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), so 6/8 reduces to 3/4 once you divide both by the GCD of 2, and it converts an improper result such as 7/3 back into the mixed number 2⅓ for readability.

To add or subtract fractions with different denominators, the calculator finds the least common denominator (LCD), converts both fractions, then combines the numerators. Adding 2/3 and 3/4 means spotting an LCD of 12, rewriting them as 8/12 and 9/12, adding 8 + 9 = 17 and reading off 17/12, which is 1 5/12. The same routine handles ½ + ¼ as 2/4 + ¼ = ¾, and ⅔ + ⅗ as (3×3 + 2×5) / (3×5) = 19/15 = 1 4/15. Subtraction works identically, so ¾ − ⅓ becomes (3×3 − 4×1)/12 = 5/12.

Multiplication is the easy one, since numerators multiply together and denominators multiply together, giving ½ × ⅔ = (1×2)/(2×3) = 2/6 = 1/3. Division flips the second fraction and multiplies, turning ¾ ÷ ½ into ¾ × 2/1 = 6/4 = 3/2 = 1½. Cancelling before you multiply saves work, so ⅔ × 9/10 reduces to (2×3)/(1×10) = 6/10 = 3/5, and 4/9 × 3/8 cross-cancels the 4 against the 8 and the 3 against the 9 to leave 1/6.

Mixed numbers such as 2 3/4 are supported throughout. Internally they are converted to improper fractions, so 1½ becomes 3/2, the operation is carried out on those, and the result is converted back. Answers appear as both an improper fraction and a mixed number where applicable, alongside the decimal equivalent, which is often the quickest sanity check on whether an answer looks right.

Fractions are introduced early in the UK National Curriculum and built on for years. Year 4, at age 8-9, covers equivalence, the idea that ½, 0.5, 50% and 2/4 all describe the same quantity. Year 5, at 9-10, adds and subtracts with matching denominators. Year 6, at 10-11, moves on to different denominators, simplifying and mixed numbers. KS3, Years 7-9, covers all four operations and percentages of fractions, and GCSE work in Year 11 reaches fractions of fractions and recurring decimals such as 1/3 = 0.333... and 1/7 = 0.142857.... The emphasis on fractions over decimals is deliberate, because they show more about how numbers behave, such as why 1/3 does not divide cleanly into 10.

A short list of equivalents does most of the everyday work. A half is 0.5 or 50%, a quarter is 0.25 or 25%, three quarters is 0.75 or 75%, and an eighth is 0.125 or 12.5% with ⅞ at 0.875 or 87.5%. A third recurs as 0.333... or 33.3% and two thirds as 0.666... or 66.7%, while a sixth is 0.1666... or 16.67%. Among fifths, ⅕ is 0.2 or 20%, ⅖ is 0.4 or 40% and ⅗ is 0.6 or 60%. A tenth is 0.1 or 10% and a hundredth is 0.01 or 1%. Tips, discounts and shares of a bill all fall out of that handful.

Outside the classroom, fractions survive in the places measurement never went metric. Recipes still call for ½ tsp, ¾ cup and ⅓ pint. Carpentry works in inches and sixteenths, so 1¼ inch and 7/16 inch are everyday sizes, and plumbing keeps ½ inch and ¾ inch alongside 22mm. Music notation runs on whole, half, quarter, eighth and sixteenth durations. US stock prices were quoted in 1/8 and later 1/16 of a dollar until 2001. Cricket scoring uses forms like 2½/4, some league tables show ¾ of a goal difference, and Ordnance Survey maps use a 1/25,000 scale.