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Fraction, percentage and ratio calculator

Add, subtract, multiply and divide fractions and mixed numbers, simplify them, and work out percentages and ratios, with every step shown. For KS3 and GCSE maths homework and checking your working.

Learn this properly

Lessons from the Maths course on this topic: worked steps, then exam-style questions with new numbers every time.

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Formulas

Addinga/b + c/d = (ad + bc) / bd, then simplify
Dividinga/b ÷ c/d = a/b × d/c
Percentage change(new − original) / original × 100
Sharing in a ratioamount × one part / total of the parts

Worked example

Work out 2 1/3 + 1 3/4.

  1. Write both as improper fractions: 2 1/3 = 7/3 and 1 3/4 = 7/4.
  2. The lowest common denominator is 12: 7/3 = 28/12 and 7/4 = 21/12.
  3. 28/12 + 21/12 = 49/12.
  4. 49 ÷ 12 = 4 remainder 1, so 49/12 = 4 1/12.

Answer: 4 1/12, or 49/12 as an improper fraction.

Common mistakes

  • Adding the denominators: 1/2 + 1/3 is 5/6, not 2/5.
  • Turning the wrong fraction upside down when dividing: only the second one flips.
  • Working out a percentage change from the new value instead of the original.
  • Leaving an answer unsimplified: divide the top and bottom by their highest common factor.

How it works

This calculator covers three topics that keep coming up together: fractions, percentages and ratios. Add, subtract, multiply or divide fractions and mixed numbers, work out percentages and percentage change, and simplify or share in a ratio. Every answer comes with the working laid out step by step, so you can follow the method and use it in your own answers.

  1. Pick a tab: Fractions, Percentages or Ratios.
  2. Fractions: enter two fractions, choose +, -, × or ÷, and read the answer as a simplified fraction, a mixed number, a decimal and a percentage. Mixed numbers like 1 1/2 are fine.
  3. Percentages: choose the type of question (X% of Y, X as a percentage of Y, percentage change from A to B, or increase or decrease by X%) and fill in the numbers.
  4. Ratios: enter 2 or 3 parts to simplify the ratio, or add an amount to share it in that ratio.
  5. Read the working under each answer and compare it with your own method.

Tips

  • To add or subtract fractions, write both over the lowest common multiple of the denominators: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
  • Dividing by a fraction is multiplying by its reciprocal: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2, or 1 1/2.
  • Percentage change is (new - old) / old × 100. Going from 40 to 50 is a 25% increase, but going from 50 back to 40 is a 20% decrease.
  • To share an amount in a ratio, add the parts first. £60 in the ratio 2:3 means 5 parts of £12, so £24 and £36.

FAQ

How does it simplify a fraction?
It divides the top and bottom by their highest common factor. For 18/24 the highest common factor is 6, so the fraction simplifies to 3/4. The working shows which factor was used.
Can it handle mixed numbers and decimals?
Mixed numbers work in the Fractions tab: type 2 3/4 with a space between the whole number and the fraction. In the Ratios tab, decimal parts are scaled up to whole numbers before simplifying, so 1.5 : 2 becomes 3 : 4.
How do I increase an amount by a percentage?
Use the increase or decrease option in the Percentages tab. Increasing 80 by 15% means multiplying by 1.15, which gives 92. Decreasing 80 by 15% means multiplying by 0.85, which gives 68.

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