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RoomCalcs

Fraction calculator with steps

Add, subtract, multiply and divide fractions and mixed numbers — two or more at once — and see the working a teacher would write: the LCM and GCD, the common denominator, simplifying, the mixed number and the exact decimal. Also simplifies, compares and turns any decimal (even 0.333…) into a fraction.

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How do you add fractions with different denominators?

  1. 1Pick what you want to do: calculate, simplify, convert or compare.
  2. 2Type each fraction in the boxes — whole number, top and bottom. Leave “whole” empty for an ordinary fraction; tap ± to make it negative.
  3. 3Choose +, −, × or ÷ between the fractions, and add more fractions if you need.
  4. 4Read the answer in simplest form, as a mixed number and a decimal, then follow the step-by-step working underneath.

Fraction rules: common denominator, LCM and GCD

  1. 01a/b + c/d = (a × d′ + c × b′) / LCM(b, d), where d′ = LCM ÷ b and b′ = LCM ÷ d
  2. 02a/b × c/d = (a × c) / (b × d)
  3. 03a/b ÷ c/d = a/b × d/c
  4. 04Simplify: divide top and bottom by GCD(top, bottom)
  5. 05LCM(b, d) = b × d ÷ GCD(b, d)

To add or subtract fractions they need the same denominator. The calculator uses the lowest common denominator — the least common multiple (LCM) of the denominators — so the numbers stay as small as possible, rewrites each fraction over it, then adds or subtracts the numerators. Multiplying is simpler: multiply the tops and the bottoms. Dividing means multiplying by the reciprocal (the second fraction turned upside down).

Every answer is put in its simplest form by dividing the top and bottom by their greatest common divisor (GCD). The GCD comes from Euclid's algorithm — divide, keep the remainder, repeat until the remainder is 0 — which works for numbers of any size. With several operations, × and ÷ are done before + and −, as the order of operations requires.

Decimals: a fraction gives a decimal by long division, and because there are only so many possible remainders, the digits either stop or repeat. Going back, a repeating decimal such as 0.1666… becomes a fraction by multiplying by 10 and 100 and subtracting, so the endless part cancels: 90x = 15, x = 1/6. All the arithmetic is exact (no rounding), with whole numbers of any length.

Good to know

  • Check the answer is simplified: if the top and bottom are both even, it isn't yet.
  • To divide by a fraction, flip it and multiply — 3/4 ÷ 2/5 = 3/4 × 5/2.
  • A mixed number like 2 ⅓ becomes (2 × 3 + 1)/3 = 7/3 before multiplying or dividing.
  • Only the denominator 2s and 5s give a decimal that stops; anything else (like 3 or 7) repeats.

Fractions — questions students ask

How do you add fractions with different denominators?

Find the lowest common denominator (the LCM of the denominators), rewrite each fraction over it, add the numerators and simplify. For 1/4 + 1/6: LCM(4, 6) = 12, so 3/12 + 2/12 = 5/12.

How do you simplify a fraction?

Divide the top and the bottom by their greatest common divisor. For 84/36 the GCD is 12, so 84/36 = 7/3, which is 2 ⅓ as a mixed number.

How do you divide fractions?

Keep the first fraction, change ÷ to ×, and flip the second fraction: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 ⅞.

How do I turn a repeating decimal into a fraction?

Let x be the decimal, multiply by a power of 10 so the repeating part lines up, and subtract. For 0.333…: 10x = 3.333…, so 9x = 3 and x = 1/3. Type it here as 0.(3) or 0.333...

How do you multiply mixed numbers?

Turn each mixed number into an improper fraction first, then multiply the tops and bottoms: 1 ½ × 2 ⅔ = 3/2 × 8/3 = 24/6 = 4.

Which fraction is bigger, 2/3 or 3/5?

Give them a common denominator: 2/3 = 10/15 and 3/5 = 9/15, so 2/3 is bigger. Cross-multiplying gives the same answer: 2 × 5 = 10 is more than 3 × 3 = 9.

Sources

Formulas last reviewed: September 30, 2026 ·How we check our formulas

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