How to Multiply Fractions

Multiplying fractions might seem a little daunting at first, but once you get the hang of setting up your equation, you’ll be able to get those answers in no time! Turn mixed numbers into improper fractions, multiply numerators and denominators, and simplify your fraction to get the final answer to the question. Take your time and work step by step so you can check your work as you go.

Multiplying Simple Fractions

Write down the problem on a piece of paper. Being able to see your work will help you learn how to multiply fractions better. Plus, if you make a mistake, it’ll be easier to go back in your work to see the error. Each fraction has a numerator (the number on the top) and a denominator (the number on the bottom). Separate the numerator from the denominator with a straight, horizontal line.
Try your best to keep your fractions in a straight line. This will just make it easier to stay organized and work efficiently.

Multiply the numerators first

For example, if you’re asked to solve for 5/6 * 2/3, the first thing you’ll need to do is multiply 5 * 2, which gives you 10. This will be the numerator for your answer.
In another example, solve for the numerator of 3/4 * 1/3. Any number times 1 will be itself, so your new numerator is 3.

Figure out the new denominator

In the example given, 5/6 * 2/3, multiply 6 * 3 to get 18. This is your new denominator.
For 3/4 * 1/3, multiply 4 * 3 to get the new denominator of 12. The answer to your multiplication problem is 3/12.
Simplify your new fraction to get it in the lowest form possible. If the numerator and denominator share common factors (they can be divided equally by the same number), you can simply your answer. For the example of 5/6 * 2/3, the answer you got was 10/18. Both 10 and 18 are divisible by 2. Divide both numbers by 2 to get your final, simplified answer, which is 5/9.
Simply the fraction 3/12. 3 goes into both itself and 12 evenly. The simplified answer is 1/4.

Working with Mixed Numbers

Write the problem down on paper so you can keep track of your work. You may be tempted to solve math problems in your head, but when you’re first starting out it’s a good idea to write everything down, step by step. This way, if you make a mistake, it’s easy to go back and see what happened so you can fix it moving forward.
Fractions are made up of 2 parts, the numerator (the top number) and the denominator (the bottom number), and they are separated with a straight, horizontal line. To write a mixed number, put the whole number on the left-hand side of the fraction.

Change the mixed

For example, let’s say the problem you’re solving for is 1 and 3/4 * 7 and 1/5. The first thing you need to do is change both of those mixed fractions into improper fractions, meaning that the numerator will be greater than the denominator. Here’s how to do this:
1 and 3/4 = 7/4 when it’s made into an improper fraction. The denominator will always stay the same when making improper fractions. Multiply the denominator by the whole number (4 *1) and add that answer to the current numerator (3). (4*1) + 3 = 7.
For 7 and 1/5, multiply the denominator by the whole number (5*7) and add that answer to the current numerator (1). (5*7) + 1 = 36. Put the new numerator over the original denominator for your improper fraction. 7 and 1/5 = 36/5.

Simplify the improper fractions to make the numbers easier to multiply. In the example given, we are left with 7/4 * 36/5. While you could just multiply the numerators and the denominators, it will be easier to do the math if you can simplify the fractions first. When simplifying, check to see if the cross numerator and denominator can be divided equally by the same number. 7 and 5 cannot be, but 36 and 4 are both equally divisible by 4. To get your simplified fraction:

Divide 4 by 4 to get 1, changing the first fraction from 7/4 to 7/1.

Divide 36 by 4 to get 9, changing the second fraction from 36/5 to 9/5.

You can also simplify single fractions if the numerator and denominator have a common factor. For example, if 7/4 were instead 8/4, you could simplify that fraction to 2/1.

Solve for the problem by multiplying

Now all you have to do is solve for your fraction by multiplying 7 * 9 to get 63 for the new numerator. Multiply 1 * 5 to get 5 for the new denominator. The final improper fraction is 63/5.
Tip: Remember to keep writing down your work step by step so you don’t get lost in the process. Mixed numbers and improper fractions can be a little tricky, but with practice, you’ll get the hang of it.

Convert the fraction back to a mixed number get the final answer. To get back to a mixed number, you just need to do some simple division. Divide the numerator by the denominator, so 63/5. 5 goes into 63 12 times, with 3 left over. 12 becomes the whole number and 3 becomes the new numerator. The denominator of 5 stays the same. In the end, 1 and 3/4 * 7 and 1/5 = 12 and 3/5.[12]

If you can’t do the division in your head for the whole number, write it out on your piece of paper.