Comparing Fractions

🎯 What Will We Learn Today?

Which is bigger: 3/8 of a pizza or 4/9 of a pizza? Today we'll learn some simple tricks to compare fractions and figure out which one is larger!

📚 When Denominators or Numerators Are the Same

Same Denominator

When the bottom numbers are the same, the fraction with the bigger numerator wins!

3/8 < 5/8（5 slices is more than 3 slices）

Same Numerator

When the top numbers are the same, the fraction with the smaller denominator is actually bigger — because each piece is thicker!

2/5 > 2/7（splitting into 5 parts gives bigger slices than splitting into 7）

🎮 The Butterfly Method (Cross-Multiplication)

When the denominators are different, here's the easiest trick:

Multiply the first numerator × the second denominator = Cross 1

Multiply the second numerator × the first denominator = Cross 2

Cross 1 > Cross 2 → the first fraction is bigger!

Example: 3/4 vs 5/6
Cross 1: 3 × 6 = 18
Cross 2: 5 × 4 = 20
18 < 20 → 3/4 < 5/6

📊 Using a Number Line

Place fractions on a number line — the fraction farther to the right is always larger. This is a great visual way to check your answers!

📝 Practice Problems

3/8 ___ 5/8（fill in: <, >, or =）

2/9 ___ 2/7（which is bigger?）

Use the butterfly method: 2/3 ___ 3/4

Why is a fraction with a smaller denominator bigger when numerators are the same?

🎮 Play a Game!

Practice comparing fractions with Tugboat Addition and sharpen your fraction skills!