ACT proportional reasoning strategies
ACT Math tests proportional reasoning through ratios, proportions, scale factors, and unit conversions. These questions appear in pre-algebra and elementary algebra items within the 60-question, 60-minute section. These strategies cover setting up a proportion correctly, cross-multiplying to solve, and the trap of matching the wrong quantities in the ratio.
The core principle
A proportion states that two ratios are equal. If 3 pens cost $6, then 5 pens cost $10, because gives . The key is matching the units on each side: both numerators are pens, both denominators are dollars. Cross-multiplication solves any proportion in one step. For , multiply diagonally: . This works because you are multiplying both sides by , which clears the denominators. For scale factor problems, the ratio of any two corresponding lengths is constant. If a map uses a scale where 1 inch represents 50 miles, then 3.5 inches represents miles.
The most common trap
Matching the wrong quantities in the proportion
You set up the proportion with pens in the numerator on one side and dollars in the numerator on the other. The proportion \(\frac{3 \text{ pens}}{6 \text{ dollars}} = \frac{x \text{ dollars}}{5 \text{ pens}}\) mixes units across the equals sign. The correct setup keeps the same unit in the same position on both sides: \(\frac{3 \text{ pens}}{6 \text{ dollars}} = \frac{5 \text{ pens}}{x \text{ dollars}}\). The answer choices include the mismatched result because the test writers know this mistake. Label each quantity with its unit before you write the proportion.
Step-by-step strategy
When to use: any question that compares two ratios, uses a scale factor, or requires a unit conversion.
- 1Identify the two ratios being compared. Label each quantity with its unit.
- 2Write the proportion so the same unit occupies the same position on both sides. Both numerators should share a unit, and both denominators should share a unit.
- 3Cross-multiply to clear the fractions and solve for the unknown.
- 4Check that the answer has the correct unit. If the question asks for dollars and the answer has no unit label, verify the setup.
When not to use: when the relationship is not proportional, such as a fixed fee plus a per-unit rate. Use a linear equation instead.
Related pages
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