Comparing Fractions

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The folks who make the GED Math test love asking you to compare numbers. They usually want you to place a set of numbers in ascending (least to greatest) or descending (greatest to least) order. Sometimes it is a set of whole numbers, sometimes decimals, sometimes fractions, and sometimes a mixture of the three.


In this lesson we're going to look at ordering fractions. If the fractions have the same denominator, comparing them is easy: just look for the fraction with the largest numerator. For example, 7/10 is bigger than 4/10.


When the fractions have different denominators, things get a little more tricky. At first glance, the fraction 5/8 might look bigger than 2/3: after all, 5 is bigger than 2 and 8 is bigger than 3. But it's not, and there are a couple of ways to prove it.


One way is to find equivalent fractions with a common denominator. (Remember, equivalent fractions have the same value but different numbers: think 1/2 and 2/4.) Finding the lowest common denominator is an important skill in math, but when you're comparing fractions you don't need to worry about finding the lowest common denominator. Any common denominator will do, and an easy way to find a common denominator is to multiply the denominators together: using our example of 5/8 and 2/3, then, we can multiply 3 by 8 to produce a common denominator of 24.


We can now find our equivalent fractions by multiplying each numerator by the denominator of the other fraction. In other words, since we multiplied the 8 in 5/8 by 3 to get 24, we must also multiply the 5 by 3: 5/8 × 3/3 = 15/24. Let's do the same for the other fraction, except multiplying by the 8 in 5/8 this time: 2/3 × 8/8 = 16/24. 16/24 is greater than 15/24, so 2/3 must be greater than 5/8. Simple, right?


If finding equivalent fractions with a common denominator seems too hard, however, there's another way to compare fractions. And, even better, you can use your calculator with this one! To compare fractions, convert them into decimals by dividing the numerator by the denominator. Using our previous example, divide 5 by 8 and 2 by 3:

  • 5 ÷ 8 = 0.625
  • 2 ÷ 3 = 0.667 (no need to go farther than the thousandths place)

Again, it is clear that 0.667 is greater than 0.625, and therefore that 2/3 is greater than 5/8.


That's all it takes to compare fractions and place them in ascending (least to greatest) or descending (greatest to least) order. Here are a few practice questions to lock in what you've learned: good luck!