3rd Grade Math Help: How to Compare Fractions

Comparing Fractions in 3rd Grade

Before you start comparing fractions, it helps to understand what a fraction is. Fractions show parts of a whole. Every fraction has a denominator, which tells you the total number of parts that make up the whole. All fractions also have numerators, which tell you the number of parts the fraction has. If a pie has seven slices, and you take three, you have taken 3/7 of the slices because you took three out of the seven total pieces.

If Lisa took two slices of pie, or 2/7, and Sam took one slice of the same pie, or 1/7, you could be sure that Lisa took more pie than Sam, since two slices is more than one slice. Since the denominators of the fractions are the same, you can just compare the numerators to figure out which fraction is bigger. Here are some more examples:

• 1/3 is less than 2/3
• 5/7 greater than 3/7
• 3/10 less than 9/10

Using Inequality Signs

When we're comparing fractions, we can use the inequality signs for greater than and less than. Just like the equals sign is used to show that two things are the same, like 1 + 2 = 3, the inequality signs are used to show that one quantity is larger or smaller than another quantity. The sign looks like this '>,' or this '<.' The 'open' end of the sign always points to the larger quantity. For instance, we could write, '5/6 is greater than 1/6,' like this: 5/6 > 1/6. If we wanted to write, '2/7 is less than 4/7,' it would look like this: 2/7 < 4/7. Here are a few more examples:

• 1/12 is less than 5/12: 1/12 < 5/12
• 3/8 is greater than 1/8: 3/8 > 1/8
• 7/9 is greater than 5/9: 7/9 > 5/9

Fractions with the Same Numerators

Imagine that you're given two pies of the exact same size. You cut one of the pies into eight slices and the other pie into four slices. The slices from the pie cut into four pieces will be larger than the slices from the pie that's cut into eight pieces. Now, imagine that you take one slice from each of the pies, and represent each of those slices as a fraction. The slice from the 4-piece pie would be represented by the fraction 1/4, and the slice from the 8-piece pie would be represented by 1/8.

Now, knowing what each of these fractions represents, which one is larger? You know that 1/4 must be greater than 1/8, since one slice from the 4-piece pie is bigger than a slice from the 8-piece pie. You could also tell that 3/4 > 3/8, since three of the larger-sized slices would give you more pie than three of the smaller slices.

Tip: When you're dealing with fractions that have the same numerators, the fraction with the smaller denominator is bigger, and the fraction with the larger denominator is smaller. In the examples above, 4 < 8, so 1/4 > 1/8.

Practice Problems

For each set of fractions below, write in the appropriate > or < sign between the two fractions.

1. 8/9, 7/9

2. 2/5, 4/5

3. 1/6, 5/6

4. 7/20, 20/20

5. 3/11, 3/4

6. 5/9, 5/12

7. 1/3, 1/4

8. 2/7, 2/5

9. 7/12, 1/12

10. 8/9, 8/10

Answer Key

1. 8/9 > 7/9

2. 2/5 < 4/5

3. 1/6 < 5/6

4. 7/20 < 20/20

5. 3/11 < 3/4

6. 5/9 > 5/12

7. 1/3 > 1/4

8. 2/7 < 2/5

9. 7/12 > 1/12

10. 8/9 > 8/10