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 \frac{a}{b} where a (the numerator) counts how many equal parts you have and b (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 \frac{1}{4} of the pizza.
What is Ratios?
A ratio compares two or more quantities by showing how many times one contains the other, written as a:b or \frac{a}{b}. 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 2:1 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.