Cross multiplication is an incredibly useful math skill to know. In fact, you may just find that it will come in handy throughout your life, even long after you leave school. Before learning how to cross multiply fractions, though, you’ll need to be familiar with a couple of simple math terms:
- The top number of a fraction is known as the numerator
- The bottom number of a fraction is known as the denominator
- When you multiply two numbers together, the answer is referred to as the “product”
The purpose of cross multiplying is to compare two fractions that have different denominators and come out with a standardized answer. Since you cannot easily compare fractions when the denominators are different, cross multiplication can help you to tell whether the two fractions are equivalent or whether one is larger than the other.
Cross Multiplication: Step 1
When cross multiplying two fractions, start by multiplying the top number (numerator) of the first fraction by the bottom number (denominator) of the second fraction. Jot down your answer.
In the example above, step 1 would be to multiply the numerator of the first fraction, which is 4, by the denominator of the second one, which is 7.
4 x 7 = 28
Cross Multiplication: Step 2
Once you’ve made a note of the product you found in step 1, the next step is similar. Now, you will multiply the numerator (the top number) of the second fraction by the denominator (which is the bottom number) of the first fraction. Jot down the answer (product).
For the example above, step 2 would be to multiply the two 5s together to get 25.
So, you have 4 x 7 = 28 and 5 x 5 = 25.
Since 28 is larger than 25, which we found when beginning with the numerator of the second fraction, this tells us that the first fraction — ⅘ — is larger than the second one — 5/7.
Cross Multiplying: Important Things to Remember
This method is extremely helpful when you’re attempting to find out which fraction is greater than the other. When you use cross multiplying, you must make sure that you start with the numerator of the first fraction, rather than the top number of the second one. Otherwise, you won’t get the right answer.
Make sure that as you cross multiply, you place the two products you end up with right under each relevant fraction. In other words, when you multiply the top number of the first fraction, put the result under that first fraction. Do the same with the second one.
Cross multiplication only works when you compare two fractions at a time. If you need to work with more fractions, instead of multiplying all of them, you will pick two fractions to start with and cross multiply them. Throw out the lesser fraction. Then, cross multiply using the remaining fraction and the third fraction to see which is greatest.
Become a Cross Multiplying Pro with Jantzi
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