Fraction Calculator

To add or subtract fractions, first find a common denominator by multiplying the two denominators together, then combine the numerators. To multiply fractions, multiply straight across (numerator × numerator, denominator × denominator). To divide, multiply the first fraction by the reciprocal of the second.

Every result is automatically reduced to lowest terms by dividing both the numerator and denominator by their greatest common factor (GCF). A negative sign is always kept in the numerator so the denominator stays positive.

Example: 1/2 + 1/3 uses the common denominator 6 — that's 3/6 + 2/6 = 5/6, which is already in lowest terms. Multiplying the same two fractions instead gives 1/2 × 1/3 = 1/6.

Improper fractions (numerator larger than denominator) reduce the same way — 8/6 becomes 4/3. Mixed numbers are not entered directly; convert to an improper fraction first if your recipe uses them.

Recipe scaling often chains fraction math with the recipe scaler — scale servings first, then convert cups to grams if you need weight on a scale.

Worked example with defaults: 1/2 + 1/3 → common denominator 6 → 3/6 + 2/6 = 5/6 ≈ 0.8333 decimal. Multiplying 1/2 × 1/3 gives 1/6 ≈ 0.1667.

Common denominators for 1/2 and 1/3 need only 6, not 2×3=6 from the blind multiply rule when lcm(2,3)=6 suffices — the calculator handles lcm internally so you do not hand-pick denominators. lcm(2,3)=6 suffices for 1/2 + 1/3 — the tool finds common denominators internally so you focus on operation selection, not lcm by hand.

Negative fractions keep sign in numerator — −1/2 + 1/3 = −3/6 + 2/6 = −1/6, useful for temperature deltas or budget deficits expressed as fractional parts of a whole. Negative fractions keep sign in the numerator — −1/2 + 1/3 = −1/6 for deficit or temperature delta problems on homework sets. Teachers often want common-denominator work shown even when an app returns 5/6 instantly.

Divide mode with defaults: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2 = 1.5 decimal — multiplying by the reciprocal is easy to forget when rushing homework without this tool. 1/2 ÷ 1/3 = 3/2 = 1.5 — reciprocal multiplication is the step students skip most often when rushing without showing work. Write the reciprocal flip (× 3/1) on paper before trusting the 1.5 decimal for divide problems.