We included **H****MH Into Math Grade 6 Answer Key**** PDF** **Module 4 Lesson 3 Divide Multi-Digit Whole Numbers** to make students experts in learning maths.

## HMH Into Math Grade 6 Module 4 Lesson 3 Answer Key Divide Multi-Digit Whole Numbers

I Can divide multi-digit whole numbers by multi-digit numbers with or without remainders.

**Step It Out**

1. Mr. Soto buys a new phone for $432 on a payment plan. He pays $18 each month. How many months will it take him to pay for his phone?

A. Write an expression that could be used to find the number of months Mr. Soto will pay for the phone.

____________________

Answer:

The total cost of a mobile phone = $432

The amount he pays each month = $18

The number of months will it take him to pay for his phone = P

The expression that could be find the number of months will be:

P = 432/18

B. Estimate the quotient. Explain how you found your estimate.

____________________

Answer:

The estimated quotient is 24.

First, we see the first two digits of the dividend which are 43 so what we do is multiply 18 x 2 = 36. so we put 36 below the 43 and subtract then 72 and we know that 18×4=72 so automatically the quotient will be 24.

C. Complete the division problem shown to find the number of months Mr. Soto will be paying for his new phone.

____________________

Answer:

D. How many months will Mr. Soto be paying for his new phone?

____________________

Answer:

The total cost of a mobile phone = $432

The amount he pays each month = $18

The number of months will it take him to pay for his phone = P

The expression that could find the number of months will be:

P = 432/18

P = 24

Therefore, he takes 24 months to complete his phone payment.

E. How can you use your estimate to check if your answer is reasonable?

____________________

Answer:

First, we need to make our estimation. Once we have completed our exact calculations, compare our answer to our estimated value. If our answer is close to our estimated value then our answer is reasonable.

2. An experimental aeroplane is flying at an altitude of 8,000 feet when it begins descending to land. If the plane descends at a constant rate of 125 feet per minute, how long will it take to land the plane?

A. Estimate the quotient. Explain how you found your estimate.

_________________________

Answer:

My estimated value is 64.

B. How do you decide where to place the first number in the quotient?

_________________________

_________________________

Answer:

the place value minus one for the first digit of the estimate tells where to place the first digit of the quotient for example if the estimate is 60 the first digit should be placed in the hundreds place

C. How long will it take the plane to land? How can you use your estimate to check if your answer is reasonable?

____________________

Answer:

The plane will take time to land 64 minutes.

First, we need to make our estimation. Once we have completed our exact calculations, compare our answer to our estimated value. If our answer is close to our estimated value then our answer is reasonable.

**Turn and Talk** Why is it important to estimate before finding the exact answer?

3. An art class is making mosaics with glass squares. Each of the 121 students will get the same number of glass squares to use. The total number of glass squares for the students to use is

shown. How many glass squares will each student get?

A. Write an expression that can be used to find the number of glass squares each student will receive.

____________________

Answer:

The total number of students = 121

The total number of glass squares = 1240

The number of glass squares will get each student = X

The expression to find the number of glass squares each student will receive.

X = 1240/121

B. Complete the given division problem to find the number of squares each student will receive. _________________________

Answer:

The quotient is 10 and the remainder is 30.

C. How many whole glass squares will each student receive?

_____________________

Answer:

The total number of students = 121

The total number of glass squares = 1240

The number of glass squares will get each student = X

The expression to find the number of glass squares each student will receive.

X = 1240/121

X = 10.24 approximately 10

Therefore, 10 glass squares will receive by each student.

D. A remainder is the amount left over when an amount cannot be divided equally. What does the remainder mean in this context?

_____________________

_____________________

Answer;

The remainder is 10

Properties of remainder:

The properties of the remainder are as follows:

– The remainder is always less than the divisor. A remainder that is either greater than or equal to the divisor indicates that the division is incorrect.

– If one number (divisor) divides the other number (dividend) completely, then the remainder is 0.

– The remainder can be either greater, lesser, or equal to the quotient.

**Turn and Talk** What is another way you could find the total number of squares each student would get?

**Check Understanding**

Question 1.

It took the Pioneer 11 spacecraft 2,372 days to reach Saturn.

A. How many whole years did it take Pioneer 11 to reach Saturn?

Note: 1 year = 365 days.

____________________

Answer:

Therefore, pioneer 11 took 6.5 years to reach Saturn.

B. Is there a remainder? Explain what it means.

____________________

____________________

____________________

Answer:

The remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.

Remainder formula:

We know that,

Dividend = Divisor x Quotient + Remainder

Therefore,

Remainder = Dividend – (Divisor x Quotient)

This is the formula for the remainder.

Question 2.

A college student has $4,032 he earned from working during the summer. If he earned $288 per week, how many weeks did he work? Complete the division problem to find the quotient.

____________________

Answer:

The amount earned by a college student during the summer = $4032

The amount he earned per week = $288

The number of weeks he worked = S

S = 4032/288

S = 14

Therefore, he worked 14 weeks.

**On Your Own**

Question 3.

**Reason** A clothing company has 4,630 shirts to ship. It can fit 130 shirts in a shipping box.

A. How many boxes are needed to ship all the shirts? ______

Answer:

The total number of shirts = 4630

The number of shirts in each shipping box = 130

The number of boxes is needed to ship all the shirts = S

S = 4630/130

S = 35.61 approximately 36.

Therefore, 36 boxes are needed to ship all the shirts.

B. What does the remainder mean in this context?

____________________

Answer:

The remainder is 60

Properties of remainder:

The properties of the remainder are as follows:

– The remainder is always less than the divisor. A remainder that is either greater than or equal to the divisor indicates that the division is incorrect.

– If one number (divisor) divides the other number (dividend) completely, then the remainder is 0.

– The remainder can be either greater, lesser, or equal to the quotient.

Question 4.

Trevor runs laps on the track. If he runs 9,200 meters total, and each lap is 400 meters, how many laps does he run?

____________________

Answer:

The total number of metres he runs = 9200

The number of metres each lap = 400

The number of laps he ran = R

R = 9200/400

R = 23

Therefore, he ran 23 laps.

Question 5.

A liter of water from the Dead Sea has 250 grams of salt. A tank of similarly salted water holds 5,750 grams of salt. How many liters of water are in the tank?

Answer:

The number of grams of salt a dead sea has = is 250

The tank holds = 5750 grams

The number of litres of water a tank holds = T

Therefore, a tank holds 23 litres.

Question 6.

A gallon of water contains 128 fluid ounces. A rain barrel can hold 6,400 ounces of rain water. How many gallons of water can the barrel hold?

____________________

Answer:

The number of fluid ounces is in a gallon of water = 128

The total number of ounces = 6400

The number of gallons of water can the barrel hold = B

Therefore, a barrel can hold 50 litres of water.

Question 7.

**Critique Reasoning** An express train travels at a constant speed of 280 kilometers per hour. Keiko calculates the amount of time it would take to travel 3,360 kilometers. Her work is shown. Is Keiko’s work correct? Explain your reasoning.

Answer:

The constant speed of express train = 280 km

The total time calculated = 3360 km

If we want to calculate the number of hours a train can travel 3360 km then we need to divide. So Keiko’s work is wrong..

The amount of time be X.

X = 3360/280

X = 12

The correct division problem is:

**For Problems 8—10, estimate. Then find the quotient.**

Question 8.

7,371 ÷ 189

Estimate _____

Quotient ______

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

The estimation of 7371 ÷ 189 is:

For example, if we rounded up 7371 as 7400 and 189 will be 190 then the quotient is 38.94

The actual division quotient is 39.

We can verify the answer:

Now take the actual division. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

7371 = (189 x 39) + 0

7371 = 7371 + 0

7371 = 7371

Hence, verified.

Question 9.

5,104 ÷ 116

Estimate _____

Quotient ______

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

The dividend is estimated to be 5100 ÷ 120 and the quotient is 42.5

The actual division of quotient is 44

We can verify the answer:

Now take the estimated division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

5100 = (120 x 42.5) + 0

5100 = 5100 + 0

5100 = 5100

Hence verified.

Question 10.

6,322 ÷ 109

Estimate _____

Quotient ______

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

The dividend can be estimated as 6300 and the divisor can be estimated as 110

The quotient for the estimated division of 6300 ÷ 110 is 57.27

The actual division quotient is 58

We can verify the answer:

Now take the estimated division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

Now take the actual division or you can take the estimated division also.

6322 = (109 x 58) + 0

6322 = 6322 + 0

6322 = 6322

Hence verified.

**For Problems 11—13, estimate. Then find the whole-number quotient and remainder.**

Question 11.

64,000 ÷ 110

Estimate _____

Quotient ______

Remainder ____

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

In this problem, we need to divide the given numbers because there is no chance of estimating the given values.

The nearest value of 64000 is 64000 and the 110 is 110 only.

Therefore, the quotient is 581.81 and the remainder is 90

We can verify the answer:

Now take the estimated division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

6400 = (110 x 581.81) + 90

6400 = 6400

Hence verified

Question 12.

3,045 ÷ 85

Estimate _____

Quotient ______

Remainder ____

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

The dividend can be estimated as 3000 and the divisor can be 90

The quotient of estimated division is 33.33

Therefore the remainder is 30.

Question 13.

10,169 ÷ 342

Estimate _____

Quotient ______

Remainder ____

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

The estimated dividend is 10,000 and the divisor is 300

The quotient of the estimated division is 33.333

Therefore, the remainder is 100

Question 14.

**Reason** Mr. Simmons buys a car for a total cost of $9,899. He can pay $206 a month but no more. He determines that he will make 49 payments. Is he correct? Explain your reasoning.

Answer:

The total cost of a car = $9899

The amount he should pay per month = $206

In how many months he can complete it. Already given the assumption that 49 payments. Let it be C.

C = 9899/206

C = 48.05339 approximately 48.

But in the question, 49 payments were given which is wrong. He could complete it in 48 months.

Question 15.

A blue whale can weigh up to 400,000 pounds A standard school bus has a gross weight of 25,000 pounds. How many school buses are equivalent to the weight of a blue whale?

Answer:

The weight of blue whale = 400,000 pounds

The weight of a school bus = 25,000 pounds.

The number of school buses is equivalent to the weight of a blue whale = S

S = 400000/25000

S = 16

therefore, 16 school buses are equal to the weight of a blue whale.

Question 16.

**Attend to Precision** A jug contains 3,840 milliliters of water. How many cups of water does the jug contain? Show your work.

Note: 1 cup is equivalent to 240 milliliters.

Answer:

the total number of millilitres in a jug = 3840

The number of cups of water does the jug contain = W

therefore, a jug contains 16 cups of water.

Question 17.

An office building is renting offices that each have an area of 500 square feet. The office building is renting a total of 7,000 square feet of offices. How many offices does the building have to rent?

____________________

Answer:

Each area of renting office = 500 square feet

The total area = 7000 square feet

The number of offices does the building have to rent = R

R = 7000/500

R = 14

therefore, 14 offices have to rent.

**For Problems 18—23. find the whole-number quotient and remainder, if there is one.**

Question 18.

7,874 ÷ 127

____________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 62 and the remainder is 0.

We can verify the answer:

Now take the division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

7874 = (127 x 62) + 0

7874 = 7874 + 0

7874 = 7874

Hence verified.

Question 19.

4,995 ÷ 333

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 15 and the remainder is 0.

We can verify the answer:

Now take the division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

4995 = (333 x 15) + 0

4995 = 4995 + 0

4995 = 4995

Hence verified.

Question 20.

945 ÷ 35

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 27 and the remainder is 0.

We can verify the answer:

Now take the division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

945 = (35 x 27) + 0

945 = 945 + 0

945 = 945

Hence verified.

Question 21.

8,588 ÷ 452

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 19 and the remainder is 0.

We can verify the answer:

Now take the division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

8588 = (452 x 19) + 0

8588 = 8588 + 0

8588 = 8588

Hence verified.

Question 22.

880 ÷ 91

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

We stopped at 3 decimals.

Therefore, the quotient is 9.670 and the remainder is 30.

Question 23.

58,000 ÷ 600

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 96.66 and the remainder is 400

**Lesson 4.3 More Practice Homework**

**Divide Multi-Digit Whole Numbers**

Question 1.

At a paper mill, paper is placed into reams, or stacks of 500 sheets. A robot separates big stacks of sheets into reams. How many reams can the robot make with 9,500 sheets of paper?

Answer:

The papers in each stack = 500

The number of papers a robot can make with 9,500 sheets of paper = P

Therefore, a robot can make 19 reams.

Question 2.

**STEM** Osmium is the densest chemical element. A cubic centimeter of osmium has a mass of about 23 grams. If a chemist has 2,530 grams of osmium, about how many cubic centimeters does the chemist have?

Answer:

The mass of osmium = 23 grams

For suppose, a chemist is having 2530 grams then how many cubic centimeters does the chemist have = C

C = 2530/23

C = 110 cubic centimetres.

Therefore, a chemist would have 110 cubic centimetres of osmium.

Question 3.

The Burj Khalifa building in Dubai, United Arab Emirates, is one of the tallest buildings in the world at 2,722 feet tall. An American football field is 360 feet in length. Approximately how many football fields tall is the Bun Khalifa building? Round to the nearest tenth.

Answer:

The height of the building = 2722

The length of an American football field is 360 feet

The number of football fields tall in the building = B

B = 2722/360

B = 7.56

By checking the nearest tenth then it will be 8

Therefore, there are 8 football fields tall.

Question 4.

**Construct Arguments** The longest road in the United States is U.S. Route 20, measuring 3,365 miles long from coast to coast. A transport truck driver drives about 520 miles per day. How many days would it take the driver to drive from one end of U.S. Route 20 to the other end? Explain.

____________________

____________________

____________________

Answer:

The longest route in US = 3365 miles

The number of miles per day a transport truck driver drives = 520

The number of days he will take time to drive the end of the US route = R

R = 3365/520

R = 6.47

Approximately a driver can take 7 days.

Therefore, a driver can take time to drive from one end to another end in 7 days.

Question 5.

**Math on the Spot** A total of 1,043 players signed up for a citywide soccer league. Each team in the league can have up to 18 members. How many teams will be needed?

_________________________

Answer:

The total number of players = 1043

The members in each team = 18

The number of teams is needed = T

T = 1043/18

T = 58

Therefore, 58 trams will be needed.

Question 6.

**Attend to Precision** There are 365 days in a year and 24 hours in a day. An airport video camera records for 18 hours and then automatically resets itself to start recording again.

A. How many times does the video camera reset itself in a year?

_____________________

Answer:

The number of days in a year = 365

The number of hours in a day = 24

The number of the camera works =18

The number of times the video camera resets in a year = C

C = 365 x 18

C = 6570

Therefore, the camera resets 6570 times in a year.

B. If the camera is started at the beginning of a year, how many hours will it record in the following year before resetting again?

_________________________

Answer:

**For Problems 7—10, find the whole-number quotient and remainder, if there is one.**

Question 7.

3,760 ÷ 145

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 25.93 and the remainder is 15

Question 8.

500 ÷ 25

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 20 and the remainder is 0.

Question 9.

646 ÷ 38

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 17 and the remainder is 0.

Question 10.

9,311 ÷ 400

___________

Answer:

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Therefore, the quotient is 23.27 and the remainder is 300

**Test Prep**

Question 11.

A cattle ranch has 1,400 acres of grazing land. The ranch has 140 cows. How many acres of grazing land does the ranch have per cow?

_________________________

Answer:

The total number of acres = 1400

The number of cows in each ranch = 140

The number of acres of grazing land does the ranch have per cow = X

X = 1400/140

X = 10.

therefore, 10 acres of ranch per cow.

Question 12.

A new amusement-park ride that lasts 1 minute can have up to 1,200 riders per hour of operation. How many riders can ride per minute?

_________________________

Answer:

1 hour = 60 minutes

The number of rides per hour = 1200

The number of rides in 1 minute = R

Therefore, in one minute 20 rides

Question 13.

A small concert venue earned $6,804 in ticket sales. All tickets were the same price. If the venue sold 252 tickets, how much did each ticket cost?

_________________________

Answer:

The total amount earned in ticket sales = $6804

The number of tickets the venue sold = 252

The cost of each ticket = X

X = 6804/252

X = 27

Therefore, the cost of each ticket is $27.

Question 14.

What is the whole-number quotient and remainder?

7,810 ÷ 215

A. 36 R33

B. 36 R70

C. 36 R79

D. 36 R170

Answer: Option B is correct.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

Question 15.

Which is a reasonable estimate for 89,877 ÷ 31?

A. 30

B. 300

C. 3,000

D. 30,000

Answer: Option C is correct

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. For example, 6 ÷ 2 = 3. This can be written as a multiplication fact as 2 × 3 = 6.

We can verify the answer:

Now take the division in this problem. According to the division algorithm, the formula is:

Dividend = (Divisor × Quotient) + Remainder

– The above formula helps us to verify the values of quotient and remainder obtained after performing division. We can substitute the values of the quotient, remainder, and divisor in the above equation and check whether the result is the same as the dividend or not. If we get the dividend, it means we have done the steps of division correctly. If not, it means there is an error in our calculations that we need to rectify.

90000 = ( 30 x 3000) + 0

90000 = 90000 + 0

90000 = 90000

Hence verified

**Spiral Review**

Question 16.

Bea withdraws $25 from her bank account. What integer represents the withdrawal?

____________________

Answer:

The amount Bea withdrew from her bank account = $25

It represents -25 because Bea is withdrawing the money so it gets ‘-‘.

Question 17.

Which two points on the number line represent a number and its absolute value?

____________________

Answer:

The absolute value of a number can be thought of as the distance of that number from 0. As distance can never be negative hence, the absolute value of a number is always positive.

According to the formula,

|x| = x, if x > 0 (x is positive)

The absolute value of |10| = 10

According to the formula,

|x| = -x, if x < 0 (x is negative)

|-10| = 10

Hence, the absolute value of -10 is 10.

The line O represents the number 2

The absolute value of |O| = O

|2| = 2

the absolute value of |P| = 6

The absolute value of |Q| = 8

The absolute value of |N| = |-3| = 3

The absolute value of |M| = |-6| = 6

Question 18.

Naruto practices his harmonica \(\frac{1}{4}\) hour, spends \(\frac{2}{3}\) hour working on homework, and takes another \(\frac{1}{2}\) hour to do chores every day. How much longer does Naruto spend practising his harmonica and doing his chores than working on homework?

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Answer:

The time Naruto practices his harmonica = 1/4

The time he spends on homework = 2/3

The time he spends on chores = 1/2

We need to find out the more time he spends practising and doing his chores than working on homework. Let it be X.

Now add the time he spent practising and doing chores. Let it be Y.

Y = 1/4 + 1/2

Now we should find out X.

X = Y – time spent on homework

X = 3/4 – 2/3

Therefore, 1/12 times more he spends on practising and doing chores than homework.