Comparing fractions (age 9+)
Compare and order fractions with different numerators and denominators by creating common denominators/numerators or comparing to a benchmark such as 1/2; justify conclusions with visual models
What a learner can do afterwards
- Compare 3/8 and 5/12 by finding a common denominator of 24
- Order 2/3, 3/5, and 7/10 from smallest to largest
- Use the benchmark 1/2 to decide that 5/8 > 3/7
1 · Read
You already know how to compare fractions that share the same bottom number, or that sit near one-half. Now you'll compare fractions where the top and bottom numbers are both different, like 3/8 and 5/12. The trick is to rewrite both fractions with a common denominator, or check each one against the benchmark 1/2.
Compare 3/8 and 5/12. Both 8 and 12 divide evenly into 24, so rewrite each fraction with 24 as the denominator: 3/8 becomes 9/24, and 5/12 becomes 10/24. Since 10/24 is more than 9/24, 5/12 is the bigger fraction.
If you're not sure, draw a quick picture or check both fractions against one-half. If one fraction is under 1/2 and the other is over 1/2, you already know which is bigger.
To compare fractions with different tops and bottoms, make a common denominator or check each one against one-half.
More to read
Key ideas: Common denominators and common numerators
Have you ever wondered how to tell which fraction is bigger when the bottoms are different? There are two clever tricks.
Trick one: make the bottoms the same. Once two fractions have the same denominator, you only need to look at the tops. The bigger top wins. For example, is 1/2 or 1/3 bigger? Rewrite them as 3/6 and 2/6. Now it is easy to see that 3/6, which is 1/2, is bigger.
Trick two: make the tops the same. Then the fraction with the smaller bottom is bigger, because its pieces are larger. For example, 2/5 and 2/7 both have 2 on top. Fifths are bigger pieces than sevenths, so 2/5 is bigger.
You can also use 1/2 as a landmark. If one fraction is more than 1/2 and the other is less than 1/2, you know the answer right away.
Try it yourself: which is bigger, 5/6 or 7/12? Use a common denominator and see!
Finding a Common Denominator
Before you can compare fractions with different bottoms, it helps to give them the same bottom. That shared bottom is called the least common denominator, or LCD for short.
Here is how to find it. Say you want to compare 3/8 and 5/12. List the multiples of each denominator. Multiples of 8 are 8, 16, 24, 32. Multiples of 12 are 12, 24, 36. The smallest number in both lists is 24, so 24 is the least common denominator.
Now rewrite each fraction with the bottom 24. For 3/8, multiply the top and bottom by 3 to get 9/24. For 5/12, multiply the top and bottom by 2 to get 10/24.
Comparing is now simple: 9/24 and 10/24 have the same bottom, and 10 is bigger than 9. So 5/12 is bigger than 3/8.
The LCD is also the first step when you add or subtract fractions later on, so practicing it now will help you twice.
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