Use proportional relationships to set up and solve equations. | Ratios, rates, proportional relationships, and units | SAT Math

Core Idea

Set equal ratios side by side — $𝑎 𝑏 = 𝑐 𝑑$ — then cross-multiply: $𝑎 𝑑 = 𝑏 𝑐$ . Keep units consistent on each side.

Understanding

Set up matching quantities first. Cross-multiply only after both fractions describe the same units in the same order.

Write the proportion with like quantities aligned.
Cross-multiply.
Solve for the missing value.
If a unit rate is faster, find that first and scale up.

The setup is the part that protects you from unit mistakes.

Step by Step

Identify the known ratio and the unknown quantity.
Write two fractions with matching units: same type in each numerator, same type in each denominator.
Cross-multiply and solve for the unknown.
Check: does the answer make sense in context?

Misconceptions

Flipping one of the fractions so units don't align — the most common error.
Setting up an additive relationship instead of multiplicative (adding the difference rather than scaling).
Forgetting to check whether the relationship is actually proportional.

Question

Worked Example

A map uses a scale where 2 centimeters represents 35 kilometers. Two cities are 7.5 centimeters apart on the map. What is the actual distance, in kilometers, between the two cities?

Select an answer to see the explanation