How to Solve a Ratio with Cross Multiplication, Step by Step

Published 2026-10-01

Solving a ratio means finding the one missing value in a proportion like 2 : 7 = x : 35. Cross multiplication is the fastest reliable way to do it, and it works the same every time. This guide walks through the method step by step, with fully worked examples you can verify by hand. If you want the answer instantly, the solver on our homepage does the same math as you type.

The one rule you need

A proportion is two ratios set equal: A : B = C : D. When two ratios are equal, their cross products are equal too. That means:

A times D = B times C

The name comes from the picture: if you write the proportion as two fractions, A/B = C/D, the products you need sit on the diagonals of an X. Multiply along one diagonal, multiply along the other, and the two results match whenever the proportion is true.

To find a missing value, you multiply the two known values on one diagonal, then divide by the remaining known value on the other. That is the whole method: one multiplication, one division.

Step by step method

Write the proportion as A : B = C : D and mark which value is missing.
Multiply the two known values that sit diagonally opposite each other.
Divide that product by the remaining known value.
Check the answer by confirming both ratios simplify to the same thing.

Worked example with whole numbers

Solve 2 : 7 = x : 35.

The missing value x sits in the C position.
Multiply the known diagonal: 2 times 35 = 70.
Divide by the remaining known value: 70 / 7 = 10.
So x = 10.

Check: 10 : 35 simplifies to 2 : 7 (divide both sides by 5), and 2/7 equals 10/35. The proportion holds, so the answer is right.

Worked example with decimals

Decimals change nothing about the method. Solve 1.5 : 4 = 6 : x.

The missing value x sits in the D position.
Multiply the known diagonal: 4 times 6 = 24.
Divide by the remaining known value: 24 / 1.5 = 16.
So x = 16.

Check: 1.5/16 = 0.09375 and 6/… wait, compare correctly: 1.5 : 4 means 1.5/4 = 0.375, and 6/16 = 0.375 as well. Both ratios are equal, so x = 16 is correct.

The same works in reverse. If 3.2 : x = 8 : 10, the known diagonal is 3.2 times 10 = 32, and 32 / 8 = 4, so x = 4. Check: 3.2/4 = 0.8 and 8/10 = 0.8.

Why the shortcut works

Cross multiplication is not a trick, it is just algebra done once so you never have to repeat it. Starting from A/B = C/D, multiplying both sides by B and then by D gives A times D = B times C. Every step is a legal move on an equation, so the result always holds. When you multiply the diagonal and divide by the remaining value, you are doing those algebra steps in compressed form.

Common mistakes to avoid

Mixing up positions. The proportion 2 : 7 = x : 35 pairs 2 with x (the first terms) and 7 with 35 (the second terms). If you accidentally pair 2 with 35 as a ratio, the whole setup is wrong before you compute anything. Keep the order consistent.

Dividing the wrong way. After multiplying the diagonal, you divide by the number that is diagonally opposite the missing value, not the one next to it. In 2 : 7 = x : 35, you divide by 7, not by 2.

Dividing by zero. If the value you need to divide by is zero, the proportion has no solution in that arrangement. Our solver says so in plain words instead of showing an error.

Skipping the check. Simplify both sides and confirm they match. It takes ten seconds and catches position mix ups every time.

Practice problems

3 : 5 = x : 40. Diagonal: 3 times 40 = 120. Then 120 / 5 = 24. Answer: x = 24.
9 : 12 = 15 : x. Diagonal: 12 times 15 = 180. Then 180 / 9 = 20. Answer: x = 20.
0.5 : 2 = 3 : x. Diagonal: 2 times 3 = 6. Then 6 / 0.5 = 12. Answer: x = 12.

Check each one by simplifying both ratios. They all reduce cleanly.

Tools that do it for you

The ratio solver on our homepage solves any of the four positions as you type, decimals included. To see a solved proportion as a single number, try the ratio to fraction converter, and for screen and image ratios the aspect ratio calculator handles the reduction automatically.