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Math

Attribution

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY 4.0 International License .

Dividing Fractions 

Check out this presentation by our Math Tutor Dr. Shohreh Rahmati about how to divide fractions. 

Division of Fractions

Let's suppose that we have two fractions a/b and c/d, where b and d are not equal to zero. A general division of fractions is given by:
                                                                            
                                                                              (a/b) ÷ (c/d),         where b≠ 0, d≠0.

 

In order to divide two fractions, we do the following steps:
Step (1): Find the reciprocal of the second fraction, d/c.
Step (2): Multiply the first fraction by the reciprocal of the second fraction, (a/b) × (d/c).
Step (3): Multiply numerators together and denominators together, (a × d)(b × c)
Step (4): Simplify the result, if possible.

 

Example: Divide (4/5) ÷ (6/10).
Step (1): We find the reciprocal of 6/10 which is 10/6
Step (2): We multiply the first fraction by the reciprocal of the second fraction 
                                                                              (4/5) × (10/6)
Step (3): We multiply numerators together and denominators together
                                                                         (4 × 10)(5 × 6)=40/30.
Step (4): We simplify the final result. The greatest common factor of 40 and 30 is 10, therefore, we divide both 40 and 30 by 10
                                                                                40/30=4/3.

Simplify First!

In some cases where we deal with large numbers, it is easier to simplify fractions first and then multiply. 

 

Example: Divide (9/16) ÷ (6/8).
We multiply the first fraction by the reciprocal of the second fraction:
Now, we simplify the fractions before we proceed with the division. The greatest common factor of 9 and 6 is 3, and the greatest common factor between 8 and 16 is 8. Therefore, we divide 9 and 6 by 3 and 8 and 16 by 8, as shown below:  
Finally, we multiply numerators together and denominators together:
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