A fraction consists of a numerator (top number, the parts you have) and a denominator (bottom number, total equal parts).
Operations
- Adding/Subtracting: Find a common denominator first. 1/3 + 1/4 = 4/12 + 3/12 = 7/12
- Multiplying: Multiply numerators and denominators. 2/3 × 3/5 = 6/15 = 2/5
- Dividing: Flip the second fraction and multiply. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8
Converting
- Fraction → Decimal: Divide numerator by denominator (3/8 = 0.375)
- Fraction → Percentage: Convert to decimal, multiply by 100 (3/8 = 37.5%)
Simplifying Fractions
A fraction is in simplest form when the numerator and denominator share no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD): 12/18 → GCD is 6 → simplifies to 2/3. Calculators and most math problems expect answers in simplest form.
Mixed Numbers vs. Improper Fractions
A mixed number (like 2¾) combines a whole number and a fraction; an improper fraction (like 11/4) has a numerator larger than its denominator — they represent the same value. To convert a mixed number to improper form: multiply the whole number by the denominator, add the numerator, and keep the same denominator.