ASVAB Preparation: How to Multiply and Divide Fractions

By Rod Powers

You will be expected to have a firm grasp of basic mathematical knowledge when you take the ASVAB. Multiplying and dividing fractions are two of the things you will need to know.

Multiplying fractions

Multiplying fractions is very easy. All you have to do is multiply the numerators by each other, multiply the denominators by each other, and then simplify the result, as shown in the following equation:


The fraction 108/525 can be simplified to 36/175.

Before multiplying mixed numbers, change them to improper fractions by multiplying the denominator by the integer and adding it to the numerator. For example,


is a mixed number. To convert it to an improper fraction, multiply 8 by 2 and add 5 to the result:


The end result is 21/8.

Dividing fractions

Dividing fractions is almost the same as multiplying, with one important difference: You have to convert the second fraction (the divisor) to the reciprocal and then multiply. The reciprocal is simply a fraction flipped over.



Take the reciprocal of the second fraction and multiply it with the other fraction:


The fraction 15/10 is an improper fraction, which you can convert to


Then you can simplify