# 3rd Grade Math Help: How to Compare Fractions

In 3rd grade, you'll learn all about fractions. Continue reading for instructions on how to compare fractions, and then complete a set of ten practice problems to test your knowledge!

## 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

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

Did you find this useful? If so, please let others know!

## Other Articles You May Be Interested In

• Tips to Help Kids Understand Fractions

Fractions can be a confusing topic for some students. Read on to learn how you can help your children better understand the uses of fractions.

• 5 Free and Fun Math Games for Kids

Looking for a way to get your child engaged with math? There are many free, fun math games online that explore basic concepts such as addition, subtraction, multiplication and division, as well as more advanced games that offer practice with decimals and fractions. Read on to discover five of our favorite educational - and fun! -...

## We Found 7 Tutors You Might Be Interested In

### Huntington Learning

• What Huntington Learning offers:
• Online and in-center tutoring
• One on one tutoring
• Every Huntington tutor is certified and trained extensively on the most effective teaching methods
In-Center and Online

### K12

• What K12 offers:
• Online tutoring
• Has a strong and effective partnership with public and private schools
• AdvancED-accredited corporation meeting the highest standards of educational management
Online Only

### Kaplan Kids

• What Kaplan Kids offers:
• Online tutoring
• Customized learning plans
• Real-Time Progress Reports track your child's progress
Online Only

### Kumon

• What Kumon offers:
• In-center tutoring
• Individualized programs for your child
• Helps your child develop the skills and study habits needed to improve their academic performance
In-Center and Online

### Sylvan Learning

• What Sylvan Learning offers:
• Online and in-center tutoring
• Sylvan tutors are certified teachers who provide personalized instruction
• Regular assessment and progress reports
In-Home, In-Center and Online

### Tutor Doctor

• What Tutor Doctor offers:
• In-Home tutoring
• One on one attention by the tutor
• Develops personlized programs by working with your child's existing homework
In-Home Only

### TutorVista

• What TutorVista offers:
• Online tutoring
• Student works one-on-one with a professional tutor
• Using the virtual whiteboard workspace to share problems, solutions and explanations
Online Only