Fraction Calculator

Same denominator: just add the numerators and keep the bottom: 2/7 + 3/7 = 5/7.

Different denominators: find the Least Common Denominator, rewrite both fractions, then add: 1/2 + 3/4 → 2/4 + 3/4 = 5/4.

The LCD is the smallest number both denominators divide into. The calculator always shows the multiples it compares.

Exactly like addition, but take the numerators apart: 3/4 − 1/6 → 9/12 − 2/12 = 7/12.

Never subtract the denominators! 3/4 − 1/6 is not 2/2 — the denominators name the size of the pieces, they do not change.

A negative answer is fine and is shown with a minus sign on the numerator.

Straight across: 2/3 × 4/5 = 8/15. No common denominator needed.

“of” means multiply: 1/3 of 3/4 = 1/3 × 3/4 = 1/4. In word problems: “of” → ×, “is” → =.

Shortcut: cancel common factors diagonally before multiplying to keep numbers small.

Keep the first fraction, change ÷ to ×, flip the second fraction (its reciprocal): 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

Why it works: dividing by 2/5 is the same as multiplying by 5/2, because those two numbers multiply to 1.

You can never divide by zero — a fraction with a numerator of 0 has no reciprocal.

A fraction is in lowest terms when its only common factor is 1. Divide top and bottom by the Greatest Common Factor: 12/18 ÷ 6/6 = 2/3.

Quick test: if both numbers are even, divide by 2. If the digits sum to a multiple of 3, divide by 3.

Reducing does not change the value — 12/18 and 2/3 describe exactly the same amount.

Proper: numerator < denominator (3/4). Improper: numerator ≥ denominator (7/4). Mixed: a whole number plus a proper fraction (1 3/4).

Mixed → improper: (whole × denominator) + numerator over the denominator: 2 1/3 = (2×3+1)/3 = 7/3.

Improper → mixed: divide and keep the remainder: 7/3 → 7 ÷ 3 = 2 r 1 → 2 1/3.