Ratio calculator with steps
Simplify a ratio, check if two ratios are equivalent, solve a proportion or share an amount in a ratio, with every step shown.
🧒 Kids: pick what you want to do, type a ratio like 12 : 18 and read the steps. Then try one on paper!
Ratio calculator
What the calculator shows
Every answer comes with the steps a teacher would want to see. Simplify mode also draws a tape diagram and a table of equivalent ratios. Share mode labels each box with its value, so children see where the answer comes from.
Use it to check homework, not to replace it. Ask your child to solve the problem first, then compare their working line by line.
Ready-made examples to try
Each link opens the calculator with the problem filled in.
- Simplify 12 : 18: Divide by the GCF
- Simplify 1.5 : 2.5: A ratio with decimals
- Simplify 6 : 9 : 12: A three-part ratio
- Is 2 : 3 = 10 : 15?: Equivalent ratios
- Is 3 : 4 = 4 : 5?: Adding is not scaling
- 3 : 4 = 15 : x: A whole-number scale factor
- 6 : 8 = x : 12: Cross-multiplying
- Share 35 in the ratio 2 : 5: A tape diagram
- Share 120 in the ratio 1 : 2 : 3: Three parts
How to simplify a ratio
A ratio is in simplest form when its parts have no common factor except 1. To get there, divide every part by the greatest common factor. For example, 24 : 36 has a greatest common factor of 12, so it simplifies to 2 : 3.
Decimals need one extra step first. Multiply 1.5 : 2.5 by 10 to get 15 : 25, which is 3 : 5.
Mixed units need the same unit first. For 40 cm : 2 m, change 2 m to 200 cm, then simplify 40 : 200 to 1 : 5. See ratios for kids.
How to check equivalent ratios
Equivalent ratios describe the same mix. For example, 2 cups of juice to 3 cups of water tastes the same as 4 to 6, because both parts were doubled. Simplify both ratios and compare, or cross-multiply.
A common trap is adding the same number to both parts. For example, 3 : 4 and 4 : 5 look close. But 3 × 5 = 15 and 4 × 4 = 16, so they are not equivalent.
How to solve a proportion
A proportion says two ratios are equal, like 3 : 4 = 15 : x. If a part was multiplied by a whole number, use the same scale factor. Here 3 × 5 = 15, so x = 4 × 5 = 20.
When the numbers don’t scale neatly, cross-multiply. In 6 : 8 = x : 12, the cross products give 8 × x = 6 × 12 = 72, so x = 9. The calculator shows both methods when both work.
How to share an amount in a ratio
Draw a tape diagram with one box for each part of the ratio. Sharing $35 in the ratio 2 : 5 needs 7 equal boxes, so each box is $35 ÷ 7 = $5. The first person gets 2 boxes ($10) and the second gets 5 boxes ($25).
Common ratio mistakes the steps catch
- Stopping too early: dividing 24 : 36 by 2 to get 12 : 18. Divide by the greatest common factor, 12.
- Swapping the order when solving a proportion. Keep the same kind of amount in the same position on both sides.
- Sharing by the ratio numbers: giving 2 and 5 of the $35. Add the parts first and find the size of one part.
- Forgetting units: 40 cm : 2 m is not 20 : 1. Change both to centimetres first.
Ratio skills by grade
| Grade | What children calculate | Standard |
|---|---|---|
| Grade 6 | Ratio language, equivalent ratios, ratio tables, tape diagrams and unit rates | 6.RP.A.1–3 |
| Grade 7 | Proportions, proportional relationships, unit rates with fractions and scale drawings | 7.RP.A.1–2, 7.G.A.1 |
In India, ratio and proportion appear in class 6 and grow in classes 7 and 8 with direct proportion and unitary method problems.
For teachers
Project the calculator and ask the class to predict the simplest form before you type it.
To set homework checks, share a link with the problem filled in, like ?mode=share&r=2:5&n=35. The mode can be simplify, equivalent, proportion or share. Nothing is stored and no login is needed.
More ratio help
- Ratio practice: 10 questions on any of 13 skills, marked as you go.
- Ratio calculator with steps: simplify, check equivalent ratios, solve a proportion or share an amount.
- Unit rate calculator: find a rate for 1 and compare two deals to find the best buy.
- Worksheets: ratios worksheet · unit rates (PDF) · proportional relationships (PDF) · make a ratio test
Back to ratios for kids · percentages · fractions · 6th grade math · 7th grade math
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Questions parents ask
How do I use the ratio calculator?
Choose what you want to do: simplify a ratio, check two ratios, solve a proportion or share an amount. Type the numbers and the answer appears with every step.
How do you simplify a ratio?
Divide every part by the greatest common factor. For 12 : 18 the greatest common factor is 6, so 12 : 18 = 2 : 3. Clear any decimals first by multiplying by 10 or 100.
How do you know if two ratios are equivalent?
Simplify both and compare the simplest forms. You can also cross-multiply: for 2 : 3 and 6 : 9, 2 × 9 = 18 and 3 × 6 = 18.
How do you solve a proportion?
Find the scale factor between the complete parts and use it on the other part. Or cross-multiply: in 3 : 4 = 15 : x, 3 × x = 4 × 15 = 60, so x = 20.
How do you share an amount in a ratio?
Add the parts, divide the amount by that total to find one part, then multiply. Sharing 35 in the ratio 2 : 5 gives 7 parts of 5, so 10 and 25.
Is it OK for my child to use a ratio calculator?
Yes, for checking. Ask your child to work the problem on paper first, then compare each step with the calculator’s.