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 !

Dividing fractions word problem

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

Have A Great Basic Math Word Problem?

Share it here with a very detailed solution!

[ ? ]

Upload 1-4 Pictures or Graphics (optional)[ ? ]

 

Click here to upload more images (optional)

Author Information (optional)

To receive credit as the author, enter your information below.

(first or full name)

(e.g., City, State, Country)

Submit Your Contribution

  •  submission guidelines.


(You can preview and edit on the next page)

What Other Visitors Have Said

Click below to see contributions from other visitors to this page...

12 Pieces of Chalk 
Ming and Chuck were walking home one afternoon and decided to draw a chalk line on the road from school to Chuck's house. They started out with a box …

Click here to write your own.

Recent Articles

  1. Quadratic Formula: Easy To Follow Steps

    Jan 26, 23 11:44 AM

    Quadratic formula
    Learn about the quadratic formula, the discriminant, important definitions related to the formula, and applications.

    Read More

  2. Area Formula - List of Important Formulas

    Jan 25, 23 05:54 AM

    Frequently used area formulas
    What is the area formula for a two-dimensional figure? Here is a list of the ones that you must know!

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes