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Proportion Calculator

Enter three known numbers and one unknown (x) to calculate the proportional relationship between two ratios instantly.

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Proportion Calculator

Discover missing values in proportional relationships with our easy-to-use proportion calculator. This tool supports both cross-multiplication and the ratio formula to quickly solve your problems.

Understanding Proportions

Definition: A proportion occurs when two ratios are equal to each other.

It can be expressed using either the symbols :: or =. For instance:

a:b :: c:d or \(\frac{a}{b} = \frac{c}{d}\)

Additional Notes:

Variables are directly proportional if multiplying one variable by a constant gives the other.
Variables are inversely proportional if their product remains constant (x · y = constant).

Ratio Formula

The proportion can be written as:

a:b :: c:d ⇔ \(\frac{a}{b} = \frac{c}{d}\)

Steps to Solve Proportions

You can solve proportions using two main approaches:

Cross Multiplication Method
Ratio Formula Method

Example Problem

Find the unknown x in the proportion 5 : ? :: 10 : 8.

Solution Using Cross Multiplication:

Convert the proportion to a fraction: \(\frac{5}{x} = \frac{10}{8}\)
Multiply diagonally: \(10 \cdot x = 5 \cdot 8\)
Solve for x: \(10x = 40 \Rightarrow x = \frac{40}{10} = 4\)

Solution Using Ratio Formula:

Start with \(\frac{a}{b} = \frac{c}{d}\)
Substitute values: \(\frac{5}{x} = \frac{10}{8} = 1.25\)
Find x: \(x = \frac{5}{1.25} = 4\)

Both methods confirm that x = 4.

For faster results, use the Proportion Calculator to solve any proportion instantly.

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