Fraction vs Ratio
Fractions and ratios both compare quantities, but they answer different questions and behave differently in calculations. A fraction tells you "what part of the whole?" while a ratio tells you "how do these parts compare to each other?"
What is Fractions?
A fraction is a number of the form where (the numerator) counts how many equal parts you have and (the denominator, which must not be zero) tells how many equal parts the whole is divided into.
💡 A pizza cut into 4 slices—eating 1 slice means you ate of the pizza.
What is Ratios?
A ratio compares two or more quantities by showing how many times one contains the other, written as or . Unlike fractions, ratios can compare parts to parts, not just parts to wholes.
💡 A recipe that uses 2 cups flour for every 1 cup sugar has a ratio.
Key Differences
| Aspect | Fractions | Ratios |
|---|---|---|
| What it compares | Part to whole (3 out of 5) | Part to part (3 to 2) |
| Notation | 3/5 (fraction bar) | 3:2 or 3 to 2 |
| Must add to whole? | Yes, parts make the whole | No, can compare anything |
| Addition rules | Need common denominator | Cannot directly add ratios |
⚠️ Where People Get Stuck
- • Using ratio notation (3:2) when a fraction (3/5) is needed
- • Adding ratios like fractions (3:2 + 1:2 ≠ 4:4)
- • Forgetting that 3/5 and 3:2 describe the same situation differently
- • Converting between them without understanding what changes
A Simple Example
A class has 3 boys and 2 girls
Fractions
Fraction of boys: 3/5 (3 out of 5 total)
Ratios
Ratio of boys to girls: 3:2
🎯 When to Use Which
Use a fraction when you need "what part of the total." Use a ratio when comparing two separate quantities to each other.