Proportion Calculator

Solve for missing values in A:B = C:D proportions. Use cross multiplication to find any unknown value in proportional relationships.

Proportion Solver (A:B = C:D)

:
=
:

Formula & Guide

Formula

×

Cross Multiplication

A × D = B × C

If A:B = C:D, then cross multiply

A

Solving for A

A = (B × C) / D

Find A when B, C, and D are known

B

Solving for B

B = (A × D) / C

Find B when A, C, and D are known

C

Solving for C

C = (A × D) / B

Find C when A, B, and D are known

D

Solving for D

D = (B × C) / A

Find D when A, B, and C are known

Formula Variables

A

First Value (First Ratio)

The first number in the first ratio

B

Second Value (First Ratio)

The second number in the first ratio

C

First Value (Second Ratio)

The first number in the second ratio

D

Second Value (Second Ratio)

The second number in the second ratio

Step-by-Step Scenario

Example Scenario

A

2

B

3

C

4

D (unknown)

x

1

Set Up the Proportion

  • 2:3 = 4:x

We need to find the value of x

2

Apply Cross Multiplication

  • 2 × x = 3 × 4
  • 2x = 12
3

Solve for x

  • x = 12 ÷ 2
x = 6

Additional Examples

Recipe Scaling

Original: 2 cups:3 people

New: x cups:12 people

Proportion

2:3 = x:12

Solution

x = (2 × 12) / 3 = 8 cups

Map Distance

Map: 1 inch:5 miles

Actual: 3 inches:x miles

Proportion

1:5 = 3:x

Solution

x = (5 × 3) / 1 = 15 miles

Characteristics of Proportions

Cross Multiplication

The fundamental method for solving proportions, based on the property that if A/B = C/D, then A × D = B × C.

Scaling Applications

Proportions are essential for scaling recipes, maps, models, and any situation where relationships must be maintained.

Real-World Use

Used extensively in cooking, construction, engineering, art, photography, and many practical applications.

Mathematical Foundation

Proportions are fundamental to similar triangles, scale factors, and many geometric and algebraic concepts.

Important Notes

  • You need exactly three known values to solve for the fourth unknown in a proportion.
  • Cross multiplication only works when the proportion is in the form A:B = C:D.
  • The order matters: 2:3 = 4:6 is true, but 2:3 = 6:4 is false.
  • Proportions can be written as fractions: A/B = C/D is equivalent to A:B = C:D.
  • Always check your answer by verifying that the cross products are equal: A × D should equal B × C.

Frequently Asked Questions

Find answers to common questions about proportion calculations.

To solve a proportion A:B = C:D, use cross multiplication: A × D = B × C. Then solve for the unknown variable. For example, if 2:3 = 4:x, then 2x = 12, so x = 6.

Cross multiplication is a method to solve proportions by multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa. If A/B = C/D, then A × D = B × C.

In a standard proportion A:B = C:D, you can solve for only one unknown at a time. You need to know three of the four values to find the fourth.

A ratio compares two quantities (A:B), while a proportion is an equation stating that two ratios are equal (A:B = C:D).

Proportions are used in scaling recipes, calculating map distances, determining similar shapes in geometry, mixing solutions in chemistry, and many other practical applications.

Yes, proportions can contain decimal numbers. The cross multiplication method works the same way with decimals as it does with whole numbers.