Fraction multiplication is a lot easier than you may think. Unlike adding and subtracting fractions, you don't have to keep the denominator the same. However, you can only work with improper and proper fractions, which means you have to convert mixed numbers into improper fractions.

Once you have multiplied two fractions together, you can simplify the answer so that the fraction is easier to work with in future equations.

Multiplying fractions can seem daunting, so we've compiled this guide to give you a better understanding of the process, as well as common mistakes to avoid.

The simplest way to multiply two fractions is to multiply the two numerators (the top number in a fraction) together and write the result as the new numerator in your answer. You need to repeat the process and multiply the two denominators (the bottom number in a fraction) together to find the resulting denominator in your answer.

You can also cross-multiply fractions together if you want to compare the value of two fractions, as well as multiply a fraction by a whole number.

Continue reading for more tips on how to multiply fractions using different methods.

The purpose of multiplying two fractions together is to find a portion of the original fraction. For example, if you multiply 2/12 by 1/3, you are trying to find one-third of 2/12.

Example 1

2/12 x 1/3

The calculations to work this sum out are as follows:

  • The two numerators are two and one, so the equation is 2 x 1 = 2
  • The two denominators are 12 and 3, so the equation is 12 x 3 = 36
  • The answer is 2/36, which can be further simplified. The only shared factor for the denominator and numerator is two, so you need to divide both numbers by two. This means the simplified fraction is 1/18.

Example 2

4/6 x 2/9

The calculations to work this sum out are as follows:

  • The two numerators are four and two, so the equation is 4 x 2 = 8
  • The two denominators are six and nine, so the equation is 6 x 9 = 54
  • The answer is 8/54, which can be further simplified. The only shared factor for the denominator and numerator is two, so you need to divide both numbers by two. This means the simplified fraction is 4/27.

Example 3

3/15 x 3/6

The calculations to work this sum out are as follows:

  • The two numerators are three and three, so the equation is 3 x 3 = 9
  • The two denominators are 15 and six, so the equation is 15 x 6 = 90
  • The answer is 9/90, which can be further simplified. The largest shared factor between the numerator and denominator is 10, so you need to divide both numbers by 10. This means the simplified fraction is 1/10.

The easiest way of multiplying two fractions together is to multiply the two numerators together and then multiply the two denominators together. If possible, it's a good idea to simplify the fraction to make it easier to understand at a glance and to work with in future equations.

When you are trying to work out the equation a x d = b x c, you can use the cross-multiplication method a/b = c/d. This means multiplying the numerator of the first fraction with the denominator of the second and multiplying the numerator of the second fraction with the denominator of the first fraction.

This method is used to compare fractions. You can work out which fraction is greater or if they have the same value.

Example 1

Cross-multiply 3/4 x 6/8

The calculations to work this sum out are as follows:

  • 3 x 8 = 24
  • 4 x 6 = 24

These equations cross-multiplied a/b = c/d to get a x d = b x c.

Example 2

You can also use cross-multiplication to compare, unlike fractions. Unlike fractions are two fractions that have different denominators.

Compare 3/7 and 5/8

You need to make the above fractions have the same denominator. This can be done by creating a new denominator that is the product of both original denominators (7 x 8 = 56). Next, you need to cross-multiply the two numerators:

  • 3 x 8 = 24

The first fraction becomes 24/56. You then need to cross-multiply the two original denominators:

  • 5 x 7 = 35

The second fraction becomes 35/56. This means that 24/56 = 35/56. Therefore, you know that 3/7 > 5/8.

Simplifying fractions can make them clearer to read and easier to work with in future calculations.

When you simplify a fraction, you turn the fraction into its simplest form. For example, you could simplify 4/8 to 1/2. Even though the two fractions have the same value, one half is easier to work with as it just means dividing an amount into two rather than eight pieces.

Example 1

An easy way to simplify fractions is to keep dividing the numerator and denominator by two, three, five and seven until you are left with the last possible whole numbers. For example:

24/108 ÷ 2 = 12/54

12/54 ÷ 2 = 6/27

27 divided by 2 won't leave you with a whole number. However, you can divide both 6 and 27 by three to give whole numbers:

6/27 = 2/9

Therefore, the simplified version of 24/108 is 2/9.

Example 2

A quick method is to try and find the largest shared factor of both the numerator and the denominator. In the instance of 10/35, the largest factor is five, which means you can divide both the numerator and denominator by 5:

10 ÷ 5 = 2

35 ÷ 5 = 7

Therefore, the simplified version of 10/35 is 2/7.

You may need to multiply a whole number by a fraction if you are trying to find a portion of the whole number. For example, if you multiply 2/5 by four, you are trying to find two-fifths of four. Unlike when you multiply two fractions together, you must only multiply the numerator by the whole number, and the denominator stays the same.

Another way to calculate the value when you multiply a fraction by a whole number is to turn the whole number into a fraction too. You need to write the whole number as a fraction out of one. For example, if you wanted to multiply a fraction by four, you could convert the whole number to 4/1. You can then use the method used previously to multiply two fractions together.

Example 1

2/5 x 4

You will have to multiply the numerator by four. The denominator stays the same.

  • 2 x 4 = 8

The answer is 8/5, which is an improper fraction as the numerator is larger than the denominator. You can turn this fraction into a mixed number, which is a whole number and a proper fraction combined.

Example 2

3/11 x 2

You will have to multiply the numerator by two.

  • 3 x 2 = 6

The answer is 6/11.

Example 2

2/7 x 3

You will have to multiply the numerator by three. The denominator stays the same.

  • 2 x 3 = 6

The answer is, therefore, 6/7, which is your final answer, as the fraction can't be further simplified.

A mixed number combines a whole number and a fraction, such as 1 2/3 or 4 2/6. To multiply two mixed numbers together or a mixed number multiplied by a whole number, you need to convert the mixed number into an improper fraction. You can multiply improper fractions in the same way that you would multiply proper fractions together.

Example 1

1 3/8 x 3

You need to rewrite the whole number in the mixed number as a fraction. In the example of 1 3/8, this would become 11/8 because the whole number one represents 8/8, and then you must add the numerator as 8 + 3 = 11.

Next, you need to multiply 11/8 by three, which means multiplying the 11 by three and keeping the denominator as 8.

  • 11 x 3 = 33

The answer is 33/8, which you can keep as an improper fraction or convert back to a mixed number. You can use the same method as you did to convert 1 3/8 to 11/8. The final answer as a mixed number is 4 1/8.

Example 2

1 1/2 x 2 1/5

You can also multiply two mixed numbers together by converting both mixed numbers into improper fractions.

1 1/2 becomes 3/2 and 2 1/5 becomes 11/5. You need to multiply these numbers together by multiplying the two numerators and the two denominators together, as shown below:

  • 3 x 11 = 33
  • 2 x 5 = 10

Therefore, the answer is 33/10, which you can convert into a mixed number of 3 3/10.

People commonly use fractions when they are baking and cooking. The recipe may call for 1/4 of a cup or half a dozen eggs. However, you might want to double the quantity of the recipe to create more portions, which means multiplying these ingredients by two.

You also use fractions when serving food. For example, if you have a pizza and eight guests, you would cut the pizza into eight slices. However, Guest A and Guest B may not want a slice, but Guest C wants three slices. You would automatically multiply 1/8 by three and serve Guest C 3/8 of the pizza.

It's a good idea to be aware of common calculation mistakes when you learn or teach multiplying fractions to someone else so that you can avoid making the mistakes yourself.

When you first learn about fractions, you may get confused between the numerator and the denominator. This could mean you end up multiplying the denominator and not the numerator when you are multiplying fractions with whole numbers. An easy way to remember the difference is that 'd' is for down (the bottom value) and denominator.

You might get confused about which values you need to multiply together and multiply the numerator of the first fraction with the denominator of the second fraction and vice versa. Whilst this is the method for cross-multiplying fractions, you need to multiply the two numerators together and the two denominators together when you multiply proper fractions.

When you multiply mixed numbers together, it's important that you don't just multiply the two fractions together and add the whole number. You need to convert the mixed numbers into improper fractions and multiply the two together using the method given above.

Once you understand the fraction form and which values are the numerator and denominator, you can start to apply fraction multiplication methods. You can multiply the two numerators together, and the two denominators together to find the product of two proper fractions multiplied together.

When you want to multiply a mixed number, you need to convert the mixed fraction into an improper fraction and use the same method as explained above. When you have your result, you can convert the improper fraction back to a mixed number.