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Quotients of Fractions

Understand the process of how to find a quotient between two fractions.

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Quotients of Fractions
Credit: Efraimstochter
Source: https://pixabay.com/en/waffle-waffle-irons-waffle-bake-203024/
License: CC BY-NC 3.0

Corey is planning on making waffles. The recipe says to use  cups of flour, but Corey can only find the -cup measuring cup. How many -cups does Corey need to make his waffles?

In this concept, you will learn how to divide a fraction by a fraction.

Dividing Fractions

When dividing whole numbers and fractions, you first change the operation to multiplication and then change the divisor to its reciprocal. The same rule applies to dividing a fraction by another fraction. Here is a division problem.

Start by applying the first part of the rule and change the sign to multiplication. Then apply the second part of the rule, the reciprocal of one-third is three over one.

Then, multiply the fractions.

Next, simply the fraction. Convert the improper fraction a mixed number. 

The quotient is .

As long as you apply the rules, the problem is very straightforward and simple to figure out. Here is another one.

First, change the operation and change  to its reciprocal.

Then, multiply the fractions.

Next, simplify the fraction. Convert the improper fraction to a mixed number. 

The quotient is .

Examples

Example 1

Earlier, you were given a problem about Corey and his waffles.

Corey needs to measure out  cups of flour for his waffles, but can only find a  measuring cup. Divide  by  to find how many  cups Corey should use. 

First, write an expression.

Then, change the operation to multiplication and change the divisor to its reciprocal. 

Next, multiply the fractions. 

Finally, convert the improper fraction to a mixed number. 

Corey can use a little more than 2 of the  measuring cup to make his waffles.  

Example 2

Divide the fractions: = _____. Answer in simplest form.

First, change the operation to multiplication and  to its reciprocal.

Next, multiply the fractions. 

The quotient is .

Example 3

Divide the fractions: . Answer in simplest form.

First, change the expression. Multiply by the inverse of the divisor. 

Then, multiply.

The quotient is .

Example 4

Divide the fractions: . Answer in simplest form.

First, change the expression. Multiply by the inverse of the divisor.

Then, multiply. 

Next, convert the improper fraction to a mixed number. 

The quotient is 

Example 5

Divide the fractions: . Answer in simplest form.

First, change the expression. Multiply by the inverse of the divisor. 

Then, multiply. 

The quotient is .

Review

Divide the fractions. Answer in simplest form.

Review (Answers)

To see the Review answers, open this PDF file and look for section 7.10. 

Resources

Vocabulary

Inverse Operation

Inverse operations are operations that "undo" each other. Multiplication is the inverse operation of division. Addition is the inverse operation of subtraction.

reciprocal

The reciprocal of a number is the number you can multiply it by to get one. The reciprocal of 2 is 1/2. It is also called the multiplicative inverse, or just inverse.

Image Attributions

  1. [1]^ Credit: Efraimstochter; Source: https://pixabay.com/en/waffle-waffle-irons-waffle-bake-203024/; License: CC BY-NC 3.0

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