Quick Answer

In the proportion 3/4 = x/20, the missing value x is 15 (because 3 x 20 = 4 x 15 = 60).

Enter three values to solve for the missing one, or enter all four to check proportionality.

a

/

b

=

c

/

d

Common Examples

Input	Result
3/4 = x/20	x = 15
x/6 = 10/15	x = 4
5/8 = 25/x	x = 40
2/7 = x/21	x = 6
Check 6/9 = 8/12	Proportional (both simplify to 2/3)

How It Works

The Formula

A proportion states that two ratios are equal:

a / b = c / d

The fundamental property of proportions is cross-multiplication: multiplying the numerator of each fraction by the denominator of the other yields equal products.

a x d = b x c

This property allows solving for any one unknown value when the other three are known.

Solving for Each Variable

Starting from a x d = b x c:

• Solve for a: a = (b x c) / d
• Solve for b: b = (a x d) / c
• Solve for c: c = (a x d) / b
• Solve for d: d = (b x c) / a

Each formula is simply an algebraic rearrangement of the cross-multiplication equation.

Checking Proportionality

To verify whether two ratios form a valid proportion, compute both cross products. If a x d equals b x c, the ratios are proportional. For example, testing 6/9 = 8/12: cross products are 6 x 12 = 72 and 9 x 8 = 72. Since both equal 72, the proportion is valid.

Worked Example

To solve 3/4 = x/20: cross-multiply to get 3 x 20 = 4 x x. That gives 60 = 4x, so x = 60/4 = 15. The proportion is 3/4 = 15/20, and both fractions simplify to 0.75.

To solve x/6 = 10/15: cross-multiply to get x x 15 = 6 x 10. That gives 15x = 60, so x = 60/15 = 4. Verification: 4/6 = 0.6667 and 10/15 = 0.6667.

Related Calculators

Ratio Calculator

Simplify ratios, solve proportions, and scale ratios up or down.

Fraction Calculator

Add, subtract, multiply, and divide fractions. Simplify fractions and convert between fractions and decimals.

Frequently Asked Questions

What is the difference between a ratio and a proportion?

A ratio is a comparison of two quantities (like 3:4), while a proportion is an equation stating that two ratios are equal (like 3:4 = 6:8). A ratio is a single comparison; a proportion is a relationship between two ratios.

Why does cross-multiplication work?

Cross-multiplication works because if a/b = c/d, multiplying both sides by b*d gives a*d = b*c. This is a standard algebraic operation that eliminates the fractions. The resulting equation has no denominators, making it straightforward to solve for any unknown.

Can proportions include decimals?

Yes. Proportions work with any real numbers, including decimals and fractions. For example, 1.5/2 = 3/4 is a valid proportion because 1.5 x 4 = 6 = 2 x 3. The cross-multiplication method applies regardless of whether the values are whole numbers, decimals, or fractions.

What are proportions used for in real life?

Proportions are used in recipe scaling (doubling or halving ingredient amounts), map reading (converting between map distance and actual distance), unit conversion, similar triangles in geometry, mixing solutions to specific concentrations, and resizing images while maintaining aspect ratios.

What happens if the divisor is zero?

Division by zero is undefined in mathematics. If b or d is zero, the proportion a/b = c/d is not valid. Similarly, when solving for a missing value, if the denominator in the solving formula is zero, no solution exists. This calculator displays an error message in those cases.