbers close to 146.26 are easily divided by 40?

Choose 160 because 146.26 is closer to 160. So, 146.26 ÷ 41.2 is about _____.

**Example**

Estimate 4.2 ÷ 8.

Rename 4.2 as tenths.

4.2 is 42 tenths. 42 tenths is close to40 tenths. 40 and 8 are compatible numbers.

40 tenths ÷ 8 = _______ tenths, or ______

So, 4.2 ÷ 8 is about ______.

**Show and Grow**

**Estimate the quotient.**

Question 1.

17.4 ÷ 3.1

Answer:

Round the divisor 3.1 to 3.

Think: What numbers close to 17.4 are easily divided by 3?

Use 18.

18 ÷ 3 = 6

So, 17.4 ÷ 3.1 is about 6.

Question 2.

57.5 ÷ 6.89

Answer:

Round the divisor 6.89 to 7.

Think: What numbers close to 57.5 are easily divided by 7?

Use 56.

56 ÷ 7 = 8

So, 57.5 ÷ 6.89 is about 8.

Question 3.

3.7 ÷ 5

Answer:

Rename 3.7 as tenths

3.7 is 37 tenths. 37 is close to 35.

35 tenths ÷ 5 = 7 tenths or 0.7

So, 3.7 ÷ 5 is about 0.7

Question 4.

25.8 ÷ 30

Answer:

Rename 25.8 as tenths

25.8 is 258 tenths. 258 is close to 270.

270 tenths ÷ 30 = 9 tenths or 0.9

So, 25.8 ÷ 30 is about 0.9

**Apply and Grow: Practice**

**Estimate the quotient.**

Question 5.

3.5 ÷ 6

Answer:

Rename 3.5 as tenths

3.5 is 35 tenths. 35 is close to 36.

36 tenths ÷ 6 = 6 tenths or 0.6

So, 3.5 ÷ 6 is about 0.6

Question 6.

1.87 ÷ 9

Answer:

Rename 1.87 as tenths

1.87 is 18.7 tenths. 18.7 is close to 18.

18 tenths ÷ 9 = 2 tenths or 0.2

So, 1.87 ÷ 9 is about 0.2

Question 7.

46 ÷ 2.3

Answer:

Round the divisor 2.3 to 2.

46 ÷ 2 = 23

Question 8.

31.1 ÷ 6.5

Answer:

Round the divisor 6.5 to 6.

31.1 is closer to 30.

30 ÷ 6 = 5

So, 31.1 ÷ 6.5 is about 5.

Question 9.

91.08 ÷ 5.2

Answer:

Round the divisor 5.2 to 5.

91.08 is closer to 90.

90 ÷ 5 = 18

So, 91.08 ÷ 5.2 is about 18.

Question 10.

137.14 ÷ 12.2

Answer:

Round the divisor 12.2 to 12.

137.14 is closer to 144.

12 and 144 are compatible numbers.

144 ÷ 12 = 12

So, 137.14 ÷ 12.2 is about 12.

Question 11.

A group of 6 friends goes ice skating. They pay $43.50 altogether for admission and skate rental. The friends share the cost equally. How much does each friend pay?

Answer:

Total amount paid = $43.50

6 friends goes ice skating.

43.5 is closer to 42.

42 ÷ 6 = 7

So, each friend pay about $7.

Question 12.

**Reasoning**

Descartes estimates 43.2 ÷ 7.3 using mental math. Do you think he uses 43 ÷ 7 or 42 ÷ 7? Explain.

Answer:

Round the divisor 7.3 to 7

Think: What numbers close to 43.2 are easily divided by 7?

Use 42.

42 and 7 are compatible numbers.

42 ÷ 7 = 6

So, 42 ÷ 7 is correct.

Question 13.

**DIG DEEPER!**

Describe a division situation in which an estimate of two decimals is appropriate.

Answer:

**Think and Grow: Modeling Real Life**

**Example**

Your friend types 25 words each minute. About how many more words can your friend type each minute than you?

To find how many words you can type each minute, divide the number of words you type in 15 minutes by 15.

Think: What numbers close to 307.5 are easily divided by 15?

Choose 300 because 307.5 is closer to 300. So, 307.5 ÷ 15 is about _______.

So, you type about _______ words each minute.

Subtract the words you type each minute from the words your friend types each minute.

Your friend can type about ______ more words each minute than you.

**Show and Grow**

Question 14.

Newton subscribes to a television streaming service and buys a gym membership. He spends $143.99 on the streaming service for 12 months. About how much more does it cost each month for the gym membership than the streaming service?

Answer:

To find much more does it cost each month, divide how much he spends for 12 months by 12.

Think: What numbers close to $143.99 are easily divided by 12?

Use 144

144 ÷ 12 = 12

Gym Membership each month = $19.99 = $20

20 – 12 = $8

The gym membership costs $8 more than the streaming service.

Question 15.

A fish tank pump filters 158.5 gallons of water each hour. About how many gallons of water does the pump filter each minute?

Answer:

Fish tank pump filters 158.5 gallons of water

1 hour = 60 minutes

Think: What numbers close to 158.5 are easily divided by 60?

Use 180

180 ÷ 60 = 3

Pump filters about 3 gallons of water each minute.

Question 16.

**DIG DEEPER!**

A group of 32 students goes to a museum and a play. The total cost for the museum is $358.98 and the total cost for the play is $256.48. About how much does it cost for each student to go to the museum and the play?

Answer:

Cost for museum = $358.98

Cost for the play = $256.48

358.98 + 256.48 = $615.46

Think: What numbers close to 615.46 are easily divided by 32?

Use 608. It is closer to 615.46

608 ÷ 32 = $19

Each student go to the museum and the play costs about $19.

### Estimate Decimals Quotients Homework & Practice 7.2

**Estimate the quotient.**

Question 1.

2.3 ÷ 6

Answer:

Rename 2.3 as tenths

2.3 is 23 tenths. 23 is close to 24.

24 tenths ÷ 6 = 4 tenths or 0.4

So, 2.3 ÷ 6 is about 0.4

Question 2.

1.67 ÷ 8

Answer:

Rename 1.67 as hundredths

1.67 is 167 hundredths. 167 is close to 168.

168 hundredths ÷ 8 = 21 hundredths or 0.21

So, 1.67 ÷ 8 is about 0.21

Question 3.

28 ÷ 4.7

Answer:

Round the divisor 4.7 to 5

28 is closer to 30

30 ÷ 5 = 6

So, 28 ÷ 4.7 is about 6.

Question 4.

13.8 ÷ 4.9

Answer:

Round the divisor 4.9 to 5

Think: What numbers close to 13.8 are easily divided by 5?

Use 15.

15 ÷ 5 = 3

So, 13.8 ÷ 4.9 is about 3.

Question 5.

42.1 ÷ 7.3

Answer:

Round the divisor 7.3 to 7

Think: What numbers close to 42.1 are easily divided by 7?

Use 42.

42 ÷ 7 = 6

So, 42.1 ÷ 7.3 is about 6.

Question 6.

201.94 ÷ 18.1

Answer:

Round the divisor 18.1 to 18

Think: What numbers close to 201.94 are easily divided by 18?

Use 198.

198 ÷ 18 = 11

So, 201.94 ÷ 18.1 is about 11.

Question 7.

A carpenter has a plank of wood that is 121.92 centimeters long. He cuts the plank into 4 equal pieces. About how long is each piece?

Answer:

Given that,

Plank of wood = 121.92 cm long

121.92 is closer to 120.

120 ÷ 4 = 30

So, each piece is 30 cm long.

Question 8.

**Reasoning**

A family used 9.8 gallons of gasoline to drive 275.5 miles. To determine how far they drove using one gallon of gasoline, can they use an estimate, or is an exact answer required? Explain.

Answer:

Given that,

9.8 gallons of gasoline drives = 275.5 miles

1 gallon = 275.5 ÷ 9.8

Divisor 9.8 is rounded to 10.

275.5 is closer to 276.

276 ÷ 10 is about 27.6

Question 9.

**YOU BE THE TEACHER**

Your friend says 9 ÷ 2.5 is about 3. Is your friend’s estimate reasonable? Explain.

Answer:

Round the divisor 2.5 to 3.

9 ÷ 3 =3

So, my friend’s estimate is reasonable.

**Number Sense**

**Without calculating, tell whether the quotient is greater than or less than 1. Explain.**

Question 10.

4.58 ÷ 0.3

Answer:

When the dividend is greater than the divisor, the quotient is **greater than 1.**

Question 11.

0.6 ÷ 12

Answer:

When the divisor is greater than the dividend, the quotient is **less than 1.**

Question 12.

**Modeling Real Life**

The maximum allowed flow rate for a shower head in California is 42.5 gallons of water in 17 minutes. About how much greater is this than the maximum allowed flow rate for a kitchen faucet in California?

Answer:

To find much much greater it is, divide how much gallons of water in 17 minutes by 17.

Think: What numbers close to 42.5 are easily divided by 17?

Use 34. 34 is closer to 42.5.

34 ÷ 17 =2

Kitchen faucet = 2.2 gallons

2.2 – 2 = 0.2

Shower head in California is about **0.2 gallons** greater than the maximum allowed flow rate for a kitchen faucet in California.

Question 13.

**Modeling Real Life**

To compare the amounts in the table, you assume the same amount of snow fell each hour for 24 hours. About how many more inches of snow fell in Colorado each hour than in Utah?

Answer:

Time t = 24 hours

Colorado snowfall = 75.8 is closer to 72

Illinois snowfall = 37.8

Utah snowfall = 55.5 is closer to 48

(72 – 48)/24 = 1

Snow fall in Colorado each hour is about 1 inch more than in Utah.

**Review & Refresh**

**Find the product. Check whether your answer is reasonable.**

Question 14.

56 × 78 = _____

Answer: 4368

Question 15.

902 × 27 = ______

Answer: 24,354

Question 16.

4,602 × 35 = _______

Answer: 1,61,070

### Lesson 7.3 Use Models to Divide Decimals by Whole Numbers

**Explore and Grow**

Complete the table.

Answer:

**Reasoning**

When you divide a decimal by a whole number, what does the quotient represent?

Answer:

**Think and Grow: Use Models to Divide Decimals**

**Example**

Use a model to find 2.16 ÷ 3.

Think: 2.16 is 2 ones, 1 tenth, and 6 hundredths.

• 21 tenths can be divided equally as 3 groups of _______ tenths.

• 6 hundredths can be divided equally as 3 groups of _______ hundredths.

So, 216 hundredths can be divided equally as 3 groups of _______ hundredths.

So, 2.16 ÷ 3 = _______

**Show and Grow**

Question 1.

Use the model to find 3.25 ÷ 5.

3.25 ÷ 5 = ______

Answer:

Think: 3.25 is 3 ones, 2 tenths and 5 hundredths.

32 tenths can be divided equally as 5 groups

So, 325 hundredths can be divided equally as 5 groups

So, 3.25 ÷ 5 = 0.65

**Apply and Grow: Practice**

**Use the model to find the quotient.**

Question 2.

2.4 ÷ 4

Answer:

Think: 2.4 is 2 ones and 4 tenths

24 tenths can be divided equally as 4 groups of 6 tenths.

So, 2.4 ÷ 4 = 6 tenths = 0.6

Question 3.

1.36 ÷ 2

Answer:

Think: 1.36 is 1 ones, 3 tenth and 6 hundredths.

13 tenths can be divided equally as 2 groups

So, 136 hundredths can be divided equally as 2 groups

So, 1.36 ÷ 2 = 0.68

**Use a model to find the quotient.**

Question 4.

1.5 ÷ 3

Answer:

Think: 1.5 is 1 ones and 5 tenths

15 tenths can be divided equally as 3 groups of 5 tenths.

So, 1.5 ÷ 3 = 5 tenths = 0.5

Question 5.

2.7 ÷ 9

Answer:

Think: 2.7 is 2 ones and 7 tenths

27 tenths can be divided equally as 9 groups of 3 tenths.

So, 2.7 ÷ 9 = 3 tenths = 0.3

Question 6.

1.44 ÷ 8

Answer:

Think: 1.44 is 1 ones, 4 tenth and 4 hundredths.

14 tenths can be divided equally as 8 groups

So, 144 hundredths can be divided equally as 8 groups

So, 1.44 ÷ 8 = 0.18

Question 7.

3.12 ÷ 6

Answer:

Think: 3.12 is 3 ones, 1 tenth and 2 hundredths.

31 tenths can be divided equally as 6 groups

So, 312 hundredths can be divided equally as 6 groups

So, 3.12 ÷ 6 = 0.52

Question 8.

**Reasoning**

Do you start dividing the ones first when finding 5.95 ÷ 7? Explain.

Answer:

Think: 5.95 is 5 ones, 9 tenth and 5 hundredths.

We have to start dividing the tenths first because 5 ones is less than 7.

59 tenths can be divided equally as 7 groups

So, 595 hundredths can be divided equally as 7 groups

So, 5.95 ÷ 7 = 0.85

Question 9.

**Number Sense**

Without dividing, determine whether the quotient of 9.85 and 5 is greater than or less than 2. Explain.

Answer: Quotient of 9.85 and 5 is less than 2, because 5 x 2 =10 and 9.85 is less than 10.

**Think and Grow: Modeling Real Life**

**Example**

A bag of 3 racquetballs weighs 4.2 ounces. What is the weight of each racquetball?

Divide the weight of the bag by 3 to find the weight of each racquetball.

Think: 4.2 is 4 ones and 2 tenths.

Shade 42 tenths to represent 4.2. Divide the model to show 3 equal groups.

42 tenths can be divided equally as 3 groups of ______ tenths.

4.2 ÷ 3 = ______

So, each racquetball weighs ______ ounces.

**Show and Grow**

Question 10.

You cut a 3.75-foot-long string into 5 pieces of equal length to make a beaded wind chime. What is the length of each piece of string?

Answer:

Divide the length of the string by 5 to find the length of each piece of string.

Think: 3.75 is 3 ones, 7 tenths and 5 hundredths.

37 tenths can be divided equally as 5 groups of 7 tenths with remainder 2. Remainder has to place before 5 hundredths.

25 hundredths can be divided equally as 5 groups of 5 hundredths.

So, 375 hundredths can be divided equally as 5 groups of 75 hundredths.

3.75 ÷ 5 = 0.75

Question 11.

**DIG DEEPER!**

You pay $5.49 for 3 pounds of plums and $6.36 for 4 pounds of peaches. Which fruit costs more per pound? How much more?

Answer:

Think: 5.49 is 5 ones, 4 tenths and 9 hundredths.

5 ones can be divided equally as 3 groups of **1 ones** with remainder 2. Remainder has to place before 4 tenths.

24 tenths can be divided equally as 3 groups of **8 tenths
**9 hundredths can be divided equally as 3 groups of

**3 hundredths**

So, 549 hundredths can be divided equally as 3 groups of 183 hundredths.

Plums = 5.49 ÷ 3 = 1.83

Think: 6.36 is 6 ones, 3 tenths and 6 hundredths.

6 ones can be divided equally as 4 groups of

**1 ones**with remainder 2. Remainder has to place before 3 tenths.

23 tenths can be divided equally as 4 groups of

**5 tenths**with remainder 3. Remainder has to place before 6 hundredths.

36 hundredths can be divided equally as 4 groups of

**9 hundredths**

So, 636 hundredths can be divided equally as 4 groups of 159 hundredths.

Peaches = 6.36 ÷ 4 = 1.59

1.83 – 1.59 = 0.24

So, plums costs 0.24 more per pound than peaches.

### Use Models to Divide Decimals by Whole Numbers Homework & Practice 7.3

**Use the model to find the quotient.**

Question 1.

1.5 ÷ 5

Answer:

Think: 1.5 is 1 ones and 5 tenths

15 tenths can be divided equally as 5 groups of **3 tenths**.

So, 1.5 ÷ 5 = 3 tenths = 0.3

Question 2.

2.55 ÷ 3

Answer:

Think: 2.55 is 2 ones, 5 tenths and 5 hundredths.

25 tenths can be divided equally as 3 groups of **8 tenths** with remainder 1. Remainder has to place before 5 hundredths.

15 hundredths can be divided equally as 3 groups of **5 hundredths**.

So, 255 hundredths can be divided equally as 3 groups of 85 hundredths.

2.55 ÷ 3 = 0.85

**Use a model to find the quotient.**

Question 3.

1.6 ÷ 8

Answer:

Think: 1.6 is 1 ones and 6 tenths

16 tenths can be divided equally as 8 groups of **2 tenths**.

So, 1.6 ÷ 8 = 2 tenths = 0.2

Question 4.

2.1 ÷ 7

Answer:

Think: 2.1 is 2 ones and 1 tenths

21 tenths can be divided equally as 7 groups of **3 tenths**.

So, 2.1 ÷ 7 = 3tenths = 0.3

Question 5.

1.56 ÷ 2

Answer:

Think: 1.56 is 1 ones, 5 tenths and 6 hundredths.

15 tenths can be divided equally as 2 groups of **7 tenths** with remainder 1. Remainder has to place before 6 hundredths.

16 hundredths can be divided equally as 2 groups of **8 hundredths**.

So, 156 hundredths can be divided equally as 2 groups of 78 hundredths.

1.56 ÷ 2 = 0.78

Question 6.

2.84 ÷ 4

Answer:

Think: 2.84 is 2 ones, 8 tenths and 4 hundredths.

28 tenths can be divided equally as 4 groups of **7 tenths.
**4 hundredths can be divided equally as 4 groups of

**1 hundredths.**

So, 284 hundredths can be divided equally as 4 groups of 71 hundredths.

2.84 ÷ 4 = 0.71

Question 7.

**Structure**

Write a decimal division equation represented by the model.

Answer:

1.8 ÷ 3

Question 8.

**Writing**

Explain how dividing a decimal by a whole number is similar to dividing a whole number by a whole number.

Answer:

When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.

So , dividing a decimal by a whole number is similar to dividing a whole number by a whole number.

Question 9.

**Modeling Real Life**

A designer learns there are 5.08 centimeters in 2 inches. How many centimeters are in 1 inch?

Answer:

5.08 ÷ 2

Think: 5.08 is 5 ones, 0 tenths and 8 hundredths.

50 tenths can be divided equally as 2 groups of **25 tenths.
**8 hundredths can be divided equally as 2 groups of

**4 hundredths.**

So, 508 hundredths can be divided equally as 2 groups of 254 hundredths.

So,

**2.54 cm**are in 1 inch.

Question 10.

**Modeling Real Life**

Newton buys 4 gallons of gasoline. He pays $8.64. How much does 1 gallon of gasoline cost?

Answer:

8.64 ÷ 4

Think: 8.64 is 8 ones, 6 tenths and 4 hundredths.

8 ones can be divided equally as 4 groups of **2 ones.
**6 tenths can be divided equally as 4 groups of

**1 tenths**with remainder 2. Remainder has to place before 4 hundredths.

24 hundredths can be divided equally as 4 groups of

**6 hundredths.**

So, 864 hundredths can be divided equally as 4 groups of 216 hundredths.

1 gallon of gasoline cost is 216 hundredths =

**$2.16**

**Review & Refresh**

**Find the product. Explain the strategy you used.**

Question 11.

0.9 × 1.1 = ______

Answer:

First multiply 9 x 11 = 99, then put the decimal point in the answer as sum of the decimal places in the both numbers.

decimal places = 1 + 1 = 2

99 after putting decimal places = 0.99

Question 12.

1.2 × 2.7 = ______

Answer:

First multiply 12 x 27 = 324 then put the decimal point in the answer as sum of the decimal places in the both numbers.

decimal places = 1 + 1 = 2

324 after putting decimal places = 3.24

Question 13.

1.4 × 0.8 = ______

Answer: 1.12

### Lesson 7.4 Divide Decimals by One-Digit Numbers

**Explore and Grow**

Complete the table.

What pattern do you notice in the placement of the decimal point?

Answer:

**Reasoning**

How is dividing decimals by one-digit whole numbers similar to dividing whole numbers?

Answer:

**Think and Grow: Divide Decimals by One-Digit Numbers**

**Example**

Find

Find 7.38 ÷ 6. Estimate ________

**Show and Grow**

**Find the quotient. Then check your answer.**

Question 1.

\(\sqrt [ 2 ]{ 9.16 } \)

Answer:

Divide the ones

9 ÷ 2

**4 ones** x 2 = 8

9 ones – 8 ones

There are 1 ones left over.

Divide the tenths

116 ÷ 2

**58 tenths** x 2

116 – 116 = 0

There are 0 tenths left over.

So, 9.16 ÷ 2 = 4.58

Question 2.

\(\sqrt [ 5 ]{ 23.5 } \)

Answer:

Divide the ones

23 ÷ 5

**4 ones** x 5 = 20

23 ones – 20 ones

There are 3 ones left over.

Divide the tenths

35 ÷ 5

**7 tenths** x 5

35 – 35 = 0

There are 0 tenths left over.

So, 23.5 ÷ 5 = 4.7

Question 3.

\(\sqrt [ 3 ]{ 6.27 } \)

Answer:

Divide the ones

6 ÷ 3

**2 ones** x 3 = 6

6 ones – 6 ones

There are 0 ones left over.

Divide the tenths

27 ÷ 3

**9 tenths** x 3

27 – 27 = 0

There are 0 tenths left over.

So, 6.27 ÷ 3 = 2.09

**Apply and Grow: Practice**

**Find the quotient. Then check your answer.**

Question 4.

\(\sqrt [ 4 ]{ 16.8 } \)

Answer:

Divide the ones

16 ÷ 4

**4 ones** x 4 = 16

16 ones – 16 ones

There are 0 ones left over.

Divide the tenths

8 ÷ 4

**2 tenths** x 4

8 – 8 = 0

There are 0 tenths left over.

So, 16.8 ÷ 4 = 4.2

Question 5.

\(\sqrt [ 9 ]{ 1.53 } \)

Answer:

Divide the tenths

15 ÷ 9

**1 tenths** x 9

15 – 9 = 6

There are 6 tenths left over.

Divide the hundredths

63 ÷ 9 = **7 hundredths
**So, 1.53 ÷ 9 = 0.17

Question 6.

\(\sqrt [ 5 ]{ 82.5 } \)

Answer:

Divide the ones

82 ÷ 5

**16 ones** x 5 = 80

82 ones – 80 ones

There are 2 ones left over.

Divide the tenths

25 ÷ 5

**5 tenths** x 5

25 – 25 = 0

There are 0 tenths left over.

So, 82.5 ÷ 5 = 16.5

Question 7.

77.4 ÷ 3 = ______

Answer:

Divide the ones

77 ÷ 3

**25 ones** x 3 = 75

77 ones – 75 ones

There are 2 ones left over.

Divide the tenths

24 ÷ 3

**8 tenths** x 3

24 – 24 = 0

There are 0 tenths left over.

So, 77.4 ÷ 3 = 25.8

Question 8.

113.6 ÷ 8 = ______

Answer:

Divide the ones

113 ÷ 8

**14 ones** x 8 = 112

113 ones – 112 ones

There are 1 ones left over.

Divide the tenths

16 ÷ 8

**2 tenths** x 8

16 – 16 = 0

There are 0 tenths left over.

So, 113.6 ÷ 8 = 14.2

Question 9.

129.43 ÷ 7 = ______

Answer:

Divide the ones

129 ÷ 7

**18 ones** x 7 = 126

129 ones – 126 ones

There are 3 ones left over.

Divide the tenths

34 ÷ 7

**4 tenths** x 7

34 – 28 = 6

There are 6 tenths left over.

Divide the hundredths

63 ÷ 7 = **9 hundredths
**So, 129.43 ÷ 7 = 18.49

**Find the value of y.**

Question 10.

y ÷ 2 = 4.8

Answer:

y = 4.8 x 2

y = 9.6

Question 11.

6.05 ÷ 5 = y

Answer:

6.05 ÷ 5

Divide the ones

**1 ones** x 5 = 5

6 ones – 5 ones

There are 1 ones left over.

Divide the tenths

105 ÷ 5

**21 tenths** x 5

105 – 105 = 0

There are 0 tenths left over.

So, 6.05 ÷ 5 = 1.21

**y = 1.21**

Question 12.

y ÷ 8 = 4.29

Answer:

y = 4.29 x 8

**y = 34.32**

Question 13.

**Reasoning**

Newton finds 75.15 ÷ 9. In what place is the first digit of the quotient? Explain.

Answer:

75.15 ÷ 9

Divide the ones

75 ÷ 9

**8 ones** x 9 = 72

75 ones – 72 ones

There are 3 ones left over.

Divide the tenths

31 ÷ 9

**3 tenths** x 9

31 – 27= 4

There are 4 tenths left over.

Divide the hundredths

45 ÷ 9 = **5 hundredths
**75.15 ÷ 9 = 8.35, here quotient is in

**ones place**.

Question 14.

**DIG DEEPER!**

Find the missing digits.

Answer:

Divide the ones

47 ÷ 6

**7 ones** x 6 = 42

47 ones – 42 ones = 3 ones

So, first digit of the quotient is 7.

We know that divisor x quotient = dividend

6 x 7.89 = 47.34

So, missing digits are 7 and 4.

**Think and Grow: Modeling Real Life**

**Example**

A group of 5 gold miners finds the amounts of gold shown. They divide the gold equally. How many ounces does each miner get?

To find how many ounces each miner gets, divide the total amount of gold by 5.

Add the amounts of gold.

Each miner gets _______ ounces of gold.

**Show and Grow**

Question 15.

A pharmacist combines the medicine from both vials and divides it equally into 7 doses. How much medicine is in each dose?

Answer:

To find how much medicine is in each dose, divide the total amount of medicine by 7.

Add the amounts of medicine.

4.5 + 20 = 24.5

24.5 ÷ 7

Divide the ones

24 ÷ 7

**3 ones** x 7 = 21

24 ones – 21 ones

There are 3 ones left over.

Divide the tenths

35 ÷ 7

**5 tenths** x 7

35 – 35 = 0

There are 0 tenths left over.

24.5 ÷ 7 = 3.5

So, **3.5 milliliters** medicine is in each dose.

Question 16.

Identical rectangular stepping stones form a path in a garden. What are the dimensions of each stone?

Answer:

Question 17.

**DIG DEEPER!**

A customer saves $9.24 by buying the set rather than buying them individually. What is one flying disc priced individually?

Answer:

### Divide Decimals by One-Digit Numbers Homework & Practice 7.4

**Find the quotient. Then check your answer.**

Question 1.

\(\sqrt [ 3 ]{ 9.6 } \)

Answer:

Divide the ones

9 ÷ 3

**3 ones** x 3 = 9

9 ones – 9 ones

There are 0 ones left over.

Divide the tenths

6 ÷ 3

**2 tenths** x 3

6 – 6 = 0

There are 0 tenths left over.

So, 9.6 ÷ 3 = 3.2.

Question 2.

\(\sqrt [ 6 ]{ 7.56 } \)

Answer:

Divide the ones

7 ÷ 6

**1 ones** x 6 = 6

7 ones – 6 ones

There are 1 ones left over.

Divide the tenths

15 ÷ 6

**2 tenths** x 6

15 – 12 = 3

There are 3 tenths left over.

Divide the hundredths

36 ÷ 6 = **6 hundredths.
**So, 7.56 ÷ 6 = 1.26.

Question 3.

\(\sqrt [ 8 ]{ 42.4 } \)

Answer:

Divide the ones

42 ÷ 8

**5 ones** x 8 = 40

42 ones – 40 ones

There are 2 ones left over.

Divide the tenths

24 ÷ 8

**3 tenths** x 8

24 – 24 = 0

There are 0 tenths left over.

So, 42.4 ÷ 8 = 5.3.

Question 4.

63.6 ÷ 4 = ______

Answer:

Divide the ones

63 ÷ 4

**15 ones** x 4 = 60

63 ones – 60 ones

There are 3 ones left over.

Divide the tenths

36 ÷ 4

**9 tenths** x 4

36 – 36 = 0

There are 0 tenths left over.

63.6 ÷ 4 = 15.9

Question 5.

15.68 ÷ 7 = ______

Answer:

Divide the ones

15 ÷ 7

**2 ones** x 7 = 14

15 ones – 14 ones

There are 1 ones left over.

Divide the tenths

16 ÷ 7

**2 tenths** x 7

16 – 14 = 2

There are 2 tenths left over.

Divide the hundredths

28 ÷ 7 = **4 hundredths
**15.68 ÷ 7 = 2.24

Question 6.

143.82 ÷ 9 = _______

Answer:

Divide the ones

143 ÷ 9

**15 ones** x 9 = 135

143 ones – 135 ones

There are 8 ones left over.

Divide the tenths

88 ÷ 9

**9 tenths** x 9

88 – 81 = 7

There are 7 tenths left over.

Divide the hundredths

72 ÷ 9 = **8 hundredths
**143.82 ÷ 9 = 15.98

**Find the value of y.**

Question 7.

y ÷ 6 = 7.8

Answer:

y = 7.8 x 6

**y= 46.8**

Question 8.

14.9 ÷ 5 = y

Answer:

Divide the ones

14 ÷ 5

**2 ones** x 5 = 10

14 ones – 10 ones

There are 4 ones left over.

Divide the tenths

49 ÷ 5

**9 tenths** x 5

49 – 45 = 4

There are 4 tenths left over.

Divide the hundredths

40 ÷ 5 = **8 hundredths
**14.9 ÷ 5 = 2.98

**y = 2.98**

Question 9.

y ÷ 2 = 4.7

Answer:

y = 4.7 x 2

**y = 9.4**

Question 10.

**Number Sense**

Evaluate the expression.

(213.3 – 95.7) ÷ 8

Answer:

(213.3 – 95.7) ÷ 8 = 117.6 ÷ 8

Divide the ones

117 ÷ 8

**14 ones** x 8 = 112

117 ones – 112 ones

There are 5 ones left over.

Divide the tenths

56 ÷ 8

**7 tenths** x 8

56 – 56 = 0

There are 0 tenths left over.

(213.3 – 95.7) ÷ 8 = 117.6 ÷ 8 = **14.7**

Question 11.

**Writing**

Write and solve a real-life problem that involves dividing a decimal by a whole number.

Answer:

In 5 minutes John eats 7.5 chocolates. how many chocolates can he eat in one minute?

7.5 ÷ 5

Divide the ones

7 ÷ 5

**1 ones** x 5 = 5

7 ones – 5 ones

There are 2 ones left over.

Divide the tenths

25 ÷ 5 = **5 tenths
**7.5 ÷ 5 = 1.5

In 1 minute, he can eat 1.5 chocolates.

Question 12.

**YOU BE THE TEACHER**

Your friend finds 197.2 ÷ 4. Is your friend correct? Explain.

Answer:

Divide the ones

197 ÷ 4

**49 ones** x 4 = 196

197 ones – 196 ones

There are 1 ones left over.

Divide the tenths

12 ÷ 4

**3 tenths** x 4 = 12

12 – 12 = 0

There are 0 tenths left over.

197.2 ÷ 4 = 49.3

So, my friend answer is not correct.

Question 13.

**Modeling Real Life**

You buy 2 packages of ground beef. One package contains 4.5 pounds and the other contains 2.25 pounds. You put equal amounts of meat into 9 freezer bags. How many pounds of meat are in each bag?

Answer:

To find many pounds of meat are in each bag, divide the total meat by 9.

Add the two packages of meat.

4.5 + 2.25 = 6.75

6.75 ÷ 9

Divide the tenths

67 ÷ 9

**7 tenths** x 9 = 63

67 tenths – 63 tenths

There are 4 tenths left over.

Divide the hundredths

45 ÷ 9 = **5 hundredths
**6.75 ÷ 9 = 0.75

Question 14.

**DIG DEEPER!**

A homeowner hangs wallpaper on the walls of her bathroom. What is the width of the bathroom?

Answer:

We know that perimeter of a rectangle = 2(l + w)

8.52 = 2(2.74 + w)

2.74 + w = 8.52 ÷ 2

8.52 ÷ 2

Divide the ones

8 ÷ 2 = **4 ones
**Divide the tenths

52 ÷ 2 =

**26 tenths**

8.52 ÷ 2 = 4.26

2.74 + w = 4.26

Width w = 4.26 – 2.74 = 1.52

So, width of the bathroom =

**1.52 m**

**Review & Refresh**

**Use partial quotients to divide.**

Question 15.

607 ÷ 15 = ______

Answer:

15 x 40 = 600 with remainder 7.

Question 16.

4,591 ÷ 33 = ______

Answer:

Question 17.

6,699 ÷ 87 = ______

Answer:

87 x **50** = 4350

6,699 – 4350 = 2349

87 x **20** = 1740

2349 – 1740 = 609

87 x **5** = 435

609 – 435 = 174

87 x **2** = 174

6,699 ÷ 87 = 50 + 20 + 5 + 2 = **77.**

### Lesson 7.5 Divide Decimals by Two-Digit Numbers

**Explore and Grow**

Write a division problem you can use to find the width of each rectangle. Then find the width of each rectangle.

Answer:

**Precision**

Explain how you can use estimation to check your answers.

Answer:

**Think and Grow: Divide Decimals by Two-Digit Numbers**

**Example**

Find 79.8 ÷ 14. Estimate _________

Regroup 7 tens as 70 ones and combine with 9 ones.

**Example**

Find 20.54 ÷ 26.

Step 1: Estimate the quotient.

2,000 hundredths ÷ 25 = _______ hundredths

Step 2: Divide as you do with whole numbers.

Step 3: Use the estimate to place the decimal point.

So, 20.54 ÷ 26 = _______.

**Show and Grow**

**Find the quotient. Then check your answer.**

Question 1.

\(\sqrt [ 12 ]{ 51.6 } \)

Answer:

Divide the ones

51 ÷ 12

**4 ones** x 12 = 48

51 ones – 48 ones

There are 3 ones left over.

Divide the tenths

36 ÷ 12

**3 tenths** x 12 = 36

36 – 36 = 0

There are 0 tenths left over.

So, 51.6 ÷ 12 = 4.3

Question 2.

\(\sqrt [ 17 ]{ 140.25 } \)

Answer:

Divide the ones

140 ÷ 17

**8 ones** x 17 = 136

140 ones – 136 ones

There are 4 ones left over.

Divide the tenths

42 ÷ 17

**2 tenths** x 17 = 34

42 – 34 = 8

There are 8 tenths left over.

Divide the hundredths

85 ÷ 17 = **5 hundredths.
**So, 140.25 ÷ 17 = 8.25

Question 3.

\(\sqrt [ 61 ]{ 32.33 } \)

Answer:

Divide the tenths

323 ÷ 61

**5 ones** x 61 = 305

323 tenths – 305 tenths

There are 18 tenths left over.

Divide the hundredths

183 ÷ 61 = **3 hundredths
**So, 32.33 ÷ 61 = 0.53

**Apply and Grow: Practice**

**Place a decimal point where it belongs in the quotient.**

Question 4.

251.75 ÷ 19 = 1 3 . 2 5

Answer:

When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.

Question 5.

88.04 ÷ 62 = 1 . 4 2

Answer:

Question 6.

3.22 ÷ 23 = 0 .1 4

Answer:

**Find the quotient. Then check your answer.**

Question 7.

\(\sqrt [ 54 ]{ 97.2 } \)

Answer:

Divide the ones

97 ÷ 54

**1 ones** x 54 = 54

97 ones – 54 ones

There are 43 ones left over.

Divide the tenths

432 ÷ 54 = **8 tenths
**So, 97.2 ÷ 54 = 1.8

Question 8.

\(\sqrt [ 91 ]{ 200.2 } \)

Answer:

Divide the ones

200 ÷ 91

**2 ones** x 91 = 182

200 ones – 182 ones

There are 18 ones left over.

Divide the tenths

182 ÷ 91 = **2 tenths
**So, 200.2 ÷ 91 = 2.2

Question 9.

\(\sqrt [ 2 ]{ 56.2 } \)

Answer:

Divide the ones

56 ÷ 2

**28 ones** x 2 = 56

56 ones – 56 ones

There are 0 ones left over.

Divide the tenths

2 ÷ 2 = **1 tenths
**So, 56.2 ÷ 2 = 28.1

Question 10.

6.08 ÷ 16 = _____

Answer:

Divide the tenths

60 ÷ 16

**3 tenths** x 16 = 48

60 tenths – 48 tenths

There are 12 tenths left over.

Divide the hundredths

128 ÷ 16

**8 hundredths** x 16

128 – 128 = 0

There are 0 hundredths left over.

So, 6.08 ÷ 16 = 0.38

Question 11.

7.45 ÷ 5 = _______

Answer:

Divide the tenths

74 ÷ 5

**14 tenths** x 5 = 70

74 tenths – 70 tenths

There are 4 tenths left over.

Divide the hundredths

45 ÷ 5

**9 hundredths** x 5 = 45

45 – 45 = 0

There are 0 hundredths left over.

So, 7.45 ÷ 5 = 1.49

Question 12.

147.63 ÷ 37 = _______

Answer:

Divide the ones

147 ÷ 37

**3 ones **x 37 = 111

147 ones – 111 ones

There are 36 ones left over.

Divide the tenths

366 ÷ 37

**9 tenths** x 37 = 333

366 – 333 = 33

Divide the hundredths

333 ÷ 37 = **9 hundredths
**So, 147.63 ÷ 37 = 3.99

**Find the value of y.**

Question 13.

y ÷ 44 = 1.82

Answer:

y = 44 x 1.82

y = 80.08

Question 14.

106.6 ÷ 82 = y

Answer:

Divide the ones

106 ÷ 82

**1 ones** x 82 = 82

106 ones – 82 ones

There are 24 ones left over.

Divide the tenths

246 ÷ 82

**3 tenths** x 82 = 246

246 – 246 = 0

106.6 ÷ 82 = 1.3, **y = 1.3**

Question 15.

y ÷ 13 = 2.6

Answer:

y = 13 x 2.6

y = 33.8

Question 16.

**Logic**

Newton and Descartes find 44.82 ÷ 18. Only one of them is correct. Without solving, who is correct? Explain.

Answer:

Descartes answer is correct, 44.82 ÷ 18 = 2.49

When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.

Question 17.

**DIG DEEPER!**

Find a decimal that you can divide by a two-digit whole number to get the quotient shown. Fill in the boxes with your dividend and divisor.

Dividend is **20** and divisor is **12**.

**Think and Grow: Modeling Real Life**

**Example**

You practice paddle boarding for 3 weeks. You paddle the same amount each day for 5 days each week. You paddle 22.5 miles altogether. How many miles do you paddle each day?

To find the total number of days you paddle in 3 weeks, multiply the days you paddle each week by 3.

5 × 3 = 15 So, you paddle board _______ days in 3 weeks.

To find the number of miles you paddle each day, divide the total number of miles by the number of days you paddle in 3 weeks.

You paddle _______ miles each day.

**Show and Grow**

Question 18.

Descartes borrows $6,314.76 for an all-terrain vehicle. He pays back the money in equal amounts each month for 3 years. What is his monthly payment?

Answer:

Time t = 3 years = 3 x 12 = 36 months

Descartes borrowed amount = $6,314.76

6,314.76 ÷ 36

63 ÷ 36 = 1 and 27 is left over

271 ÷ 36 = 7 and 19 is left over

194 ÷ 36 = 5 and 14 is left over

147 ÷ 36 = 4 and 3 is left over

36 ÷ 36 = 1 and 0 left over.

6,314.76 ÷ 36 = 175.41

Descartes monthly payment is **$175.41**

Question 19.

A blue car travels 297.6 miles using 12 gallons of gasoline and a red car travels 358.8 miles using 13 gallons of gasoline. Which car travels farther using 1 gallon of gasoline? How much farther?

Answer:

297 ones ÷ 12 = **24 ones** x 12 = 288

297 ones – 288 ones

There are 9 ones left over.

96 ÷ 12 = **8 tenths** x 12 = 96

96 – 96 = 0

There are 0 hundredths left over.

So, 297.6 ÷ 12 =** 24.8
**358 ones ÷ 13 =

**27 ones**x 13 = 351

358 ones – 351 ones

There are 7 ones left over.

78 ÷ 13 =

**6 tenths**x 13 = 78

78 – 78 = 0

There are 0 hundredths left over.

So, 358.8 ÷ 13 =

**27.6**

Red car – blue car = 27.6 – 24.8 = 2.8

Red car travels 2.8 miles farther than blue car using 1 gallon of gasoline.

Question 20.

**DIG DEEPER!**

The rectangular dog park has an area of 2,616.25 square feet. How much fencing does an employee need to enclose the dog park?

Answer:

### Divide Decimals by Two-Digit Numbers Homework & Practice 7.5

**Place a decimal point where it belongs in the quotient.**

Question 1.

127.2 ÷ 24 = 5 . 3

Answer:

Question 2.

48.64 ÷ 32 = 1 . 5 2

Answer:

Question 3.

514.18 ÷ 47 = 1 0 . 9 4

Answer:

**Find the quotient. Then check your answer.**

Question 4.

\(\sqrt [ 72 ]{ 93.6 } \)

Answer:

Divide the ones

93 ÷ 72

**1 ones** x 72 = 72

93 ones – 72 ones

There are 21 ones left over.

Divide the tenths

216 ÷ 72 = **3 tenths.
**So, 93.6 ÷ 72 = 1.3

Question 5.

\(\sqrt [ 7 ]{ 3.92 } \)

Answer:

Divide the tenths

39 ÷ 7

**5 ones** x 7 = 35

39 ones – 35 ones

There are 4 ones left over.

Divide the hundredths

42 ÷ 7 = **6 tenths.
**So, 3.92 ÷ 7 = 0.56

Question 6.

\(\sqrt [ 29 ]{ 1.74 } \)

Answer:

Divide the hundredths

174 ÷ 29

**6 ones** x 29 = 174

174 hundredths – 174 hundredths

There are 0 hundredths left over.

So, 1.74 ÷ 29 = 0.06

Question 7.

24.3 ÷ 9 = _______

Answer:

Divide the ones

24 ÷ 9

**2 ones** x 9 = 18

24 ones – 18 ones

There are 6 ones left over.

Divide the tenths

63 ÷ 9

**7 tenths** x 9 = 63

63 – 63 = 0

There are 0 tenths left over.

So, 24.3 ÷ 9 = 2.7

Question 8.

244.9 ÷ 31 = ______

Answer:

Divide the ones

244 ÷ 31

**7 ones** x 31 = 217

244 ones – 217 ones

There are 27 ones left over.

Divide the tenths

279 ÷ 31

**9 tenths** x 31

279 – 279 = 0

There are 0 tenths left over.

So, 244.9 ÷ 31 = 7.9

Question 9.

55.62 ÷ 27 = ______

Answer:

Divide the ones

55 ÷ 27

**2 ones** x 27 = 54

55 ones – 54 ones

There is 1 ones left over.

Divide the tenths

162 ÷ 27

**6 tenths** x 27

162 – 162 = 0

There are 0 tenths left over.

So, 55.62 ÷ 27 = 2.06

**Find the value of y.**

Question 10.

y ÷ 16 = 0.23

Answer:

y = 16 x 0.23

y = 3.68

Question 11.

44.1 ÷ 21 = y

Answer:

Divide the ones

44 ÷ 21

**2 ones** x 21 = 42

44 ones – 42 ones

There are 2 ones left over.

Divide the tenths

21 ÷ 21

**1 tenths** x 21

21 – 21 = 0

There are 0 tenths left over.

So, 44.1 ÷ 21 = 2.1

Question 12.

y ÷ 28 = 11.04

Answer:

y = 28 x 11.04

y = 309.12

Question 13.

**YOU BE THE TEACHER**

Your friend finds 21.44 ÷ 16. Is your friend correct? Explain.

Answer:

My friend answer is not correct.

When dividing a decimal by a whole number, first we will divide the decimal by the whole number ignoring decimal point. Now put the decimal point in the quotient same as the decimal places in the dividend.

Divide the ones

21 ÷ 16

**1 ones** x 16 = 16

21 ones – 16 ones

There are 5 ones left over.

Divide the tenths

54 ÷ 16

**3 tenths** x 16

54 tenths – 48 tenths

There are 6 tenths left over.

Divide the hundredths

64 ÷ 16

**4 hundredths** x 16

64 hundredths- 64 hundredths

There are 0 hundredths left over.

So, 21.44 ÷ 16 = 1.34

Question 14.

**DIG DEEPER!**

A banker divides the amount shown among 12 people. How can she regroup the money? How much money does each person get?

Answer:

Question 15.

**Modeling Real Life**

You have hip-hop dance practice for 5 weeks. You attend practice 5 days each week. Each practice is the same length of time. You practice for 37.5 hours altogether. How many hours do you practice each day?

Answer:

To find the total number of days you practice in 5 weeks, multiply the days you practice each week by 5.

5 × 5 = 25 So, you practice 25 days in 5 weeks.

To find the number of hours you practice each day, divide the total number of hours by the number of days you practice in 5 weeks.

37.5 ÷ 25

Divide the ones

37 ÷ 25

**1 ones** x 25 = 25

37 ones – 25 ones

There are 12 ones left over.

Divide the tenths

125 ÷ 25

**5 tenths** x 25

125 tenths – 125 tenths

There are 0 tenths left over.

So, 37.5 ÷ 25 = 1.5

So, I practice dance **1.5 hours** each day.

Question 16.

**DIG DEEPER!**

Your rectangular classroom rug has an area of 110.5 square feet. What is the perimeter of the rug?

Answer:

**Review & Refresh**

**Find the product.**

Question 17.

0.52 × 0.4 = _______

Answer: 0.208

Question 18.

0.7 × 21.3 = _______

Answer: 14.91

Question 19.

1.52 × 8.6 = ______

Answer: 13.072

### Lesson 7.6 Use Models to Divide Decimals

**Explore and Grow**

Use the model to find each quotient.

Answer:

**Structure**

When using a model to divide decimals, how do you determine the number of rows and columns to shade? How do you divide the shaded region?

Answer:

**Think and Grow: Use Models to Divide Decimals**

**Example**

Use a model to find 1.2 ÷ 0.3.

Shade 12 columns to represent 1.2.

Divide the model to show groups of 0.3.

There are ______ groups of ______ tenths.

So, 1.2 ÷ 0.3 = ________.

**Example**

Use a model to find 0.7 ÷ 0.14.

Shade 7 columns to represent 0.7.

Divide the model to show groups of 0.14.

There are ______ groups of _______ hundredths.

So, 0.7 ÷ 0.14 = ______.

**Show and Grow**

**Use the model to find the quotient.**

Question 1.

1.5 ÷ 0.5 = _____

Answer:

Shade 15 columns to represent 1.5.

Divide the model to show groups of 0.5.

There are 3 groups of 5 tenths.

So, 1.5 ÷ 0.5 = 3

Question 2.

1.72 ÷ 0.86 = ______

Answer:

Shade 17.2 columns to represent 1.72.

Divide the model to show groups of 0.86.

There are 2 groups of 86 hundredths.

So, 1.72 ÷ 0.86 = 2

**Apply and Grow: Practice**

**Use the model to find the quotient.**

Question 3.

0.32 ÷ 0.04 = ______

Answer:

Shade 3.2 columns to represent 0.32.

Divide the model to show groups of 0.04.

There are 8 groups of 4 hundredths.

So, 0.32 ÷ 0.04 = 8

Question 4.

0.9 ÷ 0.15 = ______

Answer:

Shade 9 columns to represent 0.9.

Divide the model to show groups of 0.15.

There are 6 groups of 15 hundredths.

So, 0.9 ÷ 0.15 = 6

Question 5.

1.4 ÷ 0.07 = _____

Answer:

Shade 14 columns to represent 1.4.

Divide the model to show groups of 0.07.

There are 20 groups of 7 hundredths.

So, 1.4 ÷ 0.07 = 20

Question 6.

1.08 ÷ 0.09 = _____

Answer:

Shade 10.8 columns to represent 1.08.

Divide the model to show groups of 0.09.

There are 12 groups of 9 hundredths.

So, 1.08 ÷ 0.09 = 12

Question 7.

You have$1.50 in dimes. You exchange all of your dimes for quarters. How many quarters do you get?

Answer:

Quarter = 0.25

1.50 ÷ 0.25

Shade 15 columns to represent 1.50.

Divide the model to show groups of 0.25.

There are 6 groups of 25 hundredths.

So, 1.50 ÷ 0.25 = 6 quarters.

Question 8.

**YOU BE THE TEACHER**

Your friend uses the model below and says 1.6 ÷ 0.08 = 2. Is your friend correct? Explain.

Answer:

1.6 ÷ 0.08

Shade 16 columns to represent 1.6.

Divide the model to show groups of 0.08.

There are 20 groups of 8 hundredths.

So, 1.6 ÷ 0.08 = 20

So, my friend answer is wrong.

Question 9.

**Structure**

Use the model to find the missing number.

0.72 ÷ ____ = 8

Answer:

Shade 7.2 columns to represent 0.72.

Divide the model to show groups of 8.

There are 0.09 groups of 800 hundredths.

So, 0.72 ÷ 0.09 = 8

Missing number is 0.09.

**Think and Grow: Modeling Real Life**

**Example**

Is aluminum more than 5 times as dense as neon?

Divide the density of aluminum by the density of neon to find how many times as dense it is.

Use a model. Shade 27 columns to represent 2.7.

Divide the model to show groups of 0.9.

There are ______ groups of ______ tenths.

So, 2.7 ÷ 0.9 = _______.

Compare the quotient to 5.

So, aluminum ________ more than 5 times as dense as neon.

**Show and Grow**

Question 10.

Use the table above. Is neon more than 9 times as dense as hydrogen?

Answer:

Divide the density of neon by the density of hydrogen to find how many times as dense it is.

Use a model. Shade 9 columns to represent 0.9.

Divide the model to show groups of 0.09.

There are 10 groups of 9 hundredths.

So, 0.9 ÷ 0.09 = 10

Compare the quotient to 9.

So, neon is more than 9 times as dense as hydrogen.

Question 11.

You fill a bag with peanuts, give the cashier $5, and receive $3.16 in change. How many pounds of peanuts do you buy?

Answer:

Amount to buy peanuts = 5 – 3.16 = 1.84

peanuts per pound = $0.23

1.84 ÷ 0.23

Shade 18.4 columns to represent 1.84.

Divide the model to show groups of 0.23.

There are 8 groups of 23 hundredths.

So, 1.84 ÷ 0.23 = 8

I can buy 8 pounds of peanuts.

Question 12.

**DIG DEEPER!**

You have 2.88 meters of copper wire and 5.85 meters of aluminum wire. You need 0.24 meter of copper wire to make one bracelet and 0.65 meter of aluminum wire to make one necklace. Can you make more bracelets or more necklaces? Explain.

Answer:

Copper wire = 2.88 ÷ 0.24

Shade 28.8 columns to represent 2.88.

Divide the model to show groups of 0.24.

There are 12 groups of 24 hundredths.

So, 2.88 ÷ 0.24 = 12

Aluminum wire = 5.85 ÷ 0.65

Shade 58.5 columns to represent 5.85.

Divide the model to show groups of 0.65.

There are 9 groups of 65 hundredths.

So, 5.85 ÷ 0.65 = 9

So, we can make more bracelets.

### Use Models to Divide Decimals Homework & Practice 7.6

**Use the model to find the quotient.**

Question 1.

0.08 ÷ 0.02 = _____

Answer:

Shade 8 columns to represent 0.08.

Divide the model to show groups of 0.02.

There are 4 groups of 2 hundredths.

So, 0.08 ÷ 0.02 = 4

Question 2.

0.4 ÷ 0.05 = ______

Answer:

Shade 5 columns to represent 0.4.

Divide the model to show groups of 0.05.

There are 8 groups of 5 hundredths.

So, 0.4 ÷ 0.05 = 8

Question 3.

1.7 ÷ 0.85 = ______

Answer:

Shade 17 columns to represent 1.7.

Divide the model to show groups of 0.85.

There are 2 groups of 85 hundredths.

So, 1.7 ÷ 0.85 = 2

Question 4.

1.5 ÷ 0.3 = _______

Answer:

Shade 15 columns to represent 1.5.

Divide the model to show groups of 0.3.

There are 5 groups of 3 tenths.

So, 1.5 ÷ 0.3 = 5

Question 5.

You have a piece of scrapbook paper that is 1.5 feet long. You cut it into pieces that are each 0.5 foot long. How many pieces of scrap book paper do you have now?

Answer:

1.5 ÷ 0.5

Shade 15 columns to represent 1.5.

Divide the model to show groups of 0.5.

There are 3 groups of 5 tenths.

So, 1.5 ÷ 0.5 = 3

So, I have 3 pieces of scrap book paper.

Question 6.

**YOU BE THE TEACHER**

Your friend uses the model below and says 0.12 ÷ 0.04 = 0.03. Is your friend correct? Explain.

Answer:

0.12 ÷ 0.04

Shade 1.2 columns to represent 0.12.

Divide the model to show groups of 0.04.

There are 3 groups of 4 hundredths.

So, 0.12 ÷ 0.04 = 3

My friend is not correct.

Question 7.

**Writing**

Write a real-life problem that involves dividing a decimal by another decimal.

Answer:

Question 8.

**Modeling Real Life**

Does the watercolor paint cost more than 3 times as much as the paintbrush? Explain.

Answer:

Divide the price of watercolor paint by the price of paintbrush to find how many times as cost it is.

Use a model. Shade 29.6 columns to represent 2.96.

Divide the model to show groups of 0.74.

There are 4 groups of 74 hundredths.

So, 2.96 ÷ 0.74

Compare the quotient to 3.

So, watercolor paint costs more than 3 times as much as the paintbrush.

Question 9.

**DIG DEEPER!**

You have 3.75 cups of popcorn kernels. You fill a machine with 0.25 cup of kernels 3 times each hour. How many hours pass before you run out of kernels?

Answer:

Filling kernels each hour = 0.25 x 3 = 0.75

Total cups of popcorn kernels = 3.75

3.75 ÷ 0.75

Shade 37.5 columns to represent 3.75.

Divide the model to show groups of 0.75.

There are 5 groups of 75 hundredths.

So, 3.75 ÷ 0.75 = **5 hours**

**Review & Refresh**

**Complete the equation. Identify the property shown.**

Question 10.

3 × 14 = 14 × 3

Answer: Commutative Property of Multiplication

Question 11.

8 × (3 + 10) = (8 × 3) + (8 × 10)

Answer: Distributive Property

### Lesson 7.7 Divide Decimals

**Explore and Grow**

Use the model to find 0.96 ÷ 0.32.

Find 96 ÷ 32.

Answer:

**Structure**

How can multiplying by a power of 10 help you divide decimals?

Answer:

**Think and Grow: Divide Decimals by Decimals**

**Key Idea**

To divide by a decimal, multiply the divisor by a power of 10 to make it a whole number. Multiply the dividend by the same power of 10. Then divide as you would with whole numbers.

**Example**

Find 6.12 ÷ 1.8. Estimate _______

**Example**

Find 2.43 ÷ 0.09.

So, 2.43 ÷ 0.09 = ______.

**Show and Grow**

**Multiply the divisor by a power of 10 to make it a whole number. Then write the equivalent expression.**

Question 1.

3.5 ÷ 0.5

Answer:

Step 1: Multiply 0.5 by a power of 10 to make it a whole number. Then multiply 3.5 by the same power of 10.

0.5 x 10 = 5

3.5 x 10 = 35

35 ÷ 5 = 7

So, 3.5 ÷ 0.5 = 7

Question 2.

9.84 ÷ 2.4

Answer:

Step 1: Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 9.84 by the same power of 10.

2.4 x 10 = 24

9.84 x 10 = 98.4

Step 2: Divide 98.4 ÷ 24

98 ÷ 24 = **4** with remainder 2.

24 ÷ 24 = **1** with remainder 0.

So, 9.84 ÷ 2.4 = 4.1

Question 3.

4.68 ÷ 0.78

Answer:

Step 1: Multiply 0.78 by a power of 10 to make it a whole number. Then multiply 4.68 by the same power of 10.

0.78 x 100 = 78

4.68 x 100 = 468

Step 2: Divide 468 ÷ 78 = 6

So, 4.68 ÷ 0.78 = 6

**Apply and Grow: Practice**

**Place a decimal point where it belongs in the quotient.**

Question 4.

28.47 ÷ 0.39 = 7 3 . 0

Answer:

Question 5.

75.85 ÷ 3.7 = 2 0 . 5

Answer:

Question 6.

4.51 ÷ 4.1 = 1 . 1

Answer:

**Find the quotient. Then check your answer.**

Question 7.

\(\sqrt [ 1.5 ]{ 7.5 } \)

Answer:

Step 1: Multiply 7.5 by a power of 10 to make it a whole number. Then multiply 1.5 by the same power of 10.

7.5 x 10 = 75

1.5 x 10 = 15

75 ÷ 15 = 5

So, 7.5 ÷ 1.5 = 5

Question 8.

\(\sqrt [ 0.13 ]{ 0.91 } \)

Answer:

Step 1: Multiply 0.91 by a power of 100 to make it a whole number. Then multiply 0.13 by the same power of 100.

0.91 x 100 = 91

0.13 x 100 = 13

91 ÷ 13 = 7

So, 0.91 ÷ 0.13 = 7

Question 9.

\(\sqrt [ 2.4 ]{ 2.88 } \)

Answer:

Step 1: Multiply 2.88 by a power of 10 to make it a whole number. Then multiply 2.4 by the same power of 10.

2.88 x 10 = 28.8

2.4 x 10 = 24

Step 2: Divide 28.8 ÷ 24

28 ÷ 24 = **1** with remainder 4.

48 ÷ 24 = **2** with remainder 0.

So, 2.88 ÷ 2.4 = 1.2

Question 10.

\(\sqrt [ 0.6 ]{ 7.8 } \)

Answer:

Step 1: Multiply 7.8 by a power of 10 to make it a whole number. Then multiply 0.6 by the same power of 10.

7.8 x 10 = 78

0.6 x 10 = 6

78 ÷ 6 = 13

So, 7.8 ÷ 0.6 = 13

Question 11.

\(\sqrt [ 3.6 ]{ 4.32 } \)

Answer:

Step 1: Multiply 4.32 by a power of 10 to make it a whole number. Then multiply 3.6 by the same power of 10.

4.32 x 10 = 43.2

3.6 x 10 = 36

Step 2: Divide 43.2 ÷ 36

43 ÷ 36 = **1** with remainder 7.

72 ÷ 36 = **2** with remainder 0.

So, 4.32 ÷ 3.6 = 1.2

Question 12.

\(\sqrt [ 0.1 ]{ 11.2 } \)

Answer:

Step 1: Multiply 11.2 by a power of 10 to make it a whole number. Then multiply 0.1 by the same power of 10.

11.2 x 10 = 112

0.1 x 10 = 1

112 ÷ 1 = 112

So, 11.2 ÷ 0.1 = 112

Question 13.

40.42 ÷ 8.6 = ______

Answer:

Step 1: Multiply 8.6 by a power of 10 to make it a whole number. Then multiply 40.42 by the same power of 10.

8.6 x 10 = 86

40.42 x 10 = 404.2

Step 2: Divide 404.2 ÷ 86

404 ÷ 86 = **4** with remainder 60.

602 ÷ 86 = **7** with remainder 0.

So, 40.42 ÷ 8.6 = 4.7

Question 14.

7.2 ÷ 2.4 = _______

Answer:

Step 1: Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 7.2 by the same power of 10.

2.4 x 10 = 24

7.2 x 10 = 72

Step 2: Divide 72 ÷ 24 = 3

So, 7.2 ÷ 2.4 = 3

Question 15.

5.76 ÷ 1.8 = _______

Answer:

Step 1: Multiply 1.8 by a power of 10 to make it a whole number. Then multiply 5.76 by the same power of 10.

1.8 x 10 = 18

5.76 x 10 = 57.6

Step 2: Divide 57.6 ÷ 18

57 ÷ 18 = **3** with remainder 3.

36 ÷ 18 = **2** with remainder 0.

So, 5.76 ÷ 1.8 = 3.2

Question 16.

**YOU BE THE TEACHER**

Descartes says 4.14 ÷ 2.3 = 1.8. Is he correct? Explain.

Answer:

Step 1: Multiply 2.3 by a power of 10 to make it a whole number. Then multiply 4.14 by the same power of 10.

2.3 x 10 = 23

4.14 x 10 = 41.4

Step 2: Divide 41.4 ÷ 23

41 ÷ 23 = **1** with remainder 18.

184 ÷ 23 = **8** with remainder 0.

So, 4.14 ÷ 2.3 = 1.8.

Descartes answer is correct.

Question 17.

**Logic**

What can you conclude about Newton’s quotient?

Answer:

The quotient will be above 5.72.

Because if the divisor is less than 1 then the quotient must be greater than the dividend.

**Think and Grow: Modeling Real Life**

**Example**

A farmer sells a bag of papayas for $5.46. How much does the bag of papayas weigh?

Divide the price of the papayas by the price per pound to find how much the bag of papayas weighs.

5.46 ÷ 1.3 = ? Estimate _______

So, the bag of papayas weighs _______ pounds.

**Show and Grow**

**Use the table above.**

Question 18.

You buy a honeydew for $6.08. What is the weight of the honeydew?

Answer:

Honeydew price = $0.8

6.08 ÷ 0.8

Step 1: Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 6.08 by the same power of 10.

0.8 x 10 = 8

6.08 x 10 = 60.8

Step 2: Divide 60.8 ÷ 8

60 ÷ 8 = **7** with remainder 4.

48 ÷ 8 = **6** with remainder 0.

So, 6.08 ÷ 0.8 = 7.6

Weight of the honeydew = 7.6 pounds

Question 19.

You buy a pumpkin for $7.20 and a watermelon for $5.94. Does the watermelon or the pumpkin weigh more? How much more?

Answer:

Pumpkin = 7.20 ÷ 0.45

Watermelon = 5.94 ÷ 0.33

7.20 ÷ 0.45

Step 1: Multiply 0.45 by a power of 10 to make it a whole number. Then multiply 7.20 by the same power of 10.

0.45 x 100 = 45

7.20 x 100 = 720

Step 2: Divide 720 ÷ 45 = 16

Pumpkin weight = 16 pounds

5.94 ÷ 0.33

Step 1: Multiply 0.33 by a power of 10 to make it a whole number. Then multiply 5.94 by the same power of 10.

0.33 x 100 = 33

5.94 x 100 = 594

Step 2: Divide 594 ÷ 33 = 18

Watermelon weight = 18 pounds

Watermelon weighs **2 pounds** more than the pumpkin.

Question 20.

**DIG DEEPER!**

You pay $5 for a pineapple and receive $2.48 in change. The inedible parts of the pineapple weigh 1.75 pounds. How many pounds of edible pineapple do you have? Explain.

Answer:

Amount paid = 5 – 2.48 = $2.52

pineapple price per pound = $0.63

2.52 ÷ 0.63

Step 1: Multiply 0.63 by a power of 10 to make it a whole number. Then multiply 2.52 by the same power of 10.

0.63 x 100 = 63

2.52 x 100 = 252

Step 2: Divide 252 ÷ 63 = 4

Total weight = 4 pounds

Edible pineapple = total weight – inedible pineapple weight

= 4 – 1.75

= 2.25

Edible pineapple weight = 2.25 pounds.

### Divide Decimals Homework & Practice 7.7

**Multiply the divisor by a power of 10 to make it a whole number. Then write the equivalent expression.**

Question 1.

16.15 ÷ 1.9

Answer:

Step 1: Multiply 1.9 by a power of 10 to make it a whole number. Then multiply 16.15 by the same power of 10.

1.9 x 10 = 19

16.15 x 10 = 161.5

Step 2: Divide 161.5 ÷ 19

161 ÷ 19 = **8** with remainder 9.

95 ÷ 19 = **5** with remainder 0.

So, 16.15 ÷ 1.9 = 8.5

Question 2.

0.36 ÷ 0.09

Answer:

Step 1: Multiply 0.09 by a power of 10 to make it a whole number. Then multiply 0.36 by the same power of 10.

0.09 x 100 = 9

0.36 x 100 = 36

Step 2: Divide 36 ÷ 9 = 4

So, 0.36 ÷ 0.09 = 4

Question 3.

2.04 ÷ 1.7

Answer:

Step 1: Multiply 1.7 by a power of 10 to make it a whole number. Then multiply 2.04 by the same power of 10.

1.7 x 10 = 17

2.04 x 10 = 20.4

Step 2: Divide 20.4 ÷ 17

20 ÷ 17 = **1** with remainder 3.

34 ÷ 17 = **2** with remainder 0.

So, 2.04 ÷ 1.7 = 1.2

**Place a decimal point where it belongs in the quotient.**

Question 4.

81.27 ÷ 13.5 = 6 . 0 2

Answer:

Question 5.

5.76 ÷ 3.2 = 1 . 8

Answer:

Question 6.

47.15 ÷ 2.3 = 2 0 . 5

Answer:

**Find the quotient. Then check your answer.**

Question 7.

\(\sqrt [ 5.3 ]{ 21.2 } \)

Answer:

Step 1: Multiply 5.3 by a power of 10 to make it a whole number. Then multiply 21.2 by the same power of 10.

5.3 x 10 = 53

21.2 x 10 = 212

212 ÷ 53 = 4

So, 21.2 ÷ 5.3 = 4

Question 8.

\(\sqrt [ 0.03 ]{ 76.38 } \)

Answer:

Step 1: Multiply 0.03 by a power of 10 to make it a whole number. Then multiply 76.38 by the same power of 10.

0.03 x 100 = 3

76.38 x 100 = 7,638

Step 2: Divide 7638 ÷ 3

76 ÷ 3 = **25** with remainder 1.

138 ÷ 3 = **46** with remainder 0.

So, 76.38 ÷ 0.03 = 25.46

Question 9.

\(\sqrt [ 6.2 ]{ 33.48 } \)

Answer:

Step 1: Multiply 6.2 by a power of 10 to make it a whole number. Then multiply 33.48 by the same power of 10.

6.2 x 10 = 62

33.48 x 10 = 334.8

Step 2: Divide 334.8 ÷ 62

334 ÷ 62 = **5** with remainder 24.

248 ÷ 62 = **4** with remainder 0.

So, 33.48 ÷ 6.2 = 5.4

**Find the quotient. Then check your answer.**

Question 10.

0.63 ÷ 0.09 = ______

Answer:

Step 1: Multiply 0.09 by a power of 10 to make it a whole number. Then multiply 0.63 by the same power of 10.

0.09 x 100 = 9

0.63 x 100 = 63

Step 2: Divide 63 ÷ 9 = 7

So, 0.63 ÷ 0.09 = 7

Question 11.

10.53 ÷ 3.9 = ______

Answer:

Step 1: Multiply 3.9 by a power of 10 to make it a whole number. Then multiply 10.53 by the same power of 10.

3.9 x 10 = 39

10.53 x 10 = 105.3

Step 2: Divide 105.3 ÷ 39

105 ÷ 39 = **2** with remainder 27.

273 ÷ 39 = **7 **with remainder 0.

So, 10.53 ÷ 3.9 = 2.7

Question 12.

33.8 ÷ 2.6 = ______

Answer:

Step 1: Multiply 2.6 by a power of 10 to make it a whole number. Then multiply 33.8 by the same power of 10.

2.6 x 10 = 26

33.8 x 10 = 338

Step 2: Divide 338 ÷ 26 = 13

So, 33.8 ÷ 2.6 = 13

Question 13.

**Logic**

Without calculating, determine whether 5.4 ÷ 0.9 is greater than or less than 5.4. Explain.

Answer:

5.4 ÷ 0.9 is greater than 5.4

If the divisor is less than 1 then the quotient must be greater than the dividend.

Question 14.

**Structure**

Explain how 35.64 ÷ 2.97 compares to 3,564 ÷ 297.

Answer:

Both 35.64 ÷ 2.97 and 3,564 ÷ 297 are same.

Both dividend and divisor are multiplied by same power of 10.

35.64 x 100 = 3564

2.97 x 100 = 297.

Question 15.

**Modeling Real Life**

A farmer sells a bag of grapes for $5.88. How much do the grapes weigh?

Answer:

Bag of grapes price = $5.88

Grapes price per pound = $2.80

5.88 ÷ 2.8

Step 1: Multiply 2.8 by a power of 10 to make it a whole number. Then multiply 5.88 by the same power of 10.

2.8 x 10 = 28

5.88 x 10 = 58.8

Step 2: Divide 58.8 ÷ 28

58 ÷ 28 = **2** with remainder 2.

28 ÷ 28 = **1 **with remainder 0.

So, 5.88 ÷ 2.8 = 2.1

Grapes weight = **2.1 pounds**

Question 16.

**DIG DEEPER!**

Descartes makes 2.5 times as many ounces of applesauce as Newton. Newton eats 8 ounces of his applesauce, and then divides the rest equally into 3 containers. How much applesauce is in each of Newton’s containers?

Answer:

From the given information, Newton makes applesauce = 72.5 ÷ 2.5

Step 1: Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 72.5 by the same power of 10.

2.5 x 10 = 25

72.5 x 10 = 725

Step 2: Divide 725 ÷ 25 = 29

So, newton makes 29 ounces of applesauce

He eats 8 ounces = 29 – 8 = 21

21 ÷ 3 = 7 ounces.

**7 ounces** of applesauce is in each of Newton’s containers.

**Review & Refresh**

Question 17.

Write the number in two other forms.

Standard form:

Word form: two hundred thirty thousand, eighty-two

Expanded form:

Answer:

Standard form is 230,082

Expanded form is 200000 + 30000 + 80 + 2.

### Lesson 7.8 Insert Zeros in the Dividend

**Explore and Grow**

Use the model to find each quotient.

Answer:

**Reasoning**

Why is the number of digits in the quotients you found above different than the number of digits in the dividends?

Answer:

**Think and Grow: Inserting Zeros in the Dividend**

**Example**

Find 52.6 ÷ 4. Estimate ________

**Example**

Find 1 ÷ 0.08.

**Show and Grow**

**Find the quotient. Then check your answer.**

Question 1.

\(\sqrt [ 0.5 ]{ 85 } \)

Answer:

Multiply 0.5 by a power of 10 to make it a whole number. Then multiply 85 by the same power of 10.

0.5 x 10 = 5

85 x 10 = 850

850 ÷ 5 = 170

So, 85 ÷ 0.5 = 170.

Question 2.

\(\sqrt [ 15 ]{ 9.6 } \)

Answer:

Insert a zero in the dividend and continue to divide.

96 ÷ 15 = **6** with remainder 6.

60 ÷ 15 = **4** with remainder 0.

So, 9.6 ÷ 15 = 0.64

Question 3.

\(\sqrt [ 0.24 ]{ 2.52 } \)

Answer:

Multiply 0.24 by a power of 10 to make it a whole number. Then multiply 2.52 by the same power of 10.

0.24 x 100 = 24

2.52 x 100 = 252

252 ÷ 24

252 ÷ 24 = **10** with remainder 12.

Insert a zero in the dividend and continue to divide.

120 ÷ 24 = **5** with remainder 0.

So, 2.52 ÷ 0.24 = 10.5.

**Apply and Grow: Practice**

**Place a decimal point where it belongs in the quotient.**

Question 4.

3.24 ÷ 0.48 = 6 . 7 5

Answer:

Question 5.

35 ÷ 0.5 = 7 0.

Answer:

Question 6.

12.8 ÷ 2.5 = 5 .1 2

Answer:

**Find the quotient. Then check your answer.**

Question 7.

\(\sqrt [ 2.4 ]{ 0.84 } \)

Answer:

Multiply 2.4 by a power of 10 to make it a whole number. Then multiply 0.84 by the same power of 10.

2.4 x 10 = 24

0.84 x 10 = 8.4

Insert a zero in the dividend and continue to divide.

84 ÷ 24 = **3** with remainder 12.

120 ÷ 24 = **5** with remainder 0.

So, 0.84 ÷ 2.4 = 0.35

Question 8.

\(\sqrt [ 0.32 ]{ 2.08 } \)

Answer:

Multiply 0.32 by a power of 10 to make it a whole number. Then multiply 2.08 by the same power of 10.

0.32 x 100 = 32

2.08 x 100 = 208

208 ÷ 32 = **6** with remainder 16.

Insert a zero in the dividend and continue to divide.

160 ÷ 32 = **5** with remainder 0.

So, 2.08 ÷ 0.32 = 6.5

Question 9.

\(\sqrt [ 4 ]{ 45.8 } \)

Answer:

45.8 ÷ 4

45 ÷ 4 = **11** with remainder 1.

18 ÷ 4 = **4** with remainder 2.

Insert a zero in the dividend and continue to divide.

20 ÷ 4 = **5** with remainder 0.

So, 45.8 ÷ 4 = 11.45.

Question 10.

9 ÷ 1.2 = ______

Answer:

Multiply 1.2 by a power of 10 to make it a whole number. Then multiply 9 by the same power of 10.

1.2 x 10 = 12

9 x 10 = 90

90 ÷ 12

Insert a zero in the dividend and continue to divide.

12 ) 90 ( 7.5

84

——-

60

– 60

——-

0

So, 9 ÷ 1.2 = 7.5

Question 11.

3.5 ÷ 2.5 = ______

Answer:

Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 3.5 by the same power of 10.

2.5 x 10 = 25

3.5 x 10 = 35

35 ÷ 25

Insert a zero in the dividend and continue to divide.

25 ) 35 ( 1.4

25

——-

100

-100

——-

0

So, 3.5 ÷ 2.5 = 1.4

Question 12.

1.8 ÷ 12 = ______

Answer:

Insert a zero in the dividend and continue to divide.

12 ) 18 ( 1.5

12

——-

60

– 60

——-

0

So, 1.8 ÷ 12 = 0.15

Question 13.

You read 2.5 chapters of the book each night. How many nights does it take you to finish the book?

Answer:

Total chapters in the book = 15

15 ÷ 2.5

Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 15 by the same power of 10.

2.5 x 10 = 25

15 x 10 = 150

150 ÷ 25 = **6** nights to finish the book.

Question 14.

**Precision**

Why does Newton place zeros to the right of the dividend but Descartes does not?

Answer:

Newton’s dividend does not have enough digits to divide completely, so he placed zeros to the right of the dividend.

Descartes dividend is a multiple of divisor and it is divided completely, so no need of placing zeros.

**Think and Grow: Modeling Real Life**

**Example**

The John Muir Trail in Yosemite National Park is 210 miles long. A hiker completes the trail in 20 days by hiking the same distance each day. How many miles does the hiker travel each day?

Divide 210 miles by 20 to find how many miles the hiker travels each day.

So, the hiker travels _______ miles each day.

**Show and Grow**

Question 15.

A box of 15 tablets weighs 288 ounces. Each tablet weighs the same number of ounces. What is the weight of each tablet?

Answer:

Divide 288 ounces by 15 to find the weight of each tablet.

288 ÷ 15

15 ) 288 ( 19.2

15

——-

138

-135

——-

30

– 30

——-

0

288 ÷ 15 = 19.2

The weight of each tablet = 19.2 ounces.

Question 16.

Which bag of dog food costs less per pound? Explain why it makes sense to write each quotient as a decimal in this situation.

Answer:

Question 17.

**DIG DEEPER!**

A farmer sells a pound of rice for $0.12 and a pound of oats for $0.08. Can you buy more pounds of rice or oats with $3? How much more? Explain.

Answer:

Rice = 3 ÷ 0.12

Multiply 0.12 by a power of 10 to make it a whole number. Then multiply 3 by the same power of 10.

0.12 x 100 = 12

3 x 100 = 300

300 ÷ 12 = **25
**Oats = 3 ÷ 0.08

Multiply 0.08 by a power of 10 to make it a whole number. Then multiply 3 by the same power of 10.

0.08 x 100 = 8

3 x 100 = 300

300 ÷ 8 =

**37.5**

I can buy

**12.5 pounds**oats more than the rice.

### Insert Zeros in the Dividend Homework & Practice 7.8

**Place a decimal point where it belongs in the quotient.**

Question 1.

9.3 ÷ 0.31 = 3 0.

Answer:

Question 2.

10 ÷ 0.8 = 1 2 . 5

Answer:

Question 3.

0.76 ÷ 0.25 = 3 . 0 4

Answer:

**Find the quotient. Then check your answer.**

Question 4.

\(\sqrt [ 0.8 ]{ 30 } \)

Answer:

Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 30 by the same power of 10.

0.8 x 10 = 8

30 x 10 = 300

300 ÷ 8

30 ÷ 8 = **3** with remainder 6.

60 ÷ 8 = **7** with remainder 4.

Insert a zero in the dividend and continue to divide.

40 ÷ 8 = **5** with remainder 0.

So, 30 ÷ 0.8 = 37.5.

Question 5.

\(\sqrt [ 15 ]{ 91.2 } \)

Answer:

91.2 ÷ 15

91 ÷ 15 = **6** with remainder 1.

Insert a zero in the dividend and continue to divide.

120 ÷ 15 = **8** with remainder 0.

So, 91.2 ÷ 15 = 6.08

Question 6.

\(\sqrt [ 35 ]{ 97.3 } \)

Answer:

97.3 ÷ 35

97 ÷ 35 = **2** with remainder 27.

273 ÷ 35 = **7** with remainder 28.

Insert a zero in the dividend and continue to divide.

280 ÷ 35 = **8** with remainder 0.

So, 97.3 ÷ 35 = 2.78.

Question 7.

3.57 ÷ 0.84 = ______

Answer:

Multiply 0.84 by a power of 10 to make it a whole number. Then multiply 3.57 by the same power of 10.

0.84 x 100 = 84

3.57 x 100 = 357

357 ÷ 84

Insert a zero in the dividend and continue to divide.

84 ) 357 ( 4.25

336

——-

210

-168

——-

420

– 420

——-

0

3.57 ÷ 0.84 = 4.25

Question 8.

20.2 ÷ 4 = _____

Answer:

Insert a zero in the dividend and continue to divide.

4 ) 20.2 ( 5.05

20

——

20

20

——

0

20.2 ÷ 4 = 5.05

Question 9.

1.74 ÷ 0.25 = _______

Answer:

Multiply 0.25 by a power of 10 to make it a whole number. Then multiply 1.74 by the same power of 10.

0.25 x 100 = 25

1.74 x 100 = 174

174 ÷ 25

Insert a zero in the dividend and continue to divide.

25 ) 174 ( 6.96

150

——-

240

-225

——-

150

-150

——-

0

1.74 ÷ 0.25 = 6.96

Question 10.

A painter has 5 gallons of paint to use in a room. He uses 2.5 gallons of paint for 1 coat. How many coats can he paint?

Answer:

Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 5 by the same power of 10.

2.5 x 10 = 25

5 x 10 = 50

50 ÷ 25 = **2
**He can paint 2 coats.

Question 11.

**YOU BE THE TEACHER**

Your friend say she can find 5.44 ÷ 0.64 by dividing both the divisor and dividend by 0.01 to make an equivalent problem with a whole-number divisor. Is he correct? Explain.

Answer:

To divide this 5.44 ÷ 0.64, multiply 0.64 by a power of 10 to make it a whole number. Then multiply 5.44 by the same power of 10.

Multiplying by 100 and dividing by 0.01 both are same.

So, my friend is correct.

Question 12.

**Writing**

Explain when you need to insert a zero in the dividend when dividing.

Answer:

When dividend does not have enough digits to divide completely, then we need to insert a zero in the dividend.

For example, 35 ÷ 25

Here 35 is not a multiple of 25, so we have to add a zero to 35.

Question 13.

**Modeling Real Life**

You cut a 12-foot-long streamer into 8 pieces of equal length. How long is each piece?

Answer:

Length of each piece = 12 ÷ 8

8 ) 12 ( 1.5

8

—–

40

40

—–

0

So, length of each piece = 1.5

Question 14.

**DIG DEEPER!**

How many days longer does the bag of dog food last for the 20-pound dog than the 40-pound dog? Explain.

Answer:

Total cups of dog food = 200

20-pound dog eats per day = 1.25 cups

40-pound dog eats per day = 1.25 x 2 = 2.5 cups

200 ÷ 1.25

Multiply 1.25 by a power of 10 to make it a whole number. Then multiply 200 by the same power of 10.

1.25 x 100 = 125

200 x 100 = 20,000

20,000 ÷ 125

200 ÷ 125 = **1** with remainder 75

7500 ÷ 125 = **60** with remainder 0.

So, 200 ÷ 1.25 = 160

Food lasts for the 20-pound dog = **160 days
**40-pound dog = 200 ÷ 2.5

Multiply 2.5 by a power of 10 to make it a whole number. Then multiply 200 by the same power of 10.

2.5 x 10 = 25

200 x 10 = 2000

2000 ÷ 25 = 80

Food lasts for the 40-pound dog =

**80 days**

**Review & Refresh**

**Find the sum. Check whether your answer is reasonable.**

Question 15.

1.7 + 6.8 = ________

Answer: 8.5

Question 16.

150.23 + 401.79 = _______

Answer: 552.02

### Lesson 7.9 Problem Solving: Decimal Operations

**Explore and Grow**

Make a plan to solve the problem.

Three friends take a taxi ride that costs $4.75 per mile. They travel 10.2 miles and tip the driver $8. They share the total cost equally. How much does each friend pay?

Answer:

**Reasoning**

Explain how you can work backward to check your answer.

Answer:

**Think and Grow: Problem Solving: Decimal Operations**

**Example**

You spend $67.45 on the video game controller, the gaming headset, and 3 video games. The video games each cos the same amount. How much does each video game cost?

**Understand the Problem**

What do you know?

• You spend a total of $67.45.

• The controller costs $15.49 and the headset costs $21.99.

• You buy 3 video games that each cost the same amount.

What do you need to find?

• You need to find the cost of each video game.

**Make a Plan**

How will you solve?

Write and solve an equation to find the cost of each video game.

**Solve**

So, each video game costs ______.

**Show and Grow**

Question 1.

Explain how you can check whether your answer above is reasonable.

Answer:

v = (67.45 – 15.49 – 21.99) ÷ 3

= 29.97 ÷ 3

v = 9.99

So, each video game costs $9.99.

**Apply and Grow: Practice**

**Understand the problem. What do you know? What do you need to find? Explain.**

Question 2.

Your friend pays $84.29 for a sewing machine and 6 yards of fabric. The sewing machine costs $59.99. How much does each yard of fabric cost?

Answer:

**What do you know?**

• You spend a total of $84.29 for a sewing machine and 6 yards of fabric.

• The sewing machine costs $59.99 and the 6 yards of fabric costs $24.3.

**What do you need to find?**

We have to find each yard of fabric cost.

1 yard of fabric cost = 24.3 ÷ 6

So, each yard of fabric costs = $4.05

Question 3.

There are 25.8 grams of fiber in 3 cups of cooked peas. There are 52.5 grams of fiber in 5 cups of avocados. Which contains more fiber in 1 cup, cooked peas or avocados?

Answer:

Cooked peas = 25.8 ÷ 3 = 8.6 grams

Avocados = 52.5 ÷ 3 = 10.5 grams

So, avocados contains more fiber in 1 cup.

**Understand the problem. Then make a plan. How will you solve? Explain.**

Question 4.

Your friend makes a hexagonal frame with a perimeter of 7.5 feet. You make a triangular frame with a perimeter of 5.25 feet. Whose frame has longer side lengths? How much longer?

Answer:

Hexagonal perimeter = 6a = 7.5 feet

Triangular perimeter = 3sides(3a) = 5.25 feet

So, 6a ÷ 2 = 3a

7.5 ÷ 2 = 3.75 feet

5.25 – 3.75 = 1.5 feet

So, triangular frame has **1.5 feet** longer side lengths.

Question 5.

You spend $119.92 on the wet suit, the snorkeling equipment, and 2 research books. The books each cost the same amount. How much does each book cost?

Answer:

Write and solve an equation to find the cost of each book.

cost of each book = (Amount spend – wet suit cost – snorkeling equipment cost) ÷ 2

= (119.92 – 64.95 – 14.99) ÷ 2

= 39.98 ÷ 2

= 19.99

So, each book costs $19.99.

Question 6.

**DIG DEEPER!**

You pour goop into molds and bake them to make plastic lizards. You run out of goop and go shopping for more. Which package costs less per ounce of goop? Explain.

Answer:

Fluorescent package = 40.5 ÷ 2.25 = $18

Color-Changing package = 16.2 ÷ 1.8 = $9

So, Color-Changing package costs less per ounce of goop.

**Think and Grow: Modeling Real Life**

**Example**

Descartes spends $16.40 on the game app, an e-book, and 5 songs. The e-book costs 4 times as much as the game app. The songs each cost the same amount. How much does each song cost?

Think: What do you know? What do you need to find? How will you solve?

Step 1: Multiply the cost of the app by4 to find the cost of the e-book.

1.99 × 4 = 7.96 The e-book costs _______.

Step 2: Write and solve an equation to find the cost of each song.

Let c represent the cost of each song.

c = (16.40 – 1.99 – 7.96) ÷ 5c

= _____ ÷ 5

= _____

So, each song costs $ ______.

**Show and Grow**

Question 7.

You spend $2.24 on a key chain, a bookmark, and 2 pencils. The key chain costs 3 times as much as the bookmark. The pencils each cost the same amount. How much does each pencil cost?

Answer:

Given that,

Bookmark cost = $0.45

Key chain cost = 3 x 0.45 = $1.35

Write and solve an equation to find the cost of each pencil.

cost of each pencil = (Amount spend – keychain cost – bookmark cost) ÷ 2

= (2.24 – 1.35 – 0.45) ÷ 2

= 0.44 ÷ 2

= $0.22

So, cost of each pencil = $0.22.

Question 8.

Newton buys an instant-print camera, a camera bag, and 2 packs of film. He pays $113.96 after using a $5 coupon. The camera costs $69.40, which is 5 times as much as the camera case. How much does each pack of film cost?

Answer:

Total cost = 113.96 + 5 = $118.96

Camera cost = $69.40

Camera case cost = 69.40 ÷ 5 = $13.88

Write and solve an equation to find the cost of each pack of film cost.

cost of each pack of film = (amount spend – camera cost – camera case cost) ÷ 2

= (118.96 – 69.40 – 13.88) ÷ 2

= 35.68 ÷ 2

= 17.84

So, cost of each pack of film = $17.84

### Problem Solving: Decimal Operations Homework & Practice 7.9

**Understand the problem. What do you know? What do you need to find? Explain.**

Question 1.

A 20-ounce bottle of ketchup costs $2.80. A 14-ounce bottle of mustard costs $2.38. Which item costs less per ounce? How much less?

Answer:

20-ounce bottle of ketchup costs = $2.80

14-ounce bottle of mustard costs = $2.38

1 ounce ketchup = 2.8 ÷ 20 = $0.14

1 ounce mustard = 2.38 ÷ 14 = $0.17

Ketchup costs **$0.03** less per ounce than mustard.

Question 2.

Gymnast A scores the same amount in each of his 4 events. Gymnast B scores the same amount in each of his 3 events. Which gymnast scores more in each of his events? How much more?

Answer:

Gymnast A in each of his events = 33.56 ÷ 4 = 8.39 points

Gymnast B in each of his events = 25.05 ÷ 3 = 8.35 points

Gymnast A scores **0.04 points** more in each of his events than gymnast B.

**Understand the problem. Then make a plan. How will you solve? Explain.**

Question 3.

Three children’s tickets to the circus cost $53.85. Two adult tickets to the circus cost $63.90. How much more does 1 adult ticket cost than 1 children’s ticket? Which item costs more per ounce? How much more?

Answer:

3 children’s tickets cost = $53.85

2 adult tickets cost = $63.90

1 adult ticket cost = 63.90 ÷ 2 = $31.95

1 children’s ticket cost = 53.85 ÷ 3 = $17.95

One adult ticket cost is **$14** more than 1 children’s ticket.

Question 4.

A chef at a restaurant buys 50 pounds of red potatoes for $27.50 and 30 pounds of sweet potatoes for $22.50. Which kind of potato costs more per pound? How much more?

Answer:

Red potatoes per pound = 27.5 ÷ 50 = $0.55

Sweet potatoes per pound = 22.5 ÷ 30 = $0.75

Sweet potatoes costs **$0.2** more per pound than red potatoes.

Question 5.

Modeling Real Life

You download 2 music videos, a TV series, and a movie for $42.95 total. The TV series costs 2 times as much as the movie. How much does each music video cost?

Answer:

Total cost = $42.95

Movie cost = $12.99

TV series cost = $25.98

Write and solve an equation to find the cost of each music video cost.

cost of each music video = (total cost – movie cost – TV series cost) ÷ 2

= (42.95 – 12.99 – 25.98) ÷ 2

= 3.98 ÷ 2

= 1.99

So, cost of each music video = **$1.99.**

Question 6.

DIG DEEPER!

Which item costs more per ounce? How much more?

Answer:

Glue cost = 23.04 ÷ 1 = 23.04

Paste cost = 4.00 ÷ 2 = 2

Glue costs **$21.04** more than paste.

**Review & Refresh**

**Find the quotient.**

Question 7.

4,000 ÷ 20 = ______

Answer: 200

Question 8.

900 ÷ 300 = _______

Answer: 3

Question 9.

5,600 ÷ 800 = _______

Answer: 7

### Divide Decimals Performance Task

Question 1.

Multiple teams adopt different sections of a state highway to clean. The teams must clean both sides of their adopted section of the highway.

a. The teams clean their section of the highway over 4 days. They clean the same distance each day.How many miles of the highway does each team clean each day?

b. Each team divides their daily distance equally among each team member. Which team’s members clean the greatest distance each day?

c. The team that collects the greatest amount of litter per team member wins a prize.Which team wins the prize?

Answer:

Question 2.

In a community, 25 people volunteer to clean the rectangular park shown. The park is divided into sections of equal area. One section is assigned to each volunteer. What is the area of the section that each volunteer cleans? What is one possible set of dimensions for 24.5 m each section?

Answer:

### Divide Decimals Activity

**Race Around the World: Division**

**Directions:**

1. Players take turns.

2. On your turn, flip a Race Around the World: Division Card and find the quotient.

3. Move your piece to the next number on the board that is highlighted in the quotient.

4. The first player to make it back to North America wins!

Answer:

### Divide Decimals Chapter Practice

**7.1 Division Patterns with Decimals**

**Find the quotient.**

Question 1.

25 ÷ 10^{2} = ______

Answer:

First Simplify the 10^{2} which means 10 x 10 =100, then we need to calculate the fraction to a decimal just divide the numerator (25) by the denominator (100).

When we divide by 100, the decimal point moves two places to the left.

25 ÷ 10^{2} = 0.25.

Question 2.

1.69 ÷ 0.01 = ______

Answer: To convert this simple fraction to a decimal just divide the numerator (1.69) by the denominator (0.01). When we divide by 0.01, the decimal point moves two places to the right.

1.69 ÷ 0.01 = 169.

Question 3.

681 ÷ 10^{3} = ______

Answer:

First Simplify the 10^{3} which means 10 x 10 x 10 =1000, then we need to calculate the fraction to a decimal just divide the numerator (681) by the denominator (1000).

When we divide by 1000, the decimal point moves three places to the left.

681 ÷ 10^{3} = 0.681.

Question 4.

5.7 ÷ 0.1 = _____

Answer:

To convert this simple fraction to a decimal just divide the numerator (5.7) by the denominator (0.1). When we divide by 0.1, the decimal point moves one places to the right.

5.7 ÷ 0.1 = 57

Question 5.

200 ÷ 0.01 = _____

Answer:

To convert this simple fraction to a decimal just divide the numerator 200 by the denominator (0.01). When we divide by 0.01, the decimal point moves one places to the right.

Question 6.

41.3 ÷ 10 = _____

Answer: To convert this simple fraction to a decimal just divide the numerator (41.3) by the denominator (10). When we divide by 10, the decimal point moves one places to the left.

41.3 ÷ 10 = 4.13

**Find the value of k.**

Question 7.

74 ÷ k = 7,400

Answer:

74 ÷ 7400 = k

Explanation: To convert this simple fraction to a decimal just divide the numerator (74) by the denominator (7400). When we divide by 100, the decimal point moves two places to the left.

74 ÷ 7400 = 0.01

**k = 0.01.**

Question 8.

k ÷ 0.1 = 8.1

Answer:

k = 8.1 x 0.1

**k = 0.81.**

Question 9.

0.35 ÷ k = 0.035

Answer:

0.35 ÷ 0.035 = k

Explanation: To convert this simple fraction to a decimal just divide the numerator (0.35) by the denominator (0.035). When we divide by 0.01, the decimal point moves two places to the right.

0.35 ÷ 0.035 = 10

**k = 10.**

**7.2 Estimate Decimal Quotients**

**Estimate the quotient.**

Question 10.

9.6 ÷ 2

Answer:

9.6 is closer to 10.

10 ÷ 2 = 5

9.6 ÷ 2 is about 5.

Question 11.

37.2 ÷ 6.4

Answer:

Round the divisor 6.4 to 6.

Think: What numbers close to 37.2 are easily divided by 6?

Use 36.

36 ÷ 6 = 6

So, 37.2 ÷ 6.4 is about 6.

Question 12.

44.8 ÷ 4.7

Answer:

Round the divisor 4.7 to 5.

Think: What numbers close to 44.8 are easily divided by 5?

Use 45.

45 ÷ 5 = 9

So, 44.8 ÷ 4.7 is about 9.

Question 13.

78.2 ÷ 10.8

Answer:

Round the divisor 10.8 to 11.

Think: What numbers close to 78.2 are easily divided by 11?

Use 77.

77 ÷ 11 = 7

So, 78.2 ÷ 10.8 is about 7.

**7.3 Use Models to Divide Decimals by Whole Numbers**

**Use the model to find the quotient.**

Question 14.

1.4 ÷ 2

Answer:

Think: 1.4 is 1 ones and 4 tenths.

14 tenths can be divided equally as 2 groups of **7 tenths.
**1.4 ÷ 2 = 0.7

Question 15.

2.85 ÷ 3

Answer:

Think: 2.85 is 2 ones, 8 tenths and 5 hundredths.

28 tenths can be divided equally as 3 groups of **9 tenths** with remainder 1. Remainder has to place before 5 hundredths.

15 hundredths can be divided equally as 3 groups of **5 hundredths**.

So, 285 hundredths can be divided equally as 3 groups of 95 hundredths.

2.85 ÷ 3 = 0.95

**Use a model to find the quotient.**

Question 16.

1.28 ÷ 4

Answer:

Think: 1.28 is 1 ones, 2 tenths and 8 hundredths.

12 tenths can be divided equally as 4 groups of **3 tenths
**8 hundredths can be divided equally as 4 groups of

**2 hundredths**.

So, 128 hundredths can be divided equally as 4 groups of 32 hundredths.

1.28 ÷ 4 = 0.32

Question 17.

3.5 ÷ 5

Answer:

Think: 3.5 is 3 ones and 5 tenths.

35 tenths can be divided equally as 5 groups of **7 tenths.
**3.5 ÷ 5 = 0.7

**7.4 Divide Decimals by One-Digit Numbers**

**Find the quotient. Then check your answer.**

Question 18.

\(\sqrt [ 3 ]{ 14.1 } \)

Answer:

Divide the ones

14 ÷ 3

**4 ones** x 3 = 12

14 ones – 12 ones

There are 2 ones left over.

Divide the tenths

21 ÷ 3 = **7 tenths.
**So, 14.1 ÷ 3 = 4.7

Question 19.

\(\sqrt [ 6 ]{ 67.68 } \)

Answer:

Divide the ones

67 ÷ 6

**11 ones** x 6 = 66

67 ones – 66 ones

There are 1 ones left over.

Divide the tenths

16 ÷ 6

**2 tenths** x 6 = 12

16 – 12 = 4

There are 4 tenths left over.

Divide the hundredths

48 ÷ 6 = **8 hundredths.
**So, 67.68 ÷ 6 = 11.28

Question 20.

\(\sqrt [ 8 ]{ 105.6 } \)

Answer:

Divide the ones

105 ÷ 8

**13 ones** x 8 = 104

105 ones – 104 ones

There are 1 ones left over.

Divide the tenths

16 ÷ 8 = **2 tenths.
**So, 105.6 ÷ 8 = 13.2

Question 21.

Number Sense

Evaluate (84.7 + 79.8) ÷ 7.

Answer:

(84.7 + 79.8) ÷ 7 = 164.5 ÷ 7

Divide the ones

164 ÷ 7

**23 ones** x 7 = 161

164 ones – 161 ones

There are 3 ones left over.

Divide the tenths

35 ÷ 7

**5 tenths** x 7

35 – 35 = 0

There are 0 tenths left over.

So, 164.5 ÷ 7 = 23.5

**7.5 Divide Decimals by Two-Digit Numbers**

**Find the quotient. Then check your answer.**

Question 22.

\(\sqrt [ 32 ]{ 45.12 } \)

Answer:

Divide the ones

45 ÷ 32

**1 ones** x 32 = 32

45 ones – 32 ones

There are 13 ones left over.

Divide the tenths

131 ÷ 32

**4 tenths** x 32 = 128

131 – 128 = 3

There are 3 tenths left over.

Divide the hundredths

32 ÷ 32 = **1 hundredths.
**So, 45.12 ÷ 32 = 1.41

Question 23.

\(\sqrt [ 15 ]{ 9.15 } \)

Answer:

Divide the tenths

91 ÷ 15

**6 tenths** x 15 = 90

91 – 90 = 1

There are 1 tenths left over.

Divide the hundredths

15 ÷ 15 = **1 hundredths.
**So, 9.15 ÷ 15 = 0.61

Question 24.

\(\sqrt [ 73 ]{ 102.2 } \)

Answer:

Divide the ones

102 ÷ 73

**1 ones** x 73 = 73

102 ones – 73 ones

There are 29 ones left over.

Divide the tenths

292 ÷ 73 = **4 tenths.
**So, 102.2 ÷ 73 = 1.4

Question 25.

17.4 ÷ 87 = ______

Answer:

Divide the tenths

174 ÷ 87

**2 tenths** x 87

174 – 174 = 0

There are 0 tenths left over.

17.4 ÷ 87 = 0.2

Question 26.

245.82 ÷ 51 = _______

Answer:

Divide the ones

245 ÷ 51

**4 ones** x 51 = 204

245 ones – 204 ones

There are 41 ones left over.

Divide the tenths

418 ÷ 51

**8 tenths** x 51

418 – 408 = 10

There are 10 tenths left over.

Divide the hundredths

102 ÷ 51 = **2 hundredths
**So, 245.82 ÷ 51 = 4.82

Question 27.

5.88 ÷ 42 = ______

Answer:

Divide the tenths

58 ÷ 42

**1 **tenths x 42 = 42

58 tenths – 42 tenths

There are 16 tenths left over.

Divide the hundredths

168 ÷ 42

**4 hundredths** x 42

168 – 168 = 0

There are 0 hundredths left over.

So, 5.88 ÷ 42 = 0.14

**7.6 Use Models to Divide Decimals**

**Use the model to find the quotient.**

Question 28.

0.9 ÷ 0.45 = ______

Answer:

Shade 9 columns to represent 0.9.

Divide the model to show groups of 0.45.

There are 2 groups of 45 hundredths.

So, 0.9 ÷ 0.45 = 2

Question 29.

0.1 ÷ 0.05 = ______

Answer:

Shade 1 column to represent 0.1.

Divide the model to show groups of 0.05.

There are 2 groups of 5 hundredths.

So, 0.1 ÷ 0.05 = 2

Question 30.

1.6 ÷ 0.4 = ______

Answer:

Shade 16 columns to represent 1.6.

Divide the model to show groups of 0.4.

There are 4 groups of 4 tenths.

So, 1.6 ÷ 0.4 = 4

Question 31.

1.9 ÷ 0.38 = ______

Answer:

Shade 19 columns to represent 1.9.

Divide the model to show groups of 0.38.

There are 5 groups of 38 hundredths.

So, 1.9 ÷ 0.38 = 5

**7.7 Divide Decimals**

**Find the quotient. Then check your answer.**

Question 32.

\(\sqrt [ 2.57 ]{ 20.56 } \)

Answer:

Multiply 2.57 by a power of 10 to make it a whole number. Then multiply 20.56 by the same power of 10.

2.57 x 100 = 257

20.56 x 100 = 2056

2056 ÷ 257 = 8

So, 20.56 ÷ 2.57 = 8.

Question 33.

\(\sqrt [ 4.7 ]{ 16.92 } \)

Answer:

Multiply 4.7 by a power of 10 to make it a whole number. Then multiply 16.92 by the same power of 10.

4.7 x 10 = 47

16.92 x 10 = 169.2

Step 2 : Divide 169.2 ÷ 47

169 ÷ 47 = **3** with remainder 28.

282 ÷ 47 = **6** with remainder 0.

So, 16.92 ÷ 4.7 = 3.6.

Question 34.

\(\sqrt [ 5.3 ]{ 63.6 } \)

Answer:

Multiply 5.3 by a power of 10 to make it a whole number. Then multiply 63.6 by the same power of 10.

5.3 x 10 = 53

63.6 x 10 = 636

636 ÷ 53 = 12

So, 63.6 ÷ 5.3 = 12.

**7.8 Insert Zeros in the Dividend**

Question 35.

\(\sqrt [ 4 ]{ 36.2 } \)

Answer:

36.2 ÷ 4

36 ÷ 4 = **9
**Insert a zero in the dividend and continue to divide.

20 ÷ 4 =

**5**

So, 36.2 ÷ 4 = 9.05.

Question 36.

\(\sqrt [ 4.8 ]{ 85.2 } \)

Answer:

Multiply 4.8 by a power of 10 to make it a whole number. Then multiply 85.2 by the same power of 10.

4.8 x 10 = 48

85.2 x 10 = 852

852 ÷ 48

85 ÷ 48 = **1** with remainder 37.

372 ÷ 48 = **7** with remainder 36.

Insert a zero in the dividend and continue to divide.

360 ÷ 48 = **7** with remainder 24.

240 ÷ 48 = **5** with remainder 0.

So, 85.2 ÷ 4.8 = 17.75.

Question 37.

\(\sqrt [ 12 ]{ 52.2 } \)

Answer:

52.2 ÷ 12

52 ÷ 12 = **4** with remainder 4.

42 ÷ 12 = **3** with remainder 6.

Insert a zero in the dividend and continue to divide.

60 ÷ 12 = **5** with remainder 0.

So, 52.2 ÷ 12 = 4.35.

Question 38.

5 ÷ 0.8 = ______

Answer:

Multiply 0.8 by a power of 10 to make it a whole number. Then multiply 5 by the same power of 10.

0.8 x 10 = 8

5 x 10 = 50

50 ÷ 8

Insert a zero in the dividend and continue to divide.

8 ) 50 ( 6.25

48

——-

20

-16

——-

40

40

——–

0

So, 5 ÷ 0.8 = 6.25

Question 39.

23.7 ÷ 6 = ______

Answer:

Insert a zero in the dividend and continue to divide.

6 ) 23.7 ( 3.95

18

——-

57

– 54

——-

30

30

——–

0

23.7 ÷ 6 = 3.95

Question 40.

138.4 ÷ 16 = ______

Answer:

Insert a zero in the dividend and continue to divide.

16 ) 138.4 ( 8.65

128

——-

104

– 96

——–

80

80

**7.9 Problem Solving: Decimal Operations**

Question 41.

You spend $28.08 on the fabric scissors, buttons, and two craft kits. The kits each cost the same amount. How much does ASSORTED $6.13 each kit cost?

Answer:

Given that,

Total amount spent = $28.08

Fabric scissors cost = $6.13

Buttons cost = $3.97

Write and solve an equation to find the cost of each kit.

cost of each kit = (amount spend – fabric scissors cost – buttons cost) ÷ 2

= (28.08 – 6.13 – 3.97) ÷ 2

= 17.98 ÷ 2

= 8.99

So, cost of each craft kit = $8.99

### Divide Decimals Cumulative Practice

Question 1.

Which statement is true?

Answer:

According to BODMAS rule,

Statement c is correct.

Question 2.

You round 23 × 84 and get an underestimate. How did you estimate?

A. 20 × 80

B. 30 × 90

C. 25 × 90

D. 25 × 90

Answer:

23 × 84 round to 20 × 80 because it is closer to given equation.

84 is close to 80 and all the others options having number 90.

Difference between the numbers in remaining options is greater than the option A numbers.

Question 3.

Which expressions have a product that is shown?

Answer:

Except option 1, remaining all the other options have the product(0.4) shown in the image.

Question 4.

What number is \(\frac{1}{10}\) of 800?

A. 0.8

B. 8

C. 80

D. 8,000

Answer:

(800) = **80**

Question 5.

Which number divided by 0.01 is 14 more than 37?

A. 0.51

B. 5.1

C. 51

D. 5,100

Answer:

14 more than 37 = 37 + 14 = 51

51 x 0.01 = 0.51

So, the answer is **0.51**.

Question 6.

Which expressions have a quotient of 40?

Answer:

2800 ÷ 70, 160 ÷ 4, 3600 ÷ 900 and 8000 ÷ 200 have a quotient of 40.

Question 7.

Which equation is shown by the quick sketch?

Answer:

Question 8.

What is the value of k?

0.036 × k = 36

A. 10

B. 10^{3}

C. 100

D. 36

Answer:

k = 36 ÷ 0.036

k = 1000 = 10^{3}**(option B).**

Question 9.

What is the quotient of 11.76 and 8?

A. 1.47

B. 1.97

C. 14.7

D. 94.08

Answer:

11.76 ÷ 8

11 ÷ 8 = **1** with remainder 3.

37 ÷ 8 = **4** with remainder 5.

56 ÷ 8 = **7** with remainder 0.

So, quotient of 11.76 and 8 = **1.47(option A).**

Question 10.

Newton wins a race by seven thousandths of a second. What is this number in standard form?

**A. 0.007**

B. 0.07

C. 0.7

D. 7,00

Answer:

0.007 is in standard form.

Question 11.

Evaluate 30 – (9 + 6) ÷ 3.

A. 5

B. 19

C. 9

**D. 25**

Answer:

According to BODMAS rule.

30 – (9 + 6) ÷ 3

= 30 – (15 ÷ 3)

= 30 – 5

= 25

Question 12.

A food truck owner sells 237 gyros in 1 day. Each gyro costs $7.How much money does the owner collect in 1 day?

A. $659

B. $1,419

**C. $1,659**

D. $11,249

Answer:

Each gyro costs $7

237 gyros in 1 day cost = 237 x 7 = $1659

So, the owner collects **$1659** in 1 day.

Question 13.

What is the quotient of 4,521 and 3?

Answer:

4521 ÷ 3 = 1507

So, quotient of 4,521 and 3 is 1507.

Question 14.

What is the value of b?

10^{4} = 10^{b} × 10

**A. 3**

B. 4

C. 5

D. 10

Answer:

10^{4} = 10^{b} × 10

If b= 3,

10^{b} × 10 = 10^{3} × 10

= 10^{3+1
}= 10^{4
}So, b= 3.

Question 15.

Part A What is the area of the sandbox?

Part B The playground committee wants to make the area of the sandbox 2 times the original area. What is the new area? Explain.

Answer:

Question 16.

Which expressions have a product of 1,200?

Answer:

30 x 40, 12 x 10^{2 }and 120 x 10 have a product of 1,200.

Question 17.

A 5-day pass to a theme park costs $72.50. A 2-day pass to the same park costs $99.50. How much more does the 2-day pass cost each day than the 5-day pass each day?

A. $14.50

**B. $35.25**

C. $49.75

D. $64.25

Answer:

5-day pass costs each day = 72.5 ÷ 5 = $14.5

2-day pass costs each day = 99.5 ÷ 2 = $49.75

2-day pass cost each day **$35.25** more than the 5-day pass each day.

Question 18.

Which expressions have a quotient with the first digit in the tens place?

Answer:

4,536 ÷ 56 = 81

6,750 ÷ 45 = 150

2,403 ÷ 89 = 27

1,496 ÷ 17 = 88

Except option 2, all the other options have a quotient with the first digit in the tens place.

### Divide Decimals STEAM Performance Task

You experiment with levers for your school’s science fair.

Question 1.

You balance the seesaw lever by placing different weights on either side at different distances from the middle. You find the formula for balancing the seesaw lever is (left weight) × (left distance) = (right weight) × (right distance). You test the formula using various combinations of weights.

a. Use the formula to complete the table for the 2nd and 3rd attempts.

b. For your 4th attempt, you have up to 25 pounds in weights to place on each side of the lever. Choose a whole pound weight for the left side and balance the lever to complete the table.

c. The total length of your seesaw lever is 40 inches. Can you balance a 50-pound weight with a 1-pound weight? Explain.

d. For your science fair display, you balance the lever by placing another gram weight on the right side. Which gram weight should you use?

e. How can you apply what you learn from the science fair project to a playground?

Answer:

You help set up tables for the science fair. There are 93 science fair displays. You use the display boards to determine how many tables to use.

Question 2.

Each display board opens up to form three sides of a trapezoid as shown.

a. How much room do you think each display board needs to open up? Explain.

b. You place the display boards next to each other on 12-foot long tables. How many display boards can you fit on one table?

c. You use one table for snacks and one table for award ribbons. What is the least number of tables you can use? Explain.

d. The diagram shows the room where the science fair is held. Each table for the science fair is 3 feet wide. Your teacher says the ends of the tables can touch to save space. Complete the diagram to arrange the tables so that visitors and judges can see each display board.

Answer:

Question 3.

Use the Internet or some other resource to learn about other types of science fair projects. Describe one interesting science fair project you want to complete.

Answer: One of the interesting science fair project is :-

** How To Make A Bottle Rocket**

**->** Did you know you can make and launch a water bottle rocket using a plastic bottle, water, cork, needle adaptor and pump ?

** How do water bottle rockets work?**

As you pump air into the bottle the pressure inside the bottle builds up until the force of the air pushing on the water is enough to force the cork out of the end of the bottle. The water rushes out of the bottle in one direction whilst the bottle pushes back in the other. This results in the bottle shooting upwards.

** What you need to make a bottle rocket
** -> An empty plastic bottle

-> Cardboard made into a cone and 4 fins

-> A cork

-> A pump with a needle adaptor

-> Water

You can buy a kit with the parts apart from the pump and the bottle-please check the contents before buying.

**Instructions – How to make a bottle rocket**

Push the needle adaptor of the pump through the cork, it needs to go all the way through so you might have to trim the cork a little bit.

-> Decorate the bottle with the cone and fins.

-> Fill the bottle one quarter full of water and push the cork in tightly.

-> Take the bottle outside and connect the pump to the needle adaptor. Ours wouldn’t stand up on the fins so we rested it on a box, but if you make some strong fins it should stand up by itself.

-> Pump air into the bottle, making sure all spectators stand back, the bottle will lift off with force after a few seconds.

**Why does the water bottle rocket launch?**

As you pump air into the bottle pressure builds up inside. If you keep pumping, the force of the air pushing on the water eventually becomes strong enough to force the cork out of the bottle allowing water to rush out in one direction while the bottle pushes back in the other direction. This forces the rocket upwards.

Space

*Conclusion:*

I wish the information provided in the above article regarding Big Ideas Math Book 5th Grade Answer Key Chapter 7 Divide Decimals is helpful for you. For any queries, you can post the comments in the below section.