How do you solve a proportion?

Write it as two equal fractions, a/b = c/d, cross-multiply to get a × d = b × c and divide by the number that multiplies the unknown. For 2 : 3 = x : 9, 2 × 9 = 3 × x, so 18 = 3x and x = 6. The same steps find any of the four numbers; the blank can be the top or the bottom of either ratio.

What is cross-multiplication and why does it work?

It is multiplying both sides of a/b = c/d by b × d. The left side becomes a × d and the right side b × c, so a proportion is true exactly when the two diagonal products are equal. It is a shortcut for clearing both denominators at once, and it only works when neither b nor d is 0.

How do I check whether two ratios are proportional?

Fill all four boxes and the calculator tells you whether the proportion is true. It compares the cross products: 3 : 4 = 9 : 12 is true because 3 × 12 = 36 and 4 × 9 = 36, while 3 : 4 = 10 : 12 is false because 3 × 12 = 36 but 4 × 10 = 40.

Why can’t a denominator be zero?

The ratio a : 0 as a fraction a/0 would need a number that, multiplied by 0, gives a. No number does that unless a is 0, and then every number does, so a/0 has no single value and is undefined. The calculator flags a 0 in either bottom box instead of giving an answer, and it also refuses an answer that would make a denominator 0, such as x in 0 : x = 3 : 4.

What if the answer is not a whole number?

It stays exact. For 2 : 3 = x : 7 the answer is x = 14/3 (4.(6)): 2 × 7 = 14 and 14 ÷ 3 is a fraction that repeats as a decimal, shown with the repeating digits in parentheses. Nothing is rounded.

Can I use decimals, fractions or negative numbers?

Yes. Type 0.75, 3/4 or a mixed number like 2 3/8 in any box. The calculator reads each as an exact fraction first, so 0.75 : 1/2 = x : 6 gives x = 9. Negative numbers follow the usual sign rules, so −3 : 4 = x : 12 gives x = −9.

How do you simplify a ratio?

Divide every part by their greatest common divisor (GCD). The GCD of 6, 9 and 15 is 3, so 6 : 9 : 15 = 2 : 3 : 5. If a part is a decimal or a fraction, multiply all the parts by the same number first to make them whole: 1.5 : 2.5 becomes 3 : 5 after multiplying by 2, and 1/2 : 1/3 becomes 3 : 2 after multiplying by 6.

How do you split an amount in a ratio?

Add the ratio parts, divide the total by that sum to get the value of one part, then multiply each ratio part by it. To split 120 in the ratio 2 : 3 : 5, there are 10 parts, one part is 12, and the shares are 24, 36 and 60. A ratio like 4 : 6 is simplified first (to 2 : 3) and gives 40 and 60 for 100.

What if the shares are not whole numbers?

The calculator shows the exact shares and adds a note. Splitting 100 in the ratio 1 : 1 : 1 gives 100/3 (33.(3)) each, with the repeating digits in parentheses. If you are dividing things that cannot be cut, round the shares and adjust one so they still add up to the total.

How is this different from the aspect ratio calculator?

The aspect ratio calculator is about screens and images: it finds the ratio of a width and height (1920 × 1080 is 16:9), resizes to a ratio and works out a screen from its diagonal. This one is the general algebra: solve any a/b = c/d, simplify any ratio, or share any total, with the working shown.

Ratio & Proportion Calculator

To solve a proportion a/b = c/d for x, cross-multiply: a × d = b × c, then divide by the number next to x. For 3 : 4 = x : 12, 3 × 12 = 4 × x, so x = 9 (3 : 4 = 9 : 12). A blank that does not come out whole stays exact, so 2 : 3 = x : 7 gives x = 14/3 (4.(6)). To simplify a ratio, scale it to whole numbers and divide every part by the greatest common divisor: 6 : 9 : 15 = 2 : 3 : 5. To share a total in a ratio, add the parts and divide: 120 in the ratio 2 : 3 : 5 is 24, 36 and 60. Numbers can be whole, decimals or fractions like 3/4, and the calculator shows every step.

Updated 2026-10-03Runs in your browser: nothing you enter is uploadedHow this tool works

3 : 4 = 9 : 12

x = 9

x = 36 ÷ 4, from the cross products.

Value of x (box c): 9
Cross products: 36 = 36
Both ratios in lowest terms: 3 : 4
Scale factor, left to right: × 3

The working, step by step

Write the proportion, with x for the blank: 3 : 4 = x : 12.
Cross-multiply: the product of one diagonal equals the product of the other, a × d = b × c. Here 3 × 12 = 4 × x.
Multiply the two known numbers on one side: 3 × 12 = 36, so 36 = 4 × x.
Divide both sides by 4 to leave x alone: x = 36 ÷ 4 = 9.
Check: 3 : 4 = 9 : 12. The cross products are 3 × 12 = 36 and 4 × 9 = 36, equal, so the proportion holds.

Proportions solved for x

Each blank is found by cross-multiplication, worked out by the calculator above; type any of these to see the steps.
Proportion	Answer	Check (a × d = b × c)
3 : 4 = x : 12	x = 9	36 = 36
2 : 3 = x : 9	x = 6	18 = 18
5 : 8 = 15 : x	x = 24	120 = 120
x : 7 = 6 : 21	x = 2	42 = 42
4 : x = 10 : 25	x = 10	100 = 100
2 : 3 = x : 7	x = 14/3 (4.(6))	14 = 14
0.75 : 1/2 = x : 6	x = 9	9/2 = 9/2
−3 : 4 = x : 12	x = −9	−36 = −36

Common ratios in lowest terms

Decimals and fractions are first scaled to whole numbers, then every part is divided by the greatest common divisor.
Ratio	Lowest terms	Original to simplified
6 : 9	2 : 3	× 1/3
12 : 16	3 : 4	× 1/4
100 : 250	2 : 5	× 1/50
15 : 10	3 : 2	× 1/5
1.5 : 2.5	3 : 5	× 2
0.25 : 0.75	1 : 3	× 4
1/2 : 1/3	3 : 2	× 6
6 : 9 : 15	2 : 3 : 5	× 1/3
2 : 4 : 6	1 : 2 : 3	× 1/2
10 : 20 : 50	1 : 2 : 5	× 1/10

Sharing a total in a ratio

One part is the total divided by the sum of the ratio parts; each share is its ratio part times one part.
Total and ratio	Shares	One part
120 in 2 : 3 : 5	24, 36 and 60	12
50 in 1 : 1	25 and 25	25
250 in 3 : 2	150 and 100	50
60 in 1 : 2 : 3	10, 20 and 30	10
100 in 4 : 6	40 and 60	20
100 in 1 : 1 : 1	33.(3), 33.(3) and 33.(3)	100/3 = 33.(3)
7.5 in 5 : 3	4.6875 and 2.8125	15/16 = 0.9375

How to solve a proportion for x

Write the proportion. Set the two ratios equal as fractions, a/b = c/d, with x in the place you want to find: 3/4 = x/12.
Cross-multiply. Multiply along each diagonal and set the products equal, a × d = b × c: 3 × 12 = 4 × x, which is 36 = 4x.
Divide to isolate x. Divide both sides by the number multiplying x: x = 36 ÷ 4 = 9.
Check the answer. Put x back and compare the cross products: 3 : 4 = 9 : 12 gives 3 × 12 = 36 and 4 × 9 = 36, so it holds.
For a ratio of three parts, simplify or share it. Divide every part of 6 : 9 : 15 by their greatest common divisor, 3, to get 2 : 3 : 5. To share 120 in the ratio 2 : 3 : 5, add the parts (10), find one part (12) and multiply: 24, 36 and 60.

Frequently asked questions

How do you solve a proportion?: Write it as two equal fractions, a/b = c/d, cross-multiply to get a × d = b × c and divide by the number that multiplies the unknown. For 2 : 3 = x : 9, 2 × 9 = 3 × x, so 18 = 3x and x = 6. The same steps find any of the four numbers; the blank can be the top or the bottom of either ratio.
What is cross-multiplication and why does it work?: It is multiplying both sides of a/b = c/d by b × d. The left side becomes a × d and the right side b × c, so a proportion is true exactly when the two diagonal products are equal. It is a shortcut for clearing both denominators at once, and it only works when neither b nor d is 0.
How do I check whether two ratios are proportional?: Fill all four boxes and the calculator tells you whether the proportion is true. It compares the cross products: 3 : 4 = 9 : 12 is true because 3 × 12 = 36 and 4 × 9 = 36, while 3 : 4 = 10 : 12 is false because 3 × 12 = 36 but 4 × 10 = 40.
Why can’t a denominator be zero?: The ratio a : 0 as a fraction a/0 would need a number that, multiplied by 0, gives a. No number does that unless a is 0, and then every number does, so a/0 has no single value and is undefined. The calculator flags a 0 in either bottom box instead of giving an answer, and it also refuses an answer that would make a denominator 0, such as x in 0 : x = 3 : 4.
What if the answer is not a whole number?: It stays exact. For 2 : 3 = x : 7 the answer is x = 14/3 (4.(6)): 2 × 7 = 14 and 14 ÷ 3 is a fraction that repeats as a decimal, shown with the repeating digits in parentheses. Nothing is rounded.
Can I use decimals, fractions or negative numbers?: Yes. Type 0.75, 3/4 or a mixed number like 2 3/8 in any box. The calculator reads each as an exact fraction first, so 0.75 : 1/2 = x : 6 gives x = 9. Negative numbers follow the usual sign rules, so −3 : 4 = x : 12 gives x = −9.
How do you simplify a ratio?: Divide every part by their greatest common divisor (GCD). The GCD of 6, 9 and 15 is 3, so 6 : 9 : 15 = 2 : 3 : 5. If a part is a decimal or a fraction, multiply all the parts by the same number first to make them whole: 1.5 : 2.5 becomes 3 : 5 after multiplying by 2, and 1/2 : 1/3 becomes 3 : 2 after multiplying by 6.
How do you split an amount in a ratio?: Add the ratio parts, divide the total by that sum to get the value of one part, then multiply each ratio part by it. To split 120 in the ratio 2 : 3 : 5, there are 10 parts, one part is 12, and the shares are 24, 36 and 60. A ratio like 4 : 6 is simplified first (to 2 : 3) and gives 40 and 60 for 100.
What if the shares are not whole numbers?: The calculator shows the exact shares and adds a note. Splitting 100 in the ratio 1 : 1 : 1 gives 100/3 (33.(3)) each, with the repeating digits in parentheses. If you are dividing things that cannot be cut, round the shares and adjust one so they still add up to the total.
How is this different from the aspect ratio calculator?: The aspect ratio calculator is about screens and images: it finds the ratio of a width and height (1920 × 1080 is 16:9), resizes to a ratio and works out a screen from its diagonal. This one is the general algebra: solve any a/b = c/d, simplify any ratio, or share any total, with the working shown.

How it works

Every number you type is read as an exact fraction of two whole numbers (up to 30 digits each): decimals become digits over a power of 10, and mixed numbers and fractions are taken as written. To solve a proportion, the calculator uses the cross products a × d = b × c: the blank is multiplied by the number diagonally opposite it, so it equals the product of the other two numbers divided by that opposite number. If that opposite number is 0, the equation is either never true (0 = a non-zero number) or true for every value (0 = 0), and a result of 0 for a denominator is refused because a ratio with a denominator of 0 is undefined. With all four boxes filled it compares a × d and b × c. To simplify a ratio, every part is multiplied by the least common multiple of the denominators so that all parts are whole numbers, then divided by their greatest common divisor, found with Euclid’s algorithm (the GCD helper of the fraction calculator). To share a total, the parts are simplified, added, and the total divided by their sum gives one part; each share is its ratio part times one part, and the shares always add up to the total exactly. All arithmetic is done with whole-number fractions, so nothing is rounded, and a result that does not end as a decimal is shown with its repeating digits in parentheses. Everything runs in your browser and nothing you type is sent anywhere.

Sources

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