Fractions and Percentages

Formulas

• Adding a/b + c/d = (ad + bc) / bd, then simplify
• Dividing a/b ÷ c/d = a/b × d/c
• Percentage change (new − original) / original × 100
• Sharing in a ratio amount × 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.

About this tool

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.

Tips

• 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.