Equivalent Fractions

Equivalent fractions are a useful tool in your fraction handling toolbox. Once you get the hang of equivalent fractions, you can manipulate fractions with confidence. However, it’ll take some work and practice to lock this concept down.

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Why Equivalent Fractions Matter

Equivalent fractions are useful whenever you’re referencing fractions. The big thing they’re helpful for is common denominators, which are essential for adding and subtracting fractions. Without common denominators, you cannot perform those operations successfully.

Equivalent fractions are also useful when you’re discussing fractions. Equivalent fractions mean discussion can take place in real numbers, rather than large ones you cannot picture. Those concrete terms can be invaluable.

A Fraction Review

Fraction Structure Diagram

Let’s make sure we’re talking in the same terms. The top of a fraction is called the numerator, while the bottom is called the denominator. Many folks associate denominator with down to help them remember the difference.

With fractions, what you do to the upper number of the fraction, you must do to the bottom. This rule helps you maintain the fraction as the same fraction. Otherwise, you’re changing the size of the pieces and the number of pieces you’re talking about.

The bar in the middle is a division sign. While this is not relevant to equivalent fractions specifically, there will be times when the division symbol comes into play.

The Steps

To begin, an equivalent fraction problem looks like 3/5 = x/25, where you need to find the x. In this problem, you’re looking for a numerator. However, the problem may ask that you find a denominator as well. The process is the same.

So, you’ll either have two numerators or two denominators. Your job is to figure out how the multiplying worked to go from one to the other. You can do this simply by counting up using the first fraction as an interval. You can also take the second value in the pair and divide it by the first.

Once you know the factor between the fractions, it’s a simple process. You take the numerator or denominator that was on the same level as an x. You then multiply the value you know. The answer is the result.

Examples of Equivalent Fractions

Equivalent fractions sound difficult when talked about theoretically. However, concrete examples always help.

Let’s start with 4/7 = x/84. Our first step is dividing 84 by 7 since they’re both on the denominator level of the fraction. This action gives us our factor, which is 12. Now we take the four and multiply it by 12. The result is that x is equal to 48.

 Equivalent Fractions example 1

Now let’s try a denominator problem, 24/36 = 60/x. Our first step is dividing 60 by 24 since those values are both on the numerator level of the fraction. This action gives us our factor, which is 2.5. Then we take the 36 and multiply it by the factor of 2.5. The result is that x equals 90.

 Equivalent Fractions Example 2

Let’s try a big one, 54/80 = x/640. The first step is dividing 640 by 80 since both numbers are on the denominator level of the fraction. This action gives us our factor of 8. Now we take the 54 and multiply it by 8. The result tells us that x equals 432.

Equivalent Fractions example 3