How to Multiply 3 Fractions

By Jon Zamboni; Updated April 24, 2017
All fractions are composed of a numerator and a denominator.

A fraction is composed of two parts: the numerator on top and the denominator on the bottom. For instance, in 4/5, 4 is the numerator, and 5 is the denominator. The product of any number of multiplied fractions is equal to the product of all the multiplied numerators over the product of all the multiplied denominators. You can simplify the process of multiplying fractions by multiplying the numerators and denominators individually. You should also reduce your fractions after multiplication.

Multiply the Numerators

In the multiplication problem 4/5 x 3/4 x 1/7, first multiply the numerators of all the fractions. The numerators are 4, 3 and 1, so multiply 4, 3 and 1 together. The total is the numerator of the multiplied fraction:

4 x 3 x 1 = 12

Multiply the Denominators

Multiply the denominators together. This produces the denominator of the new fraction. For 4/5, 3/4 and 1/7, the denominators are 5, 4 and 7. Multiply these together:

5 x 4 x 7 = 140

Your numerator is 12, and your denominator is 140. Your equation looks like this:

4/5 x 3/4 x 1/7 = 12/140

Simplify the Fraction

You're not done yet, though. Before you confirm your answer, check if the multiplied fraction can be reduced. You can reduce a fraction if both the numerator and denominator can be divided by the same number. In 12/140, both the numerator and the denominator can be divided by 2:

12/140 = 6/70

Check again to see if the new fraction can be reduced. Both 6 and 70 can be divided by 2, so you can reduce the fraction again:

6/70 = 3/35

You cannot divide 35 by 3, so you can't reduce the fraction anymore. You now have a final answer:

4/5 x 3/4 x 1/7 = 3/35

About the Author

Jon Zamboni began writing professionally in 2010. He has previously written for The Spiritual Herald, an urban health care and religious issues newspaper based in New York City, and online music magazine eBurban. Zamboni has a Bachelor of Arts in religious studies from Wesleyan University.