How To Multiply Fractions

Last Updated on February 15, 2024.

Multiplying fractions is relatively easy. If you want to multiply two fractions, you just need to multiply both the numerators and the denominators.

Multiplying fractions isn’t hard at all. It’s just two multiplications and then, maybe, some simplifying. If you’ll be multiplying the tops and the bottoms you’re all set. I think you won’t have any problems here.

This lesson is provided by Onsego GED Prep.

Next Lesson: Dividing Fractions

Video Transcription

Multiplying Simple Fractions – Here, we’ll begin with some simple fractions that have small numbers. I guess you remember the multiplication tables up to \(10\) (ten).

First, let’s start with single digits. You may notice that we aren’t worried anymore about common denominators here. As said, just multiply the top numbers and then multiply the bottom numbers.

\(\frac{2}{5}* \frac{2}{3}\) equals ?

• First, multiply the two numerators to get the new numerator of the product. So: \(2 * 2 = 4\)

• Then, multiply the two denominators to get the new denominator of the product. So: \(5 * 3 = 15\)

• Then put the new numerator and the new denominator together. So: \(\frac{4}{15}\)

• Then simplify. There’s no simplifying possible for this fraction.

The answer is: \(\frac{2}{5}* \frac{2}{3}\) equals \(\frac{4}{15}\)

Can we also do three fractions in this way? Sure thing.

\(\frac{1}{2}* \frac{3}{4}* \frac{2}{5}\) equals ?

• First, multiply the three numerators to get the new numerator of the product. So \( 1*3*2 = 6 \)

• Then multiply the three denominators to get the new denominator of the product. So \( 2*4*5 = 40 \)

• Then put the new numerator and the new denominator together. So \(\frac{6}{40}\)

• Then simplify. \(6\) and \(40\) both have the common factor of two \((2)\). So divide both the top and the bottom by \(2\) (two) to get the simplified fraction of \(\frac{3}{20}\).

The answer is: \(\frac{1}{2}* \frac{3}{4}* \frac{2}{5}\) equals \(\frac{3}{20}\)

Multiplying Complex Fractions – There will be times that you will get stuck with more difficult fractions. So let’s try one example with a bit harder multiplication:

\(\frac{5}{12}* \frac{5}{6}\) equals ?

• First, multiply both numerators to get the new numerator. So \(5 * 5 = 25\)

• Then multiply both denominators to get the new denominator. So \(12 * 6 = 72\)

• Then, put the new numerator and the new denominator together. So \(\frac{25}{72}\)

• Then if possible, simplify. Well, there is no simplifying possible for this fraction.

The answer is: \(\frac{5}{12}* \frac{5}{6}\) equals \(\frac{25}{72}\)

Do you see? We are using the same process. Even when we have big numbers to multiply.

Multiplying Mixed Numbers – Do you remember when we subtracted mixed numbers? Then, we first made improper fractions before starting out on the problem. In this first example, we will use that same process.

\(5\,\frac{1}{3} * 2\,\frac{4}{9}\) equals ?

• First, convert all factors into improper fractions:

So \(5\,\frac{1}{3} = 5\,+\frac{1}{3} = \frac{15}{3}+ \frac{1}{3} = \frac{16}{3}\)

And \(2\,\frac{4}{9} = 2\,+\frac{4}{9} = \frac{18}{9}+ \frac{4}{9} = \frac{22}{9}\)

• Then multiply the two numerators. So \(16 * 22 = 352\)

• Then, multiply the two denominators. So \(3 * 9 = 27\)

• Then, write the raw product using the new numerator and the new denominator. So \(\frac{352}{27}\)

• Then, convert this improper fraction into a whole number.

So \(\frac{352}{27} = 352 \div 27 = 13r1 = 13\, \frac{1}{27}\)

• Then, if possible, simplify the fraction. Here is no simplification possible.

The answer is: \(5\,\frac{1}{3} * 2\,\frac{4}{9} \) equals \(13\, \frac{1}{27}\)

Keep in mind that denominators do not matter when we multiply fractions. These three are the only steps:

1. First, multiply all numerators and get the new numerator.
2. Then, multiply the denominators and get the new denominator.
3. Then, simply your answer if needed.