Fraction Calculator

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number), separated by a fraction bar. The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many of those parts you have.

Key fraction operations:

Addition and subtraction need a common denominator first: 1/3 + 1/4 = 4/12 + 3/12 = 7/12

Multiplication goes straight across, numerators then denominators: 2/3 × 3/5 = 6/15 = 2/5 (simplified)

Division means multiplying by the reciprocal of the divisor: 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 and 1/8

Simplification (reducing): Divide numerator and denominator by their Greatest Common Divisor (GCD). 24/36 → GCD is 12 → 24/12 = 2, 36/12 = 3 → simplified to 2/3

Converting:

• Fraction to decimal: divide numerator by denominator (3/4 = 0.75)
• Decimal to fraction: write it over the matching power of ten, then simplify (0.375 = 375/1000 = 3/8; 0.6 = 6/10 = 3/5)
• Mixed number to improper fraction: (2 and 3/4) = (2×4 + 3)/4 = 11/4

Worked examples:

Halving a baking recipe: Recipe needs 3/4 cup flour. Halving gives 3/4 × 1/2 = 3/8 cup.

Sharing pizza: 5 friends share 3 pizzas equally: 3/5 pizza each.

Why fractions matter: Fractions are exact, and decimals often are not. 1/3 as a decimal is 0.33333… repeating, never exactly right at any finite length. Keeping 1/3 as a fraction through a calculation preserves precision that decimal rounding throws away.

A note on the common denominator. For addition and subtraction this calculator uses the lowest common denominator rather than simply multiplying the two denominators together. For 1/4 + 1/6 that means working in twelfths rather than twenty-fourths. Both routes reach 5/12 once you simplify, but the LCD keeps the intermediate numbers small, which matters when you are doing it by hand. The working is shown in the result so you can follow the same steps on paper.