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# 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

## Summary and Worksheet

## Attribution

Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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.

- Summary: Dividing Fractions - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Dividing Fractions - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.