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

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

#### Example 2

Divide the fractions:

First, change the operation to multiplication and

Next, multiply the fractions.

The quotient is

#### Example 3

Divide the fractions:

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

Then, multiply.

The quotient is

#### Example 4

Divide the fractions:

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:

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

Then, multiply.

The quotient is

### Review

Divide the fractions. Answer in simplest form.

12÷13=−−−− 14÷15=−−−− 25÷12=−−−− 47÷13=−−−− 68÷12=−−−− 49÷13=−−−− 56÷12=−−−− 610÷12=−−−− - \begin{align*}\frac{9}{18} \div \frac{1}{3} = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}\frac{8}{9} \div \frac{1}{2} = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}\frac{15}{16} \div \frac{1}{5} = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}\frac{8}{11} \div \frac{3}{4} = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}\frac{12}{16} \div \frac{3}{4} = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}\frac{20}{24} \div \frac{3}{4} = \underline{\;\;\;\;\;\;\;}\end{align*}
- \begin{align*}\frac{18}{20} \div \frac{4}{5} = \underline{\;\;\;\;\;\;\;}\end{align*}

### Review (Answers)

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