Proportion Calculator

What is a Proportion?

A proportion is an equation stating that two ratios are equal, such as A/B = C/D. Solving proportions means finding an unknown value (X) that maintains the equality between both ratios, using a method called cross multiplication.

Proportions can involve direct or inverse relationships between quantities. Below, we explain each type with formulas and step-by-step examples:

How to Solve Proportions

To solve a proportion, use cross multiplication: given A/B = C/X, multiply diagonally (A · X = B · C) and then divide to isolate the unknown value. Proportions can be direct or inverse depending on how the quantities relate to each other.

Direct Proportion

A direct proportion means that as one quantity increases, the other increases proportionally, and vice versa. To solve for X, cross multiply the fractions and divide. The direct proportion formula is:

Example of Direct Proportion

If 5 apples cost 10 dollars, how much will 8 apples cost?

Inverse Proportion

An inverse proportion means that as one quantity increases, the other decreases proportionally. The unknown X is placed in the numerator on the opposite side. The inverse proportion formula is:

Example of Inverse Proportion

If 5 workers take 10 days to do a job, how long will 8 workers take?

Compound Proportions

Compound proportions involve more than two quantities and require solving multiple proportion equations in sequence. They can combine both direct and inverse proportional relationships between the variables.

Example of Compound Proportion

Statement

If 5 workers build 3 houses in 10 days, how many days will it take 8 workers to build 6 houses?

• Identify the quantities involved: workers, houses, and days.
• Set up the proportions so that one quantity is constant and the others vary proportionally.
• Solve each proportion equation using cross multiplication.

Solution

First, identify the proportional relationships:

• Workers and days: inversely proportional (more workers, fewer days).
• Houses and days: directly proportional (more houses, more days).

Step 1: Calculate the days for 8 workers to build 3 houses using inverse proportion:

Step 2: Since 8 workers take 6.25 days for 3 houses, use direct proportion to find the days for 6 houses:

Therefore, 8 workers will need 12.5 days to build 6 houses.