Fractions

Understanding Fractions

A fraction a/b means a parts out of b equal parts. The top number is the numerator and the bottom is the denominator.

Equivalent Fractions

Multiply or divide both numerator and denominator by the same number to get an equivalent fraction.

Example: 2/3 = 4/6 = 6/9 = 10/15

Simplifying Fractions

Divide both parts by their Greatest Common Factor (GCF).

Example: Simplify 18/24 → GCF is 6 → 18÷6 / 24÷6 = 3/4

Adding and Subtracting Fractions

Fractions must have the same denominator before adding or subtracting.

1. Find the Lowest Common Denominator (LCD)
2. Convert fractions to have the LCD
3. Add or subtract the numerators
4. Simplify if needed

Example: 1/3 + 1/4 → LCD = 12 → 4/12 + 3/12 = 7/12

Multiplying Fractions

Multiply straight across: numerator × numerator, denominator × denominator.

Example: 2/3 × 3/5 = 6/15 = 2/5

Dividing Fractions

Flip the second fraction (find its reciprocal) and multiply.

Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Mixed Numbers and Improper Fractions

To convert mixed to improper: multiply whole number by denominator, add numerator.
2¾ = (2×4 + 3)/4 = 11/4

To convert improper to mixed: divide numerator by denominator.
17/5 = 3 remainder 2 = 3 2/5

Key Tips

• Always simplify your final answer
• When comparing fractions, convert to the same denominator or use decimals
• A fraction of a quantity: 3/4 of 80 = (80 ÷ 4) × 3 = 60