Ratios, rates & proportions · SAT Maths

Concept

A ratio like a : b compares two quantities. A proportion sets two ratios equal: a/b = c/d. Cross multiply to solve: a · d = b · c.

Direct proportion — y = kx. Both grow together; double x and y doubles.
Inverse proportion — xy = k. One shrinks as the other grows.

Unit conversion is just multiplying by 1 in disguise. Build conversion fractions whose value is 1 (e.g. 1000 m / 1 km), and chain them so the unwanted units cancel.

Worked example 1

A recipe uses 3 cups of flour for every 4 cups of sugar. How much sugar is needed for 12 cups of flour?

Solution

Proportion. 3 / 4 = 12 / x

Cross multiply. 3x = 48 ⇒ x = 16

16 cups of sugar.

Worked example 2

Convert 90 km/h to m/s.

Solution

Setup. Multiply by 1 in disguise so units cancel:

Chain. 90 km/h × (1000 m / 1 km) × (1 h / 3600 s)

Compute. = 90000 / 3600 = 25

25 m/s.

Practice test

8 questions on proportions, scaling, unit conversions, and direct vs inverse relationships.

Practice test · 8 questions Question 1 of 8 · Score 0