Cross Multiplication Solver - Find X in Proportions

Cross Multiplication Solver

This calculator helps you solve for an unknown variable (often 'x') in a proportion using the cross multiplication method. Just enter three known values and leave one blank or type 'x' for the unknown.

Numerator 1 (a)

Top left value (e.g., 2)

Denominator 1 (b)

Bottom left value (e.g., 3)

Numerator 2 (c)

Top right value (e.g., x or 6)

Denominator 2 (d)

Bottom right value (e.g., 9)

Please enter only one unknown variable (or leave one field blank).

How it works

This calculator helps you solve for an unknown variable (often 'x') in a proportion using the cross multiplication method. Just enter three known values and leave one blank or type 'x' for the unknown.

The Formula

A proportion is an equation stating that two ratios are equal. For a proportion like a/b = c/d, cross multiplication means that a × d = b × c. This allows you to solve for any single unknown variable.

Worked Example

Example: Solve for x in 2/3 = x/9
To solve 2/3 = x/9 using cross multiplication, you'd set up 2 × 9 = 3 × x. This simplifies to 18 = 3x. Dividing both sides by 3 gives x = 6. Our calculator will show you this result instantly.

Tips, Assumptions & Limitations

Enter 'x' or leave a field blank for the unknown variable.
Ensure denominators are not zero, as division by zero is undefined.
You can also use this tool to check if a given proportion is true by entering all four numbers.

FAQ

Cross multiplication is a method used to solve equations involving fractions or ratios. If you have a/b = c/d, you can multiply the numerator of one fraction by the denominator of the other (a × d = b × c) to eliminate the fractions and solve for an unknown.

Simply enter the three known numbers into their respective fields. For the unknown value, you can either leave the field blank or type 'x'. The calculator will then apply cross multiplication to find the value of 'x'.

Yes! If you enter all four numbers (no 'x' or blank fields), the calculator will tell you if the proportion is true or false based on the cross multiplication principle.

It's a fundamental technique for solving many types of algebraic equations, especially those involving ratios, rates, and similar figures. It simplifies complex fractional equations into simpler linear equations.