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DayUtils

Ratio Calculator – Solve, Simplify and Split Ratios

Solve proportions such as 3 : 4 = 15 : ?, simplify any ratio to its lowest terms — including ratios with decimals — or share a total between two parts in a given ratio. Every answer shows the working.

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How to use the ratio calculator

Choose what you want to do:

  • A : B = C : ? — enter A, B and C to find the missing fourth value.
  • Simplify A : B — enter both parts to get the simplest whole-number form, the fraction and the 1 : n form.
  • Scale to a total — enter the ratio and a total to split it into two shares.

Ratio formulas

A : B = C : D → D = B × C ÷ A
Simplest form = A ÷ GCF : B ÷ GCF
Share of A = Total × A ÷ (A + B)

Worked examples

  • 3 : 4 = 15 : ? → ? = 4 × 15 ÷ 3 = 20
  • Simplify 12 : 18 → GCF is 6 → 2 : 3
  • Simplify 1.5 : 2.5 → 15 : 25 → 3 : 5
  • Share 700 in 3 : 4 → 700 ÷ 7 = 100 per part → 300 and 400

Ratios in everyday life

  • Cooking: a recipe for 4 that uses 300 g of flour needs 300 × 6 ÷ 4 = 450 g for 6 people.
  • Screens and photos: 16 : 9 for video, 4 : 3 for many tablets, 3 : 2 for many cameras, 1 : 1 for square social media posts.
  • Maps and models: a scale of 1 : 50,000 means 1 cm on the map is 50,000 cm (500 m) on the ground.
  • Mixing: paint, concrete, fertiliser and cleaning products often give mixing ratios.
  • Finance: debt-to-income and other financial ratios compare one amount with another.
  • School: ratio and proportion are a core topic in maths from middle school onwards.

Direct and inverse proportion

The calculator solves direct proportion, where both quantities rise together: more people need more flour. In inverse proportion, one goes up as the other goes down: if 4 workers take 6 days, 8 workers take 3 days. For inverse problems multiply the pair instead: 4 × 6 = 24 worker-days, so 8 workers need 24 ÷ 8 = 3 days.

Tips

  • Keep the order. 3 : 4 is not the same as 4 : 3.
  • Use the same units on both sides before comparing — convert metres and centimetres first.
  • Check your answer by simplifying both sides of a proportion: 3 : 4 and 15 : 20 both simplify to 3 : 4.

For fractions, use the fraction calculator; for percentages, the percentage calculator; and to find common factors, the LCM and GCF calculator.

Frequently asked questions

How do I solve a proportion?

For A : B = C : ?, multiply B by C and divide by A. For 3 : 4 = 15 : ?, the missing value is 4 × 15 ÷ 3 = 20.

How do I simplify a ratio?

Divide both parts by their greatest common factor. 12 : 18 has a greatest common factor of 6, so it simplifies to 2 : 3. For decimals, first multiply both parts by 10 or 100 to make them whole numbers: 1.5 : 2.5 becomes 15 : 25, then 3 : 5.

How do I split an amount in a ratio?

Add the parts of the ratio, divide the total by that sum to find one part, then multiply. To share 700 in the ratio 3 : 4: one part = 700 ÷ 7 = 100, so the shares are 300 and 400.

What is the difference between a ratio and a fraction?

A ratio compares two quantities with each other (3 boys to 4 girls). A fraction compares a part with the whole (3 out of 7 children are boys). The ratio 3 : 4 corresponds to the fractions 3/7 and 4/7 of the total.

What is a 16:9 aspect ratio?

It means the width is 16 units for every 9 units of height — the standard shape for HD video and most screens. A 1,920-pixel-wide image at 16 : 9 is 1,920 × 9 ÷ 16 = 1,080 pixels tall.

Can ratios have more than two parts?

Yes — for example concrete is often mixed 1 : 2 : 3 of cement, sand and gravel. This calculator handles two-part ratios; for more, simplify each pair or divide each part by the total.

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