DIVIDING DECIMALS WORD PROBLEMS

Problem 1 :

Mr. Adam distributed 27.5 pounds of food to 10 people. Find the amount of food that each person received.

Solution :

10 people ----> 27.5 pounds

1 person ----> (27.5/10) pounds

= 27.5/10

Since 27.5 is divided by 10, the decimal point has to be moved 1 digit to the left.

= 2.75

Each person received 2.75 pounds of food.

Problem 2 :

To vaccinate 100 people, 475.8 ml of a particular medicine is required. Find the amount of medicine required to vaccinate one person.

Solution :

100 people ----> 475.8 ml

1 person ----> (475.8/100) ml

= 475.8/100

Since 475.8 is divided by 100, the decimal point has to be moved 2 digits to the left.

= 4.758

4.758 ml of medicine required to vaccinate one person.

Problem 3 :

If 8 containers contain 9.6 gallons fresh orange juice, how many gallons of the same juice will 1 container contain?

Solution :

8 containers ----> 9.6 gallons

1 container ----> (9.6/8) miles

= 9.6/8

= 9.6 ÷ 8

= ⁹⁶⁄₁₀ ÷ ⁸⁄₁

Division can be changed to multiplication by taking reciprocal of ⁸⁄₁.

= ⁹⁶⁄₁₀ x ⅛

Simplify.

= ¹²⁄₁₀ x ¹⁄₁

= ¹²⁄₁₀

Since 12 is divided by 10, there should be one digit to the right of the decimal point in the answer.

= 1.2

1 container will contain 1.2 gallons of juice.

Problem 4 :

Lily walked 7.8 miles in 2.6 hours. What was the distance covered by her in one hour?

Solution :

2.6 hours ----> 7.8 miles

1 hour ----> (7.8/2.6) miles

= 7.8/2.6

= 7.8 ÷ 2.6

= ⁷⁸⁄₁₀ ÷ ²⁶⁄₁₀

Division can be changed to multiplication by taking reciprocal of ²⁶⁄₁₀.

= ⁷⁸⁄₁₀ x ¹⁰⁄₂₆

Simplify.

= ⁷⁸⁄₁ x ¹⁄₂₆

= ⁷⁸⁄₂₆

= 3

The distance covered by Lily in one hour was 3 miles.

Problem 5 :

Jessica ate 20.4 candies in 6 minutes. How many candies did she eat in 1 minute?

Solution :

Number of candies that Jessica ate in one minute :

= 20.4 ÷ 6

= ²⁰⁴⁄₁₀ ÷ ⁶⁄₁

Division can be changed to multiplication by taking reciprocal of ⁶⁄₁.

= ²⁰⁴⁄₁₀ x ⅙

Simplify.

= ³⁴⁄₁₀ x ¹⁄₁

= ³⁴⁄₁₀

Since 34 is divided by 10, there should be one digit to the right of the decimal point in the answer.

= 3.4 lbs.

Jessica ate 3.4 lbs. of candy in 1 minute.

Problem 6 :

James is a software engineer and he has a few important files saved on his laptop. The space occupied by the files is 171.5 megabytes in all. If each file uses a memory of 24.5 megabytes, find the number of files.

Solution :

To find the number of files, we have to divide the total space occupied by the all the files by the memory used by each file.

= 171.5/24.5

= 171.5 ÷ 24.5

= ¹⁷¹⁵⁄₁₀ ÷ ²⁴⁵⁄₁₀

Division can be changed to multiplication by taking reciprocal of ²⁴⁵⁄₁₀.

= ¹⁷¹⁵⁄₁₀ x ¹⁰⁄₂₄₅

Simplify.

= ¹⁷¹⁵⁄₁ x ¹⁄245

= ¹⁷¹⁵⁄245

= 7

There are 7 files.

Problem 7 :

Mia went to a store and bought 33.6 pounds of cookies. She divided the cookies equally and packed them in boxes. If each box of cookies weighed 4.8 pounds, how many boxes did Mia use to pack the cookies?

Solution :

Number of boxes that Mia used to pack 33.6 pounds of cookies :

= 33.6 ÷ 4.8

= ³³⁶⁄₁₀ ÷ ⁴⁸⁄₁₀

Division can be changed to multiplication by taking reciprocal of ⁴⁸⁄₁₀.

= ³³⁶⁄₁₀ x ¹⁰⁄₄₈

Simplify.

= ³³⁶⁄₁ x ¹⁄₄₈

= ³³⁶⁄₄₈

= 7

Mia used 7 boxes to pack 33.6 pounds of cookies.

Problem 8 :

If 1.6 lbs. of candies is divided among four kids, find the amount of candy each kid get.

Solution :

Amount of candy each kid gets :

= 1.6 ÷ 4

= ¹⁶⁄₁₀ ÷ ⁴⁄₁

Division can be changed to multiplication by taking reciprocal of ⁴⁄₁.

= ¹⁶⁄₁₀ x ¼

Simplify.

= ⁴⁄₁₀ x ¹⁄₁

= ⁴⁄₁₀

Since 4 is divided by 10, there should be one digit to the right of the decimal point in the answer.

= 0.4

Each kid gets 0.4 lbs. of candy.

Problem 9 :

James had 19.55 lbs. of hot dog and he packed them in 6 boxes in which only three-fourth of the sixth box is filled. How many pounds of hot dog can be packed in one box?

Solution :

5¾ boxes ----> 19.55 lbs.

5.75 boxes ----> 19.55 lbs.

1 box ----> (19.55/5.75) lbs.

= 19.55/5.75

= 19.55 ÷ 5.75

= ¹⁹⁵⁵⁄₁₀₀ ÷ ⁵⁷⁵⁄₁₀₀

Division can be changed to multiplication by taking reciprocal of ⁵⁷⁵⁄₁₀₀.

= ¹⁹⁵⁵⁄₁₀₀ x ¹⁰⁰⁄₅₇₅

= ³⁹¹⁄₁ x ¹⁄₁₁₅

= ³⁹¹⁄₁₁₅

= 3.4

3.4 lbs. of hot dog can be packed in 1 box.

Problem 10 :

For additional strength of a building, 0.125 kilograms of a particular chemical is mixed with 12.5 kilograms of concrete. How many grams of chemical to be mixed with 1 kilogram of concrete?

Solution :

12.5 kg. of concrete ----> 0.125 kg. of chemical

1 kg. of concrete ----> (0.125/12.5) kg. of chemical

= 0.125/12.5

= 0.125 ÷ 12.5

= ¹²⁵⁄₁₀₀₀ ÷ ¹²⁵⁄₁₀

Division can be changed to multiplication by taking reciprocal of ¹²⁵⁄₁₀₀₀.

= ¹²⁵⁄₁₀₀₀ x ¹⁰⁄₁₂₅

= ¹⁄₁₀₀ x ¹⁄₁

= ¹⁄₁₀₀ kilograms

To convert kilograms to grams, multiply by 1000.

= ¹⁄₁₀₀ x 1000 grams

= 10 grams

10 grams of chemical to be mixed with 1 kilogram of concrete.

Practice Questions

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