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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

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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