Direct and Inverse Proportion Calculator – ProMathTools

Direct & Inverse Proportion

This calculator helps you solve problems involving direct and inverse proportion. Just enter your known values, select the type of proportion, and we'll find the missing one, explaining the relationship between quantities.

Type of Proportion

Choose between direct or inverse proportion.

X₁

First value of X

Y₁

First value of Y

X₂

Second value of X

Y₂

Second value of Y

Please leave exactly one input field blank to solve.

How it works

This calculator helps you solve problems involving direct and inverse proportion. Just enter your known values, select the type of proportion, and we'll find the missing one, explaining the relationship between quantities.

The Formula

Direct Proportion: y = kx or y₁/x₁ = y₂/x₂
Inverse Proportion: y = k/x or x₁y₁ = x₂y₂

Worked Example

Real-World Examples
For direct proportion: If 3 apples cost $1.50, how much do 7 apples cost? (Enter x₁=3, y₁=1.50, x₂=7, leave y₂ blank, select 'Direct'). For inverse proportion: If 4 workers can paint a house in 6 days, how many days will 8 workers take? (Enter x₁=4, y₁=6, x₂=8, leave y₂ blank, select 'Inverse').

Tips, Assumptions & Limitations

Ensure you identify whether the relationship is direct or inverse before calculating.
Always double-check your input values to avoid errors.
Remember that for direct proportion, as one quantity increases, the other increases proportionally. For inverse, as one increases, the other decreases proportionally.

FAQ

Direct proportion describes a relationship where two quantities increase or decrease at the same rate. If one quantity doubles, the other quantity also doubles. The ratio between them remains constant (y/x = k).

Inverse proportion describes a relationship where if one quantity increases, the other quantity decreases proportionally. Their product remains constant (x * y = k). For example, more workers mean less time to complete a job.

Consider how the quantities relate. If they move in the same direction (both up or both down), it's direct. If they move in opposite directions (one up, one down), it's inverse. For instance, 'more hours worked, more pay earned' is direct, while 'more people sharing a pizza, less pizza per person' is inverse.

Yes, the calculator can process negative numbers. However, in many real-world proportion problems, quantities are positive. Ensure your problem context allows for negative values if you use them.