Grade: Grade 3 Subject: Mathematics Unit: Fractions Introduction SAT: Algebra ACT: Math

Comparing Fractions

Learn how to compare fractions and decide which one is bigger, smaller, or if they are equal. We will use pictures and easy rules to help you become a fraction comparison expert!

What Does Comparing Fractions Mean?

Comparing = Finding Which is More or Less

When we compare fractions, we figure out which fraction shows a bigger part, a smaller part, or if they show the same amount.

🔢 Comparison Symbols

We use special symbols to show how fractions compare:

<
Less Than

The first number is smaller

Example: 14 < 34

>
Greater Than

The first number is bigger

Example: 34 > 14

=
Equal To

Both numbers are the same

Example: 24 = 24

Hungry Alligator Trick: The symbols < and > look like an alligator's mouth. The alligator always wants to eat the BIGGER number, so the open side points to the larger fraction!

Using Pictures to Compare Fractions

📊 Fraction Bars Help Us See

Looking at fraction bars makes it easy to see which fraction is bigger. The fraction with more shaded parts is greater!

Compare 24 and 34

24 = 2 out of 4 parts
34 = 3 out of 4 parts

34 has more shaded, so 24 < 34

Rule 1: Same Denominator (Bottom Number)

📏 When Denominators Are the Same

If two fractions have the same denominator (bottom number), just compare the numerators (top numbers).

The fraction with the bigger numerator is greater!

38 > 18

3 is more than 1, so 3/8 is greater

Compare 56 and 26

56
26

Same denominator (6), compare numerators: 5 > 2, so 56 > 26

Think About It: If you have a pizza cut into 6 slices, would you rather have 5 slices or 2 slices? More slices (bigger numerator) means more pizza!

Rule 2: Same Numerator (Top Number)

🔄 When Numerators Are the Same

If two fractions have the same numerator (top number), compare the denominators (bottom numbers).

The fraction with the smaller denominator is greater!

13 > 16

Fewer pieces = bigger pieces!

Compare 14 and 18

14 - whole divided into 4 parts
18 - whole divided into 8 parts

Same numerator (1), but 4 is smaller than 8, so each piece of 1/4 is bigger! 14 > 18

Think About It: If you share a pizza with 4 friends, each person gets a bigger slice than if you share it with 8 friends. More people sharing = smaller pieces!

Interactive Fraction Comparison Tool

Create your own fractions and see how they compare!

Build and Compare Fractions

VS

Practice Problems

Choose the correct symbol to compare each pair of fractions.

Problem 1

25 ? 45

Problem 2

34 ? 38

Problem 3

56 ? 56

Problem 4

12 ? 16

Problem 5

78 ? 38

Quick Quiz Challenge

Test your skills with random fraction comparisons!

Compare the Fractions!

24 ? 34
Score: 0 / 0

Check Your Understanding

When comparing fractions with the same denominator, which fraction is greater?

When comparing fractions with the same numerator, which fraction is greater?

Which symbol means "greater than"?

What We Learned

< > =

Comparison Symbols

Less than, greater than, and equal to help us compare.

📊

Visual Models

Fraction bars help us see which fraction is bigger.

🔢

Same Denominator

Bigger numerator = greater fraction.

🔄

Same Numerator

Smaller denominator = greater fraction.

Remember: When pieces are the same size (same denominator), more pieces is more. When you have the same number of pieces (same numerator), bigger pieces is more!

Next Steps

  • Practice comparing fractions with the interactive tool
  • Draw your own fraction bars to compare fractions
  • Look for fractions in real life (pizza slices, measuring cups)
  • When ready, move on to learn about Equivalent Fractions!