## Virtual Help

• Chat with library staff now
The Learning Portal - College Libraries Ontario

# Math: Basic Tutorials : Dividing Fractions

## Dividing Fractions

Dividing fractions is actually a lot like multiplying them! In this section, you will learn how to find the reciprocal of a fraction and how to use that reciprocal to solve your expression.

## Examples & Activity

### Examples

Click on the titles below to view each example.

Line 1: Divide the following fraction and write the answer in simplified form: negative 2 over 3 divided by 7 over 5.

Line 2: Multiply the first fraction by the reciprocal of the second fraction so the problem becomes negative 2 over 3 times 5 over 7.

Line 3: Multiply the numerators together, so the numerator is negative 2 times 5. Then multiply the denominators together, so the denominator is 3 times 7. Note the signs of the fractions are opposite so the product will be negative.

Line 4: Simplify the fraction to negative 10 over 21. There are no common factors in the numerator and denominator so this fraction is in simplified form. : Remove the common factor of 2 in the numerator and denominator so the final simplified fraction is negative 5 over 12.

Line 1: Divide the following fraction and write the answer in simplified form: 2 and 1 over 2 divided by 1 and 1 over 4.

Line 2: Convert the mixed numbers to improper fractions so that the problem is 5 over 2 divided by 5 over 4.

Line 2: Multiply the first fraction by the reciprocal of the second fraction so the problem becomes 5 over 2 times 4 over 5.

Line 3: Multiply the numerators together, so the numerator is 5 times 4. Then multiply the denominators together, so the denominator is 2 times 5.

Line 4: Look for common factors in the numerator and denominator. Rewrite the fraction showing the common factors of 2 and 5, so the numerator is written as 5 times 2 times 2 and the denominator is written as 2 times 5. Note that you can also multiply first and look for common factors after.

Line 5: Remove the common factors of 2 and 5 in the numerator and denominator, so the fraction becomes 2 over 1.

Line 6: Simplify the final answer to 2.

### Activity

Try this activity to test your skills. If you have trouble, check out the information in the module for help.