½ Fraction Calculator
Simplify fractions and perform arithmetic with step-by-step working.
Simplify a fraction
Fraction arithmetic
Fractions — the building blocks of maths
Fractions represent parts of a whole. The number on top (numerator) says how many parts you have; the number on the bottom (denominator) says how many equal parts the whole is divided into. Three quarters (¾) means 3 parts of something divided into 4.
- Simplifying: Divide both numerator and denominator by their Greatest Common Factor (GCF). 12/18 ÷ GCF(6) = 2/3. The value is unchanged — just expressed more simply.
- Adding/subtracting: You need a common denominator first. ½ + ⅓ = 3/6 + 2/6 = 5/6. Finding the Lowest Common Multiple (LCM) of the denominators is the key step.
- Multiplying: Multiply numerators together and denominators together. ½ × ⅔ = (1×2)/(2×3) = 2/6 = 1/3. Simpler than adding.
- Dividing: Flip the second fraction (reciprocal) and multiply. ½ ÷ ⅔ = ½ × 3/2 = 3/4. "Keep, change, flip" is the mnemonic.
🦘 Fun fact: Ancient Egyptians could only work with unit fractions — fractions with 1 on top (½, ⅓, ¼, etc.). To express anything else, they added unit fractions together. The Rhind Mathematical Papyrus (circa 1550 BCE) contains a table converting 2/n into sums of unit fractions — one of the earliest mathematical texts ever found.