How do you simplify a ratio?

Divide both numbers by their greatest common divisor. 24 : 36 — the GCD is 12 — becomes 2 : 3. If the numbers share no factor, as 16 and 9 do not, the ratio is already in simplest form. Enter both numbers and the page shows the GCD and the division.

How do you find the missing number in a proportion?

Cross-multiply and divide. For x/63 = 4/7 (OpenStax's example): 7x = 4 × 63 = 252, so x = 36. In a : b = c : x form, x = b × c ÷ a. Choose 'Solve a : b = c : x' and enter the three known values.

How do you divide an amount in a given ratio?

Add the parts of the ratio, divide the amount by that sum to get one part, then multiply. £500 in the ratio 3 : 2: 5 parts, one part is £100, so £300 and £200. The share mode does it and shows the percentages (60% and 40%).

What is a ratio of 1 : 10, or 5 : 3, as a percentage?

Each side as a share of the total: 1 : 10 is 1/11 and 10/11, about 9.1% and 90.9%; 5 : 3 is 5/8 and 3/8, 62.5% and 37.5%. As a single number, 5 : 3 is 1.6667, or 1 : 0.6. The page lists all these forms for any pair.

Ratio Calculator (Simplify, Solve a Proportion, Share in a Ratio)

Simplify a ratio, find the missing value in a : b = c : x, or split a total in a given ratio, working shown.

Inputs

Do what

01,000,000

0.011,000,000

c (for a : b = c : x)

01,000,000

Total to share (for the share mode)

01,000,000,000

Include CalculateEveryday mark

Ratio

16:9

First value16

Second value9

-43.75%

Simplified: 16:9
Working: the two numbers share no factor, so the ratio is already in simplest form
As a fraction / decimal: 16/9 = 1.7778
As 1 : n and n : 1: 1 : 0.5625 · 1.7778 : 1
As percentages of the whole: 64% and 36%

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What each Ratio input means

Do what: Simplify a ratio; solve a proportion a : b = c : x for the missing x; or share a total in the ratio a : b.
a: The first term of the ratio — in a recipe, the amount of the first ingredient; in a split, the first person's number of parts.
b: The second term, in the same order you will read the answer. 3 : 2 and 2 : 3 are different ratios.
c (for a : b = c : x): For a proportion only: the known term that matches a. In 3 : 4 = 15 : x, c is 15, and the page finds x, which matches b.
Total to share (for the share mode): For sharing only: the amount to split, such as money, a quantity of concrete mix or a number of hours.

Ratio formula

Simplify: a : b = (a ÷ GCD) : (b ÷ GCD) · Proportion a : b = c : x ⇒ x = b × c ÷ a · Share a total T in a : b: first part = T × a ÷ (a + b), second = T × b ÷ (a + b)

\frac{a}{b} = \frac{c}{x} \iff a x = b c \iff x = \frac{bc}{a}

A ratio compares two quantities by division, and it is unchanged when both are multiplied or divided by the same number — which is why 24 : 36 and 2 : 3 are the same ratio, and why dividing both sides by their greatest common divisor gives the simplest form. The same fact solves proportions: if a : b equals c : x then the cross products are equal, a × x = b × c, so x = b × c ÷ a. And it shares things out: to split a total in the ratio 3 : 2, there are 3 + 2 = 5 parts, so one part is the total divided by 5, and the shares are three and two of those. The page does all three, shows the ratio as a fraction, a decimal, 1 : n and n : 1, and gives each side as a percentage of the whole.

Ratio worked example

16 : 9, the widescreen ratio: 16 and 9 share no common factor, so it is already in simplest form. As a fraction it is 16/9 = 1.7778, as 1 : n it is 1 : 0.5625, and the two sides are 64% and 36% of the whole. Solving 16 : 9 = 32 : x by cross products gives x = 9 × 32 ÷ 16 = 18, which is why a 32-inch-wide 16 : 9 screen is 18 inches tall. Sharing 100 in the ratio 3 : 2 gives 5 parts of 20: 60 and 40.

More Ratio examples

A batter takes 3 cups of flour to 4 of milk; with 15 cups of flour, how much milk? 3 : 4 = 15 : x, so 3 × x = 4 × 15 = 60 and x = 20 cups.

Sharing 240 in the ratio 5 : 3: there are 8 parts of 30 each, so the shares are 150 and 90 — 62.5% and 37.5% of the whole.

Where the Ratio calculator can give the wrong answer

Ratios of decimals simplify by their greatest common divisor only after the page rounds them to integers, so 1.5 : 2.5 is best entered as 3 : 5 (multiply both by 2 first).
Order matters. 3 : 2 and 2 : 3 are different ratios, and in a proportion the corresponding parts have to be in the same positions: cups : people = cups : people, not cups : people = people : cups.
A ratio with three parts (2 : 3 : 5) is split the same way — 10 parts in total — but this page takes two; for three, share the total between the first part and the rest, then split the rest.
Ratios are not the same as differences. Going from 2 : 3 to 4 : 6 doubles both sides and changes nothing; adding 2 to both sides (4 : 5) changes the ratio.
The comparison bar under the simplify mode shows the second value as a percentage change from the first; it is a picture of the two numbers, not of the ratio's meaning.

Spotted a mistake? Tell us

Ratio FAQ

: Divide both numbers by their greatest common divisor. 24 : 36 — the GCD is 12 — becomes 2 : 3. If the numbers share no factor, as 16 and 9 do not, the ratio is already in simplest form. Enter both numbers and the page shows the GCD and the division.
: Cross-multiply and divide. For x/63 = 4/7 (OpenStax's example): 7x = 4 × 63 = 252, so x = 36. In a : b = c : x form, x = b × c ÷ a. Choose 'Solve a : b = c : x' and enter the three known values.
: Add the parts of the ratio, divide the amount by that sum to get one part, then multiply. £500 in the ratio 3 : 2: 5 parts, one part is £100, so £300 and £200. The share mode does it and shows the percentages (60% and 40%).
: Each side as a share of the total: 1 : 10 is 1/11 and 10/11, about 9.1% and 90.9%; 5 : 3 is 5/8 and 3/8, 62.5% and 37.5%. As a single number, 5 : 3 is 1.6667, or 1 : 0.6. The page lists all these forms for any pair.