What is a fraction?
A fraction represents a part of a whole. It's written as two numbers stacked with a line between them.
The top number (numerator) = how many parts you have.
The bottom number (denominator) = how many equal parts the whole is divided into.
Real-world examples
🍕 Pizza: You eat 2 slices out of 8 → you ate 2/8 (simplifies to 1/4)
💧 Water bottle: 500ml bottle, you drank 250ml → you drank 250/500 = 1/2
💰 Money: You have $3 of the $4 you need → 3/4 of the way there
Simplifying fractions
Find the largest number that divides both top and bottom evenly (called the GCD), then divide both by it.
6/9 → both divisible by 3 → 6÷3=2, 9÷3=3 → 2/3
4/8 → both divisible by 4 → 4÷4=1, 8÷4=2 → 1/2
10/15 → both divisible by 5 → 10÷5=2, 15÷5=3 → 2/3
Adding fractions
The denominators must be the same before you can add.
Same denominator: 1/5 + 2/5 = 3/5 (just add numerators)
Different denominator: 1/2 + 1/3
→ Common denominator: 6
→ Convert: 1/2 = 3/6 and 1/3 = 2/6
→ Add: 3/6 + 2/6 = 5/6
What is a percentage?
A percentage means "out of 100". The word comes from Latin per centum = per hundred.
75% = 75 out of every 100
50% = half
100% = the whole thing
0% = nothing at all
Think of a test score: 80% means you got 80 out of 100 points (or the equivalent).
Finding a percentage of a number
Formula: Percentage × Number ÷ 100
What is 20% of $85?
→ 20 × 85 ÷ 100 = $17
What is 15% of 200?
→ 15 × 200 ÷ 100 = 30
Quick trick: 10% = move the decimal one place left. Then build from there:
10% of 340 = 34 → 20% = 68 → 5% = 17
Percentage increase & decrease
Increase: Shirt costs $40, price rises 25%
→ 25% of 40 = 10 → New price: $50
Decrease (discount): $40 shirt, 25% off
→ 25% of 40 = 10 → New price: $30
% change formula: ((New − Old) / Old) × 100
Fraction → Percentage
Divide numerator by denominator, then multiply by 100.
3/4 → 3 ÷ 4 = 0.75 → × 100 = 75%
1/2 → 1 ÷ 2 = 0.5 → × 100 = 50%
2/5 → 2 ÷ 5 = 0.4 → × 100 = 40%
Percentage → Fraction
Write the percentage over 100, then simplify.
25% → 25/100 → ÷25 → 1/4
60% → 60/100 → ÷20 → 3/5
75% → 75/100 → ÷25 → 3/4
Cheat sheet — memorize these
1/2 = 50% 1/4 = 25% 3/4 = 75%
1/3 ≈ 33.3% 2/3 ≈ 66.7%
1/5 = 20% 2/5 = 40% 3/5 = 60% 4/5 = 80%
1/10 = 10% 1/8 = 12.5%