# Dividing Fractions on the ASVAB Math Knowledge Test

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

- Solve the following:

## Answer and explanation

- 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: