Definition
Inverse proportion
A relationship where one quantity is divided by a factor when the other is multiplied by it.
What it means
Inverse-proportion partners trade size while keeping one product fixed. Make one quantity twice as large and the other becomes half as large; make one three times as large and the other becomes one third as large.
Remember it
One times the other stays fixed.
Example
A rectangle has area 24 cm². If its width is 3 cm, its length is 8 cm. Doubling the width to 6 cm halves the length to 4 cm, and 3 × 8 = 6 × 4 = 24.
Watch for
One quantity going up while the other goes down is not enough. Their product must remain constant.
Common mix-up
Direct proportion keeps a constant ratio and scales both quantities together; inverse proportion keeps a constant product and scales them oppositely.
Exact meaning
When x and y are nonzero, inverse proportion has the form y = k/x, so xy = k. Scaling x by a nonzero factor f requires scaling y by 1/f.