How to Multiply Fractions

Key Takeaways

To multiply fractions, you simply multiply the numerators (top numbers) with each other and the denominators (bottom numbers) with each other.
Unlike addition or subtraction of fractions, there's no need for the denominators to be the same when multiplying fractions.
As an example, to multiply 3/4 by 2/5, you would multiply 3 (numerator) by 2 (numerator) and 4 (denominator) by 5 (denominator) to get 6/20, which can be simplified to 3/10.

You might have been in fifth grade the last time you thought about how to multiply fractions.

But if you're trying to cut a recipe in half or calculate the new price of a sale sweater using fractions, you might need to dig around in the back of your memory for how to multiply fractions and get the right answer.

Contents

Multiplying Fractions Is Easy
Step 1: Multiply the Numerators
Step 2: Multiply the Denominators
Step 3: Convert the Fraction to Its Simplest Form

Multiplying Fractions Is Easy

In every fraction, there's a top number and a bottom number, separated by a short horizontal line.

In a proper fraction, the smaller number — called the numerator — will always be on top, while the larger number — the denominator — will be on the bottom.

So 2/3, 3/4 and 6/8 are all examples of proper fractions.

The numerator tells us how many units we have of a whole and the denominator tells us how many units make up the whole. So, in the fraction 1/2, 1 is the numerator and 2 is the denominator — there are two units in the whole, but this fraction tells us that we only have one of these units.

Unlike when you are adding or subtracting fractions, you can multiply fractions with different denominators. For instance, it's not a problem to multiply 3/4 x 2/5.

Step 1: Multiply the Numerators

The first step in multiplying two fractions together is to multiply the numerators together. So, in our example:

3 x 2 = 6

Step 2: Multiply the Denominators

The second step in multiplying fractions is to use the same method and multiply the denominators together. So, in our example:

4 x 5 = 20

Easy enough! So our fraction now looks like this:

3/4 x 2/5 = 6/20

Step 3: Convert the Fraction to Its Simplest Form

The third step is to simplify, or reduce, the fraction to its lowest form, because there's a better way to read a fraction and produce your final answer.

To do this, we find the largest number by which we can divide both the numerator and denominator.

In this example, the highest number that divides evenly into both is 2, so the reduced answer to this multiplication problem is 3/10.

Frequently Asked Questions

How do you multiply mixed numbers?

The process for multiplying mixed numbers involves first converting them to improper fractions, then multiplying the numerators together and the denominators together. If the result is an improper fraction, where the numerator is larger than the denominator, you may convert it back to a mixed number by dividing the numerator by the denominator.

Can you multiply more than two fractions at a time?

Yes, you can multiply more than two fractions at a time. To do so, multiply all the numerators together to obtain the overall numerator and all the denominators together to get the overall denominator. After this, if possible, simplify the fraction that results from this multiplication.