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The cross product method is a way to compare two fractions. In this lesson, you'll learn how to perform the cross product method accurately and understand the results in order to identify which fraction is bigger or smaller or if the fractions are equivalent.
The Cross Product Method
The cross product method is used to compare two fractions. It involves multiplying the numerator of one fraction by the denominator of another fraction and then comparing the answers to show whether one fraction is bigger or smaller, or if the two are equivalent. This method is a shortcut to finding a common denominator and doesn't change the value of either of the fractions involved.
We can only compare two fractions at a time with this method, so if you're trying to compare more than two fractions, you'll need to repeat these steps using two fractions at a time. Let's look at a step-by-step example to see just how easy the cross product method can be.
Example of the Cross Product Method
Write the fractions vertically, next to each other. Be sure to leave a space in between them, like this:
Draw an 'X' diagonally between the two fractions. This helps remind you which numbers to multiply with each other:
Multiply the numerator and denominator that each line of the 'X' connects. Be sure to write your products down in such a way that you can identify which fraction they each represent. This is where mistakes tend to happen.
Step Four: Compare the Products
After you multiply the numerator 1 of the fraction 1/2 and the denominator 5 from 3/5, the product 5 is smaller than the product you get from multiplying the denominator 2 of 1/2 and the numerator 3 of 3/5. You'll see that the product 6 is larger than the product of 5, so 3/5 is larger than 1/2.
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Here are four rules for comparing fractions with the cross product method:
Always remember to multiple diagonally upward, not straight across or downward, or else your product will be representing the wrong fraction. We only multiply across when we want to multiply the fractions by one other.
If the products are identical, the fractions are equivalent. Here's an example:
If the numerators are the same, the fraction with the smallest denominator is larger.
If the denominators are the same, the fraction with the largest numerator is larger.
By multiplying fractions a certain way, you can quickly see which fraction is smaller, which fraction is larger, or if they're equivalent. This method is called cross product. It's critical that you multiply upward diagonally to get accurate products for the corresponding fractions. Since you can only compare two fractions at a time with this method, you'll need to repeat it if you are comparing more than two fractions.
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