We included **HMH Into Math Grade 5 Answer Key PDF** **Module 17 Lesson 1 Understand Decimal Division Patterns **to make students experts in learning maths.

## HMH Into Math Grade 5 Module 17 Lesson 1 Answer Key Understand Decimal Division Patterns

I Can use patterns to place the decimal point in a quotient.

**Spark Your Learning
**Jada is playing a sorting game with a deck of math cards. Each card has an expression on one side. She lays out 10 of the cards.

Sort the expressions on the cards in the boxes.

Answer:

Explanation:

752 ÷ 100 = 7.52.

936 ÷ 1000 = 0.936.

0.842 × 100 = 84.2.

842 ÷ 10 = 84.2.

0.936 × 10 = 9.36.

93.6 ÷ 100 = 0.936.

84.2 ÷ 100 = 0.842.

7520 ÷ 100 = 75.2.

0.752 ÷ 1000 = 0.000752.

842 ÷ 1000 = 0.842.

**Turn and Talk** How can you use place value to determine the value of the 7 in the quotient 752 ÷ 100?

Answer:

752 ÷ 100 = 7.52.

Place value of 7 in 752 ÷ 100 = 7.52 = 7 × 1 = 7.

Explanation:

Place value of 7 in 752 = 7 × 100 = 700.

752 ÷ 100 = 7.52.

Place value of 7 in 752 ÷ 100 = 7.52 = 7 × 1 = 7.

**Build Understanding
**Question 1.

The factory making the math cards ships a box with decks of cards to a warehouse. How much does each deck of cards weigh?

A. How can you determine the weight of one deck of cards?

Answer:

Weight of one deck of cards = 0.275 pounds.

Explanation:

Number of cards in deck of cards = 1000.

Weight of box = 275 pounds.

Weight of one deck of cards = Weight of box ÷ Number of cards in deck of cards

= 275 ÷ 1000

= 0.275 pounds.

B. Dividing by 1,000 is the same as multiplying by what fraction?

Answer:

Dividing by 1,000 is the same as multiplying by 10 three times or is the same as multiplying by 1 ÷ 10 fraction.

Explanation:

Dividing by 1,000 is the same as multiplying by 10 three times or is the same as multiplying by 1 ÷ 10 fraction.

C. What is the decimal equivalent of \(\frac{1}{1000}\)?

Answer:

The decimal equivalent of \(\frac{1}{1000}\) = 0.001.

Explanation:

The decimal equivalent of \(\frac{1}{1000}\) = 0.001.

D. Complete the pattern.

275 × 1 = _____________

275 × 0.1 = _____________

275 × 0.01 = _____________

275 × 0.001 = _____________

Answer:

The pattern:

275 × 1 = 275.

275 × 0.1 = 27.5.

275 × 0.01 = 2.75.

275 × 0.001 = 0.275.

Explanation:

275 × 1 = 275.

275 × 0.1 = 27.5.

275 × 0.01 = 2.75.

275 × 0.001 = 0.275.

E. Write a pattern for dividing 275 by 1, 10, 100, and 1,000.

Answer:

A pattern:

275 ÷ 1 = 275.

275 ÷ 10 = 27.5.

275 ÷ 100 = 2.75.

275 ÷ 1000 = 0.275.

Explanation:

275 ÷ 1 = 275.

275 ÷ 10 = 27.5.

275 ÷ 100 = 2.75.

275 ÷ 1000 = 0.275.

F. What can you conclude about the relationship between the patterns in parts D and E?

Answer:

Both are same yet different in process.

Explanation:

Parts D:

275 × 1 = 275.

275 × 0.1 = 27.5.

275 × 0.01 = 2.75.

275 × 0.001 = 0.275.

Parts E:

275 ÷ 1 = 275.

275 ÷ 10 = 27.5.

275 ÷ 100 = 2.75.

275 ÷ 1000 = 0.275.

G. How much does each deck of cards weigh?

Answer:

Weight of one deck of cards = 0.275 pounds.

Explanation:

Number of cards in deck of cards = 1000.

Weight of box = 275 pounds.

Weight of one deck of cards = Weight of box ÷ Number of cards in deck of cards

= 275 ÷ 1000

= 0.275 pounds.

**Turn and Talk** How does the position of the decimal point change as you divide by increasing powers of 10?

Answer:

The decimal point moves one place to the left for each increasing power of 10 – making the quotient 10 times smaller.

Explanation:

The decimal point moves one place to the left for each increasing power of 10 – making the quotient 10 times smaller.

Question 2.

A store receives and sells 1,000 decks of the math cards. If the amount received from selling 1,000 decks of cards is $9,450, what is the price for each deck of cards?

A. How will you find the price for each deck of cards?

Answer:

Cost price for each deck of cards = $9.450.

Explanation:

Number of decks of the math cards a store receives and sells = 1,000.

Amount received from selling 1,000 decks of cards = $9,450.

Cost price for each deck of cards = Amount received from selling 1,000 decks of cards ÷ Number of decks of the math cards a store receives and sells

= $9450 ÷ 1000

= $9.450.

B. Divide 9,450 by 1, 10, 100, and 1,000

- using numerical form.
- using exponential form.

Answer:

Numerical form:

945 divide by 1 = 945.

945 divide by 10 = 94.5.

945 divide by 100 = 9.45.

945 divide by 1000 = 0.945.

Exponential form.

945 ÷ 10^{0 }= 945.

945 ÷ 10^{1 }= 94.5.

945 ÷ 10^{2 }= 9.45

945 ÷ 10^{3 }= 0.945.

Explanation:

Numerical form:

945 divide by 1 = 945.

945 divide by 10 = 94.5.

945 divide by 100 = 9.45.

945 divide by 1000 = 0.945.

Exponential form.

945 ÷ 10^{0 }= 945.

945 ÷ 10^{1 }= 94.5.

945 ÷ 10^{2 }= 9.45

945 ÷ 10^{3 }= 0.945.

C. How is the change in the position of the decimal point related to the exponent for the power of 10?

Answer:

Yes, there is change in the values of positions of the decimal point related to the exponent for the power of 10.

Explanation:

There is change in the values of positions of the decimal point related to the exponent for the power of 10.

D. How do the place values of the digits in the quotients in your pattern change as you divide by increasing powers of 10?

Answer:

Yes, the place values of the digits in the quotients in the patterns change as divided by increasing powers of 10.

Explanation:

The place values of the digits in the quotients in the patterns will change as divided by increasing powers of 10.

E. To find the cost for each deck of cards, how will the decimal point shift?

Answer:

Cost price for each deck of cards = $9.450.

The cost for each deck of cards, decimal point will shift three places left in the number.

Explanation:

Cost price for each deck of cards = Amount received from selling 1,000 decks of cards ÷ Number of decks of the math cards a store receives and sells

= $9450 ÷ 1000

= $9.450.

F. What is the price for each deck of cards?

Answer:

Cost price for each deck of cards = $9.450.

Explanation:

Number of decks of the math cards a store receives and sells = 1,000.

Amount received from selling 1,000 decks of cards = $9,450.

Cost price for each deck of cards = Amount received from selling 1,000 decks of cards ÷ Number of decks of the math cards a store receives and sells

= $9450 ÷ 1000

= $9.450.

**Turn and Talk** How ¡s the pattern of multiplying by 1, 0.1, 0.01, and 0.001 related to the pattern of dividing by 10^{0}, 10^{1}, 10^{2}, and 10^{3}?

Answer:

The pattern is both same when dividing by 10^{0}, 10^{1}, 10^{2}, and 10^{3}, and when multiplying by 0.1, 0.01 and 0.001, the point is moved to the left as many digits as there are zeros in the multiplier.

Explanation:

When dividing by 10^{0}, 10^{1}, 10^{2}, and 10^{3}, and when multiplying by 0.1, 0.01 and 0.001, the point is moved to the left as many digits as there are zeros in the multiplier.

Question 3.

The factory making the math cards also produces game tokens. They sell them in packages of 100 tokens. Each package weighs 28 ounces. How much do 1,000 packages weigh? How much does one game token weigh?

A. What expression using a power of 10 describes the weight of 1,000 packages?

Answer:

Weight of 1,000 (10^{3 }) packages = 280 ounces.

Explanation:

Number of tokens they sell them in packages =100.

Weight of each package = 28 ounces.

Weight of 1,000 (10^{3 }) packages = 10 × Weight of each package

= 10 × 28

= 10 × 28

= 280 ounces.

B. How much do 1,000 packages weigh? How do you know?

Answer:

Weight of 1,000 (10^{3 }) packages = 280 ounces.

Explanation:

Number of tokens they sell them in packages =100.

Weight of each package = 28 ounces.

Weight of 1,000 (10^{3 }) packages = 10 × Weight of each package

= 10 × 28

= 10 × 28

= 280 ounces.

C. What expression using a power of 10 describes the weight of 1 game token?

Answer:

Weight of one game token = 0.28 ounces.

Explanation:

Number of tokens they sell them in packages =100.

Weight of each package = 28 ounces.

Weight of one game token = Weight of each package ÷ Number of tokens they sell them in packages

= 28 ÷ 10^{2
}= 0.28 ounces.

^{
}

D. How much does 1 game token weigh? How do you know?

Answer:

Weight of one game token = 0.28 ounces.

Explanation:

Number of tokens they sell them in packages =100.

Weight of each package = 28 ounces.

Weight of one game token = Weight of each package ÷ Number of tokens they sell them in packages

= 28 ÷ 10^{2
}= 0.28 ounces.

**Turn and Talk** How do you find 537 ÷ 10^{3}?

Answer:

537 ÷ 10^{3 }= 0.537.

Explanation:

537 ÷ 10^{3}

= 537 ÷ 1000

= 0.537.

**Check Understanding
**Question 1.

A shipment of 1,000 toy cars weighs 538 pounds. How many pounds does 1 toy car weigh? Find the answer by using a pattern with powers of 10.

Answer:

Weight of each toy car = 0.538 pounds.

Explanation:

Number of toy cars a shipment has = 1000.

Weight of the toy cars = 538 pounds.

Weight of each toy car = Weight of the toy cars ÷ Number of toy cars a shipment has

= 538 ÷ 10^{3}

= 538 ÷ 1000

= 0.538 pounds.

**On Your Own
**Question 2.

The container holds 100 servings of juice.

Show a pattern to find the amount of juice in one serving.

Answer:

Amount of juice in one serving = 0.066 gal.

Explanation:

Number of servings of juice the container holds = 100.

Weight of the container = 6.6 gal.

Amount of juice in one serving = Weight of the container ÷ Number of servings of juice the container holds

= 6.6 gal ÷ 100

= 0.066 gal.

How many gallons are there in one serving?

Answer:

0.066 gallons are there in one serving.

Explanation:

Number of servings of juice the container holds = 100.

Weight of the container = 6.6 gal.

Amount of juice in one serving = Weight of the container ÷ Number of servings of juice the container holds

= 6.6 gal ÷ 100

= 0.066 gal.

**Complete the pattern.
**Question 3.

278 ÷ 1 = ___________

278 ÷ 10 = ___________

278 ÷ 100 = ___________

Answer:

278 ÷ 1 = 278.

278 ÷ 10 = 27.8.

278 ÷ 100 = 2.78.

Explanation:

278 ÷ 1 = 278.

278 ÷ 10 = 27.8.

278 ÷ 100 = 2.78.

Question 4.

73.6 ÷ 10^{0} = ___________

73.6 ÷ 10^{1} = ___________

73.6 ÷ 10^{2} = ___________

Answer:

73.6 ÷ 10^{0} = 73.6.

73.6 ÷ 10^{1} = 7.36.

73.6 ÷ 10^{2} = 0.736.

Explanation:

73.6 ÷ 10^{0} = 73.6 ÷ 1 = 73.6.

73.6 ÷ 10^{1} = 73.6 ÷ 10 = 7.36.

73.6 ÷ 10^{2} = 73.6 ÷ 100 = 0.736.

Question 5.

6.5 ÷ 1 = ___________

6.5 ÷ 10 = ___________

6.5 ÷ 100 = ___________

Answer:

6.5 ÷ 1 = 6.5.

6.5 ÷ 10 = 0.65.

6.5 ÷ 100 = 0.065.

Explanation:

6.5 ÷ 1 = 6.5.

6.5 ÷ 10 = 0.65.

6.5 ÷ 100 = 0.065.

Question 6.

934 ÷ 1 = ___________

934 ÷ 10 = ___________

934 ÷ 100 = ___________

934 ÷ 1,000 = ___________

Answer:

934 ÷ 1 = 934.

934 ÷ 10 = 93.4.

934 ÷ 100 = 9.34.

934 ÷ 1,000 = 0.934.

Explanation:

934 ÷ 1 = 934.

934 ÷ 10 = 93.4.

934 ÷ 100 = 9.34.

934 ÷ 1,000 = 0.934.

Question 7.

590 ÷ 10^{0} = ___________

590 ÷ 10^{1} = ___________

590 ÷ 10^{2} = ___________

590 ÷ 10^{3} = ___________

Answer:

590 ÷ 10^{0} = 590.

590 ÷ 10^{1} = 59.0

590 ÷ 10^{2} = 5.90

590 ÷ 10^{3} = 0.590.

Explanation:

590 ÷ 10^{0} = 590 ÷ 1 = 590..

590 ÷ 10^{1} = 590 ÷ 10 = 59.0

590 ÷ 10^{2} = 590 ÷ 100 = 5.90.

590 ÷ 10^{3} = 590 ÷ 1000 = 0.590.

Question 8.

81 ÷ 10^{0} = ___________

81 ÷ 10^{1} = ___________

81 ÷ 10^{2} = ___________

81 ÷ 10^{3} = ___________

Answer:

81 ÷ 10^{0} = 81 ÷ 1 = 81.

81 ÷ 10^{1} = 81 ÷ 10 = 8.1.

81 ÷ 10^{2} = 81 ÷ 100 = 0.81.

81 ÷ 10^{3} = 81 ÷ 1000 = 0.081.

Explanation:

81 ÷ 10^{0} = 81.

81 ÷ 10^{1} = 8.1.

81 ÷ 10^{2} = 0.81.

81 ÷ 10^{3} = 0.081.

Question 9.

Use Structure Explain how to divide 47 by 10^{3}.

Answer:

Pattern:

47 ÷ 10^{3} = 0.047.

Explanation:

47 ÷ 10^{3} = 0.047.

**Use the table for 10-13.**

Question 10.

How many ounces of crushed tomatoes are in one serving?

Answer:

Number of ounces of crushed tomatoes in one serving = 1750.

Explanation:

Number of ingredient for serving of pasta sauce = 1000.

Number of ounces of crushed tomatoes = 1750.

Number of ounces of crushed tomatoes in one serving = 1750.

Question 11.

How many more pounds of sausage than ground beef are in one serving?

Answer:

15 more pounds of sausage than ground beef are in one serving.

Explanation:

Number of pounds of sausage =60.

Number of pounds of ground beef = 45.

Difference:

Number of pounds of sausage – Number of pounds of ground beef

= 60 – 45

= 15.

Question 12.

How many cups of Italian seasoning are needed for 10 servings?

Answer:

Number of cups of Italian seasoning are needed in 10 serving = 50.

Explanation:

Number of cups of Italian seasoning are needed in one serving = 5.

Number of cups of Italian seasoning are needed in 10 serving = Number of cups of Italian seasoning are needed in one serving × 10

= 5 × 10

= 50.

Question 13.

How many cups of onions are needed for 100 servings?

Answer:

Number of cups of onions are needed in 100 serving = 6400.

Explanation:

Number of cups of onions are needed in one serving = 64.

Number of cups of onions are needed in 100 serving = Number of cups of onions are needed in one serving × 100

= 64 × 100

= 6400.

**Find the unknown number.
**Question 14.

539 ÷ _____ = 5.93

Answer:

539 ÷ 100 = 5.93

Explanation:

539 ÷ ?? = 5.93

=> ?? = 539 ÷ 5.93

=> ?? = 100.

Question 15.

______ ÷ 1,000 = 3.64

Answer:

3640 ÷ 1,000 = 3.64

Explanation:

?? ÷ 1,000 = 3.64.

=> ?? = 3.64 × 1000

=> ?? = 3640.

Question 16.

0.468 = 468 ÷ _________

Answer:

0.468 = 468 ÷ 1000.

Explanation:

0.468 = 468 ÷ ??

=> ?? = 468 ÷ 0.468

=> ?? = 1000.

Question 17.

_____ ÷ 10^{2} = 8.17

Answer:

817 ÷ 10^{2} = 8.17.

Explanation:

_____ ÷ 10^{2} = 8.17

=> ?? = 8.17 × 100

=> ?? = 817.

Question 18.

0.076 = 76 ÷ ________

Answer:

0.076 = 76 ÷ 1000.

Explanation:

0.076 = 76 ÷ ??

=> ?? = 76 ÷ 0.076

=> ?? = 1000.

Question 19.

64.1 = ________ ÷ 10^{3}

Answer:

64.1 = 64100 ÷ 10^{3}

Explanation:

64.1 = ________ ÷ 10^{3
}=> ?? = 64.1 × 1000

=> ?? = 64100.

Question 20.

**Use Structure** Describe how you can use a place-value chart to help you divide a number by a power of 10.

Answer:

Place value chart is used to help in dividing a number by a power of 10 by breaking down problems according to their place value, or tens, hundreds, and thousands.

**I’m in a Learning Mindset!
**What would I like to learn more about when I’m studying division patterns?

Answer:

I learnt more about when I’m studying division patterns is that Division is pretty simple I see division is splitting a number up by any given number that’s it just splitting a number up.

Explanation:

Division is pretty simple I see division is splitting a number up by any given number that’s it just splitting a number up.