Ratio simplifier — reduce ratios and split an amount

How to use the ratio simplifier

1. Type the ratio in Ratio, with the parts separated by colons, such as 16:24. Decimals (1.5:2.25) and fractions (1/2:1/3) are allowed.
2. To share an amount, enter it in Split a total in this ratio (optional). Leave it at 0 to skip this.
3. Read Simplified, and for two parts the As 1 : n, As n : 1 and As a fraction a/b lines.
4. Check the Share of the whole table for each part as a fraction and a percentage, and the Equivalent ratios list.

What it does and when to use it

A ratio compares amounts, such as 2 parts cordial to 3 parts water. Simplifying it means dividing every part by the same number until they share no common factor, just as you simplify a fraction. Students meet this in recipe, map and mixture problems; teachers and cooks use the split feature to share a quantity fairly.

If one value in a pair of ratios is missing, use the proportion solver instead. To simplify a single fraction or add fractions, use the fraction calculator. The GCD and LCM calculator shows the common factor step in more detail.

How it works

1. Each part is read as an exact fraction, so 1.5 becomes 3/2 and 2.25 becomes 9/4.
2. All parts are multiplied by the lowest common multiple (LCM) of their denominators, which makes them whole numbers.
3. All parts are divided by their greatest common divisor (GCD).
4. For a split, each part’s share is part ÷ sum of parts, multiplied by the total.

Step by step for 1.5 : 2.25:

1. As fractions: 3/2 : 9/4.
2. The LCM of the denominators 2 and 4 is 4. Multiply both parts by 4: 6 : 9.
3. GCD(6, 9) = 3. Divide both parts by 3: 2 : 3.
4. The parts add up to 5, so the first part is 2/5 = 40% of the whole and the second 3/5 = 60%.

Worked examples

Whole numbers. 16:24 gives Simplified: 2:3, which is 1:1.5, and the fraction 2/3.

Decimals. 1.5:2.25 also gives Simplified: 2:3, as worked above.

Sharing 500 three ways. 2:3:5 with a total of 500: the parts are 1/5, 3/10 and 1/2 of the whole, so the split is 100, 150 and Part 3 (5) | 250.

Fractions. 1/2 : 1/3 gives Simplified: 3:2, because multiplying both by 6 gives 3 and 2.

Limits and tips

• Keep the same units in every part before simplifying; 1 m : 50 cm is 100 : 50 = 2 : 1, not 1 : 50.
• Split amounts are exact. If they do not divide evenly, the decimal is shown in full or to 12 significant figures, so round money yourself.
• Everything is calculated in your browser.