Unit conversion by proportion drills

Convert between units (single or multi-step / dimensional) using proportional reasoning.

Free, timed SHSAT practice sets on unit conversion by proportion— every question includes a full worked explanation, and there's no account required.

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How to solve unit conversion problems

Write down the conversion fact, then ask: am I going to a bigger unit or a smaller unit?

You can also multiply by fractions so the units cancel: \(144 \text{ in} \times \dfrac{1 \text{ ft}}{12 \text{ in}} \times \dfrac{1 \text{ yd}}{3 \text{ ft}} = 4 \text{ yd}\).

Common traps: multiplying when you must divide (check that the answer size makes sense), and stopping after the first step of a two-step conversion.

Worked examples

Example 1.
How many gallons are in 32 quarts? (1 gallon = 4 quarts)
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Answer:
C

\(32 \div 4 = 8\) gallons. (Multiplying, \(32 \times 4\), gives 128. Not converting leaves 32. Subtracting, \(32 - 4\), gives 28.)

Example 2.
How many milliliters are in 6 liters? (1 liter = 1000 milliliters)
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Answer:
A

\(6 \times 1000 = 6000\) milliliters. (Dividing, \(6 \div 1000\), gives 0.006. Not converting leaves 6. Adding, \(6 + 1000\), gives 1006.)

Example 3.
Given that 1 pint = 2 cups and 1 gallon = 8 pints, how many gallons are in 16 cups?
Show answer and explanation
Answer:
D

Convert in two steps: \(16 \div 2 = 8\) pints, then \(8 \div 8 = 1\) gallon. (Stopping after the first step leaves 8 pints. Multiplying by 8 in the second step gives 64. Dividing 16 by 8 only once gives 2.)