Fractions

Comparing fractions with different denominators

On the previous page, we compared fractions that have the same bottom numbers, or denominators. But you know that fractions can have any number as a denominator. What happens when you need to compare fractions with different bottom numbers?

For example, which of these is larger: 2/3 or 1/5? It's difficult to tell just by looking at them. After all, 2 is larger than 1, but the denominators aren't the same.

If you look at the picture, though, the difference is clear: 2/3 is larger than 1/5. With an illustration, it was easy to compare these fractions, but how could we have done it without the picture?

Click through the slideshow to learn how to compare fractions with different denominators.

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  Let's compare these fractions: 5/8 and 4/6.

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  Before we compare them, we need to change both fractions so they have the same denominator, or bottom number.

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  First, we'll find the smallest number that can be divided by both denominators. We call that the lowest common denominator.

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  Our first step is to find numbers that can be divided evenly by 8.

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  Using a multiplication table makes this easy. All of the numbers on the 8 row can be divided evenly by 8.

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  Now let's look at our second denominator: 6.

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  We can use the multiplication table again. All of the numbers in the 6 row can be divided evenly by 6.

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  Let's compare the two rows. It looks like there are a few numbers that can be divided evenly by both 6 and 8.

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  24 is the smallest number that appears on both rows, so it's the lowest common denominator.

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  Now we're going to change our fractions so they both have the same denominator: 24.

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  To do that, we'll have to change the numerators the same way we changed the denominators.

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  Let’s look at 5/8 again. In order to change the denominator to 24...

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  Let’s look at 5/8 again. In order to change the denominator to 24...we had to multiply 8 by 3.

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  Since we multiplied the denominator by 3, we'll also multiply the numerator, or top number, by 3.

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  5 times 3 equals 15. So we've changed 5/8 into 15/24.

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  We can do that because any number over itself is equal to 1.

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  So when we multiply 5/8 by 3/3...

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  So when we multiply 5/8 by 3/3...we're really multiplying 5/8 by 1.

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  Since any number times 1 is equal to itself...

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  Since any number times 1 is equal to itself...we can say that 5/8 is equal to 15/24.

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  Now we'll do the same to our other fraction: 4/6. We also changed its denominator to 24.

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  Our old denominator was 6. To get 24, we multiplied 6 by 4.

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  So we'll also multiply the numerator by 4.

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  4 times 4 is 16. So 4/6 is equal to 16/24.

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  Now that the denominators are the same, we can compare the two fractions by looking at their numerators.

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  16/24 is larger than 15/24...

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  16/24 is larger than 15/24... so 4/6 is larger than 5/8.

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Now it's your turn! Try comparing these fractions with different denominators. Click the larger fraction.