Multiplying and Reducing Fractions on the ASVAB Math Knowledge Test

By Angie Papple Johnston

Some questions on the ASVAB Mathematics Knowledge subtest may involve multiplying fractions. As you solve an equation, you may need to perform the extra step of reducing the fraction to make it easier to find the right answer.

Multiplying fractions is easy. You just multiply the numerators and then multiply the denominators. Look at the following equation:


You multiply 1 × 3 × 3 × 3 = 9 (the numerators) and then 2 × 4 × 5 = 40 (the denominators) to result in 9/40.

Occasionally, when you multiply fractions, you end up with an extremely large fraction that can be simplified or reduced. To express a fraction in its lowest terms means to put it in such a way that you can’t evenly divide the numerator and the denominator by the same number (other than 1).

A number that you can divide into both the numerator and the denominator is called a common factor. If you have the fraction 6/10, both the numerator (6) and the denominator (10) can be divided by the same number, 2. If you do the division,

6 ÷ 2 = 3 and 10 ÷ 2 = 5

you find that 6/10 can be expressed in the simpler terms of 3/5. You can’t reduce (simplify) 3/5 any further; the only other number that both the numerator and denominator can be divided by is 1, so the result would be the same, 3/5.

Remember, you can’t use a calculator on the ASVAB, so multiplying large numbers can take extra steps and valuable time. You can make your work easier by canceling out common factors before multiplying.

For example, suppose you have the following problem


Multiplying the numerators (20 × 14) = 280, then multiplying the denominators (21 × 25) = 525, and finally reducing the fraction


may require you to write out three or more separate multiplication/division problems. But you can save time if a numerator and denominator have common factors. Here, the numerator of the first fraction (20) and the denominator of the second (25) have a common factor of 5, so you can divide both of those numbers by 5: Your problem becomes


The numerator of the second fraction (14) and the denominator of the first fraction (21) are both divisible by 7, so you can cancel out a 7: Divide 14 and 21 by 7. This changes the equation to


a much simpler math problem.