Dividing Fractions on the ASVAB Math Knowledge Test

By Angie Papple Johnston

If you encounter a question on the ASVAB where you have to divide fractions, just remember this rule: Dividing a fraction by a number is the same as multiplying it by the inverse (reciprocal) of that number.

Of course, there are always exceptions. You can’t use this operation on zero. Zero has no inverse. No one knows why—it just is.

The inverse of a number is obtained by reversing the number. That means that if you want to divide a fraction by 5, you simply multiply the fraction by the inverse of 5, which is 1/5. You can understand this process more easily if you remember that 5 is the same thing as 5/1. In other words, 5 divided by 1 equals 5 (that is, 5 ÷ 1 = 5).

And the inverse of 5/1 is 1/5. To come up with the inverse of a number, simply stand the number on its head.

So to divide a fraction, use the inverse of the number that follows the division symbol and substitute a multiplication symbol for the division symbol. Therefore,


is expressed as


and then you can simply multiply the fractions.


Now, try the following practice question.

Practice question

  1. Solve the following:


Answer and explanation

  1. The correct answer choice is D.

First, change the mixed numbers to fractions:


Flip or invert the second fraction and change the symbol to multiplication:


Cross-reduce (cross-cancel) by using the greatest common factor:


Convert back to a mixed number: