Dividing fractions word problems

Dividing fractions word problems arise in numerous situations. We will show you some examples. I recommend that you review the lesson about division of fractions before starting this lesson.

Dividing fractions word problems: a few examples

Example #1:

An Italian sausage is 8 inches long. How many pieces of sausage can be cut from the 8-inch piece of sausage if each piece is to be two-thirds of an inch?

Solution

Since you are trying to find out how many two-thirds there are in 8, it is a division of fractions problem.

You will need to divide 8 by 2/3 in order to get the answer.

8 ÷ 2/3 = 8/1 ÷ 2/3

8 ÷ 2/3 = 8/1 × 3/2

8 ÷ 2/3 = (8 × 3)/(1 × 2)

8 ÷ 2/3 = 24/2

8 ÷ 2/3 = 12

Therefore, you can make 12 pieces of sausages having a length of 2/3 inches from an 8 inches long Italian sausage.

Example #2

How many halves are there in six-fourths?

Again, since you are trying to find out how many halves there are in six-fourths, it is a division of fractions problem.

You will need to divide 6/4 by 1/2 to get the answer.

6/4 ÷ 1/2 = 6/4 × 2/1

6/4 ÷ 1/2 = (6 × 2)/(4 × 1)

6/4 ÷ 1/2 = 12/4

6/4 ÷ 1/2 = 3

Therefore, there are 3 halves in six-fourths.

Example #3:

An airplane covers 50 miles in 1/5 of an hour. How many miles can the airplane cover in 5 hours?

This problem is a combination of division and multiplication of fractions.

First, find out how many fifths (1/5) are there in 5. This is a division of fractions problem.

You will need to divide 5 by 1/5.

5 ÷ 1/5 = 5/1 ÷ 1/5

5 ÷ 1/5 = 5/1 × 5/1

5 ÷ 1/5 = (5 × 5)/(1 × 1)

5 ÷ 1/5 = 25/1

5 ÷ 1/5 = 25

Then, you need to multiply 50 by 25 to get the answer.

50 × 30 = 1250

In 5 hours, the airplane will cover 1250 miles.

Example #4

3 friends share 4/5 of a pizza. what fraction of pizza does each person get?

The amount to share is 4/5

Since the amount will be shared between 3 friends, the amount must be divided between 3 people.

So each person must get 4/5 divided by 3

(4 / 5) / 3 = (4 / 5) / (3 / 1) = 4 / 5 × 1 / 3 = (4 × 1) / (5 × 3)= 4 / 15

Each person will eat 4/15.

Indeed, 4 / 15 + 4 / 15 + 4 / 15 = 12 / 15 = 4/5 (divide 12 and 15 by 3 to get 4 / 5)

Example #4

On June 21st, there were 9/10 of a billion stars visible to the naked eye.

On December 21st, there were 4/5 of a billion stars out visible to the naked eye.

How many times more stars were there visible on June 21st than December 21st?

Set it up.

9/10 divided by 4/5 = ?

Find the reciprocal of the divisor.

9/10 × 5/4 = ?

Simplify

9/10 × 5/4 = 9/2 × 1/4

Solve

9/2 × 1/4 = 9/8

Simplify again

9/8= 1 1/8

Did you have a hard time understanding the problems above? Did you not understand them at all? Take a look at this figure !

Do you need to master fractions once and for all? Check out my book about fractions.