Ratio and Proportion

Direct Proportion

A relationship where two variables change at the exact same rate; as one value increases, the other increases proportionally.

Direct Proportion Formula

y = kx (where y and x are variables, and k is the constant of proportionality).

Direct Proportion Constant

The rule that a direct proportion always maintains a constant fraction: y / x = k.

Inverse Proportion

A relationship where an increase in one variable results in a proportional decrease in the other variable.

Inverse Proportion Constant

The rule that an inverse proportion always maintains a constant product: x * y = k.

Inverse Proportion Equation

The blueprint formula used to solve inverse changes between two states: x1 * y1 = x2 * y2.

Inverse Proportion Example

If x = 6 when y = 8, the constant product is 48; therefore, when y = 12, x must equal 4.

Compound Ratio

A method used to combine two separate ratios that share a common variable but are on different scales.

Compound Ratio Bridge Trick

The process of finding the least common multiple (LCM) for the shared variable to link two separate ratios together.

Compound Ratio Example

To combine A:B = 2:3 and B:C = 4:5, change B to its LCM (12) by scaling the rows, yielding a combined ratio of A:B:C = 8:12:15.