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Comparing and Ordering Fractions

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  • 0:06 Comparing & Ordering Fractions
  • 0:33 Common Denominators
  • 1:35 Comparing Fractions
  • 2:05 Example
  • 4:08 Ordering Fractions
  • 6:59 Lesson Summary
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Lesson Transcript
Instructor: Chad Sorrells

Chad has taught Math for the last 9 years in Middle School. He has a M.S. in Instructional Technology and Elementary Education.

Comparing and ordering fractions is way to examine fractions that contain different-sized sets. In order to compare these fractions, you must find a common denominator and make equivalent fractions.

Comparing and Ordering Fractions

When comparing and ordering fractions, you must have a common denominator. After you find a common denominator, you can simply compare the numerators of the fractions. If the fraction also includes a whole number, you would compare the whole number before finding the common denominator. For example, 6 ¾ would be greater than 5 ½. We can see that because the whole number is larger in 6 ¾ than it would be in 5 ½.

Finding the Common Denominator

There are several ways to find a common denominator when getting ready to compare fractions. The easiest method to find a common denominator is to multiply your denominators together. After you have multiplied the denominators together, the product will become your new denominator. For example, when comparing 7/8 and 5/6, the two denominators are 8 and 6. To find a common denominator, I would multiply the 8 and 6 together, which equals 48. The common denominator of this problem would be 48.

Now that we know our common denominator is 48, we must get equivalent fractions. Looking at the fraction 7/8, 8 times 6 is 48, so we must also multiply the numerator times 6. 7 times 6 equals 42. The fraction 7/8 is equivalent to 42/48.

Now we must find the equivalent to 5/6. Since we multiplied the denominator 6 times 8, we must also multiply the numerator 5 times 8, which equals 40. The fraction 5/6 is equivalent to 40/48.

Comparing Fractions

In the previous example, we were comparing 7/8 to 5/6. The first step was to find a common denominator, which we found as 48. The next step was to find equivalent fractions for each of the fractions. Now we are comparing 42/48 to 40/48. Since we know that 42 is larger than 40, we can see that 42/48 would be greater than 40/48. The equivalent fraction for 42/48 was 7/8, which would be larger than 5/6.

Comparing Fractions: Example

Comparing fractions can help us compare several items that may not all be the same size. By finding a common denominator, we change our fractions so that the items will be much easier to compare.

Jimmy and Dan both had pizza for supper last night. Jimmy's family ordered pizza from Pizza Palace. Pizza Palace slices their pizzas into sixteen slices. Jimmy's family ate 10/16 of the pizza for supper last night.

Dan's family ordered pizza from Magic Pizza, which slices their pizza into 8 slices. Dan's family ate 7/8 of their pizza for supper.

Jimmy and Dan are both curious which one of their families ate more pizza for supper last night. To begin comparing the fractions of pizzas that their families ate, they must first find the common denominator. Since the denominators are 16 and 8, the easiest way to find the common denominator is to multiply the denominators together. 16 times 8 equals 128. So the common denominator for both of these fractions will be 128.

Next, they must make equivalent fractions. Jimmy's family ate 10/16 of their pizza. To find the common denominator, Jimmy had to multiply his denominator by 8, which equaled 128. He must also multiply the numerator 10 times 8, which would equal 80. So Jimmy's family ate an equivalent of 80/128 slices of pizza for supper last night.

Dan must now find the equivalent fraction for the amount of pizza his family has eaten. To find the common denominator, Dan multiplied his denominator 8 by 16, which equaled 128. He must now multiply the numerator 7 times 16, which is 112. Dan now knows that his family ate an equivalent of 112/128 slices of pizza.

So Jimmy's family ate 80/128 of their box of pizza and Dan's family ate 112/128 of their box of pizza. Jimmy and Dan now know that Dan's family ate more pizza than Jimmy's family last night, because the numerator 112 is larger than 80.

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