Fraction Calculator

This calculator performs addition, subtraction, multiplication and division on fractions and mixed numbers. It automatically simplifies results to their lowest terms by dividing numerator and denominator by their greatest common divisor (GCD).

To add or subtract fractions with different denominators, the calculator finds the least common denominator (LCD), converts both fractions, then combines the numerators. For multiplication, it multiplies numerators together and denominators together. For division, it multiplies by the reciprocal of the second fraction.

Mixed numbers (like 2 3/4) are supported — the calculator converts them to improper fractions internally, performs the operation, then converts back. Results are shown as both an improper fraction and a mixed number where applicable.

Adding and subtracting fractions. Find common denominator first. ½ + ¼ = 2/4 + ¼ = ¾. ⅔ + ⅗ = (3×3 + 2×5) / (3×5) = 19/15 = 1 4/15. For unlike denominators: multiply denominators if no obvious LCM. Subtraction same method: ¾ − ⅓ = (3×3 − 4×1)/12 = 5/12. Mixed numbers: convert to improper first (1½ = 3/2). Always simplify final answer by dividing by GCD: 6/8 → 3/4 (GCD 2). Convert improper back to mixed for clarity: 7/3 → 2⅓.

Multiplying and dividing fractions. Multiply: numerator × numerator, denominator × denominator. ½ × ⅔ = (1×2)/(2×3) = 2/6 = 1/3. Divide: multiply by reciprocal (flip second fraction). ¾ ÷ ½ = ¾ × 2/1 = 6/4 = 3/2 = 1½. Simplify before multiplying when possible: ⅔ × 9/10 = (2×9)/(3×10) = (2×3)/(1×10) = 6/10 = 3/5. Cross-cancel: 4/9 × 3/8 = (4×3)/(9×8) → cancel 4 with 8 (give 1 and 2), cancel 3 with 9 (give 1 and 3) → 1/6.

Fractions vs decimals — UK Maths curriculum. Year 4 (age 8-9): equivalence — ½ = 0.5 = 50% = 2/4. Year 5 (9-10): adding/subtracting same denominators. Year 6 (10-11): adding different denominators, simplifying, mixed numbers. KS3 (Years 7-9): all operations, percentages of fractions. GCSE (Year 11): fractions of fractions, recurring decimals (1/3 = 0.333..., 1/7 = 0.142857...). UK National Curriculum emphasis on fractions over decimals because they reveal more about number properties (e.g. why 1/3 doesn't divide cleanly into 10).

Real-world UK uses of fractions. Cooking — ½ tsp, ¾ cup, ⅓ pint. Carpentry — measurements in inches and 16ths: 1¼ inch, 7/16 inch. Music — note durations (whole, half, quarter, eighth, sixteenth). Stock markets (until 2001 in US): prices quoted in 1/8, then 1/16 of dollar. Sports scores — 2½/4 in cricket scoring; ¾ goals difference in some sports tables. DIY plumbing — pipe sizes (½ inch, ¾ inch, 22mm). Maps and surveying — 1/25,000 scale Ordnance Survey maps.

Common fraction-decimal-percentage equivalents to memorise. ½ = 0.5 = 50%. ⅓ = 0.333... = 33.3%. ¼ = 0.25 = 25%. ⅕ = 0.2 = 20%. ⅙ = 0.1666... = 16.67%. ⅛ = 0.125 = 12.5%. 1/10 = 0.1 = 10%. 1/100 = 0.01 = 1%. ⅔ = 0.666... = 66.7%. ¾ = 0.75 = 75%. ⅖ = 0.4 = 40%. ⅗ = 0.6 = 60%. ⅞ = 0.875 = 87.5%. Useful for tip calculations (½ for 50%), discounts (¼ for 25%, ¾ for 75%), shares of bills.