Mathematics CalcyZone Calculator

Proportion Calculator

Solve direct and inverse proportions to find missing variable values.

Calculation Solution

X = 15

Equation: 100 / 150 = 10 / X

Mathematical Formula

Direct Proportion: A / B = C / X => X = (B * C) / A

Overview & Explanation

A proportion states that two ratios are equal. This tool solves for an unknown fourth variable in proportional equations.

How It Works

Set up the equality equation A / B = C / X.
Multiply B by C and divide by A.

Practical Applications

Scale drawings.
Converting currency rates.
Unit conversion problems.

Solving a proportion

A proportion states that two ratios are equal, a/b = c/d. When one value is unknown, cross-multiply: a × d = b × c. For 3/4 = x/20, 4x = 60, so x = 15.

This is the 'unitary method' taught in school: if 3 kg of rice costs ₹180, 1 kg costs ₹60, so 5 kg costs ₹300. The proportion 3/180 = 5/x gives the same answer.

Direct and inverse proportion

In direct proportion, both quantities rise together at the same rate: double the ingredients, double the servings. In inverse proportion, one rises as the other falls, and their product is constant. If 6 workers finish a job in 10 days, the job takes 60 worker-days, so 4 workers would take 60 ÷ 4 = 15 days. Using direct proportion here would wrongly give fewer days.

Before solving, ask whether more of one means more or less of the other.

Practical uses

Scaling recipes, converting currencies at a fixed rate, map and model scales, dosing by weight, and estimating travel time at a constant speed are all proportions. Real situations are only approximately proportional: cooking times and bulk prices, for instance, do not scale perfectly, so treat the answer as a starting estimate.