# Ratio calculator: how to simplify a ratio and solve a proportion, with worked examples

> A ratio compares two amounts, and a proportion says two ratios are equal. This guide shows how to reduce 12:18 to 2:3, find the missing number in A : B = C : D, scale a recipe, read a map scale and split money in a given ratio, with every sum written out.

Published 2026-11-07 by Toolcloak. 5 minute read. Original: https://toolcloak.com/articles/ratio-calculator-how-to-simplify-a-ratio-and-solve-a-proportion-with-examples
Related free tool: [Ratio Calculator](https://toolcloak.com/tools/ratio-calculator)

You have 12 g of spice for 18 ml of oil and you want to make a bigger batch with 50 g of spice. How much oil keeps the taste the same? That one question is a ratio problem, and the answer (75 ml) takes a single line of arithmetic.

> **In short**
> - To simplify a ratio, divide both numbers by their greatest common divisor: 12 : 18 becomes 2 : 3.
> - To solve A : B = C : D, use D = B × C ÷ A. With 12 : 18 = 50 : D, D is 75.
> - A ratio has no units of its own, but both sides must be measured in the same unit before you compare them.

## What a ratio is

A ratio compares two quantities by division. Writing 12 : 18 says that for every 12 of the first thing there are 18 of the second. You read it as “12 to 18”, and it can also be written as the fraction 12/18. Nothing in a ratio says how large the actual amounts are. 2 : 3 describes 2 spoons to 3 cups just as well as 200 kg to 300 kg.

Two ratios are **equivalent** when they describe the same relationship. 2 : 3, 4 : 6, 6 : 9 and 50 : 75 are all equivalent, because in each one the second number is 1.5 times the first.

## How to simplify a ratio

Simplifying means finding the smallest whole numbers that keep the same relationship. The method never changes:

1. Find the greatest common divisor (GCD) of the two numbers. For 12 and 18 it is 6.
2. Divide both numbers by it. 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
3. Write the result: 2 : 3. If the GCD is 1, the ratio is already in lowest terms.

| Ratio | GCD | Simplified | Check |
| --- | --- | --- | --- |
| 12 : 18 | 6 | 2 : 3 | 12 ÷ 6 = 2, 18 ÷ 6 = 3 |
| 45 : 60 | 15 | 3 : 4 | 45 ÷ 15 = 3, 60 ÷ 15 = 4 |
| 100 : 250 | 50 | 2 : 5 | 100 ÷ 50 = 2, 250 ÷ 50 = 5 |
| 7 : 13 | 1 | 7 : 13 | Already in lowest terms |

*The GCD of two numbers is the largest number that divides both exactly.*

Try it: [Ratio Calculator](https://toolcloak.com/tools/ratio-calculator). Type A and B and leave C empty. You get the simplified ratio plus A ÷ B and B ÷ A as decimals.

### Ratios with decimals

With decimals, first make both numbers whole by multiplying by the same power of ten, then simplify. 2.5 : 4 becomes 25 : 40 after multiplying by 10, and dividing by 5 gives **5 : 8**. Likewise 0.75 : 1.5 becomes 75 : 150, which simplifies to 1 : 2. The calculator does this step for you.

### Ratios with different units

Convert to one unit before you write the ratio. 50 cm to 2 m is not 50 : 2. Change 2 m to 200 cm and you get 50 : 200, which simplifies to **1 : 4**. Skipping this step is the most common reason a ratio answer comes out wrong.

## How to solve a proportion A : B = C : D

A proportion says two ratios are equal. If you know three of the four numbers, you can find the fourth. Because A ÷ B = C ÷ D, cross-multiplying gives A × D = B × C, and so:

> **D = B × C ÷ A:** With 12 : 18 = 50 : D, D = 18 × 50 ÷ 12 = 900 ÷ 12 = 75. The answer keeps the same relationship: 50 ÷ 75 is the same as 12 ÷ 18, which is 2 ÷ 3.

The calculator expects the first pair as A and B, then the third number as C. Enter 12, 18 and 50, and the result shows D = 75. You can sanity-check any answer by dividing: A ÷ B and C ÷ D should give the same value.

## Four everyday uses

### 1. Scaling a recipe

If 12 g of spice goes with 18 ml of oil, then for 50 g of spice you need 18 × 50 ÷ 12 = **75 ml** of oil. The same method works for any list of ingredients: pick one ingredient as your anchor, find the scaling factor (50 ÷ 12 ≈ 4.17), and apply it to the rest.

### 2. Reading a map scale

A map scale of 1 : 50,000 means 1 unit on the map is 50,000 of the same unit on the ground. So 3 cm on the map is 3 × 50,000 = 150,000 cm, which is 1,500 m or **1.5 km**. Work in centimetres first, then convert.

### 3. Splitting money in a ratio

To split ₹12,000 between two people in the ratio 3 : 2, add the parts (3 + 2 = 5), find one part (12,000 ÷ 5 = 2,400), and multiply: 3 × 2,400 = **₹7,200** and 2 × 2,400 = **₹4,800**. The two shares add back to ₹12,000, which is your check.

### 4. Mixing and dilution

A cleaning concentrate diluted 1 : 9 means 1 part concentrate to 9 parts water, which is 10 parts in total. For 2 litres of finished mix you need 2 ÷ 10 = 0.2 litres of concentrate and 1.8 litres of water. Always read whether a label means “1 to 9” (parts of water) or “1 in 10” (parts of the whole), as they are not the same.

## Turning a ratio into a fraction or a percentage

A ratio of 3 : 2 has 5 parts in total, so the first share is 3/5, which is 60 percent, and the second is 2/5, which is 40 percent. Note that a ratio of 3 : 2 compares the two parts to each other, while 3/5 compares one part to the whole. Mixing these two up is a classic exam mistake.

| Ratio | Total parts | First share | Second share |
| --- | --- | --- | --- |
| 1 : 1 | 2 | 50% | 50% |
| 3 : 2 | 5 | 60% | 40% |
| 1 : 3 | 4 | 25% | 75% |
| 7 : 3 | 10 | 70% | 30% |

*Percentage of the whole = part ÷ total parts × 100.*

## Common mistakes

- **Mixing units.** Compare metres with metres, rupees with rupees, minutes with minutes.
- **Reversing the order.** 2 : 3 and 3 : 2 are different ratios. The order must match the order of the things you are comparing.
- **Adding the same number to both sides.** Adding 5 to 2 : 3 gives 7 : 8, which is not equivalent. To keep a ratio, multiply or divide both sides by the same number.
- **Treating a part as the whole.** In a 3 : 2 split, the first person gets 3/5, not 3/2.

## Frequently asked questions

### How do I simplify a ratio?

Divide both numbers by their greatest common divisor. For 12 : 18 the GCD is 6, so the simplified ratio is 2 : 3.

### How do I find the missing number in a proportion?

For A : B = C : D, use D = B × C ÷ A. For 12 : 18 = 50 : D, D = 18 × 50 ÷ 12 = 75.

### Can I use decimals in a ratio?

Yes. Multiply both numbers by the same power of ten to make them whole, then simplify. 2.5 : 4 becomes 25 : 40 and then 5 : 8.

### What is the difference between a ratio and a fraction?

A ratio like 3 : 2 compares one part with another part. A fraction like 3/5 compares one part with the whole. A 3 : 2 split gives shares of 3/5 and 2/5.

### How do I split an amount in a given ratio?

Add the parts, divide the amount by the total to find one part, then multiply by each share. ₹12,000 in the ratio 3 : 2 gives ₹7,200 and ₹4,800.

### Does the order of a ratio matter?

Yes. 2 : 3 is not the same as 3 : 2. Keep the order the same as the quantities you are comparing.