Ratios, rates, and proportional relationships — ACT practice questions

Ratios, rates, and proportional relationships on the ACT Mathematics test cover unit conversions, inverse variation, and equations that set two fractions equal. A student has to convert a rate from one pair of units to another, find a missing value when two quantities vary inversely, and solve a proportion for the ratio of two variables. Questions often appear as a short word problem or a compact equation. Common traps include mixing units, treating inverse variation as if it were direct, and canceling terms instead of cross-multiplying. Answer choices are typically five numbers or simplified ratios, with distractors that match those mistakes.

Section: Mathematics 45 questions on the paper
66 practice questions in the app

Sample questions

Question 1

The quantity $x$ varies inversely with $y$ . When $x=6$ , $y=8$ . What is $x$ when $y=12$ ?

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Answer: B — 4

For inverse variation, $xy$ is constant. Thus $6(8)=12x$ , so $x=4$ .

Question 2

A delivery drone flies at a constant speed of 54 kilometers per hour. What is the drone’s speed in meters per second?

(Note: 1 kilometer = $1{,}000$ meters)

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Answer: C — 15

Convert: $54\cdot\dfrac{1000}{3600}=54\cdot\dfrac{5}{18}=15$ meters per second.

Question 3

If $\dfrac{4x-y}{x+2y}=\dfrac{3}{5}$ , then $\dfrac{x}{y}={}$ ?

A $\dfrac{3}{5}$
B $\dfrac{11}{17}$
C $\dfrac{13}{17}$
D $\dfrac{17}{11}$

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Answer: B — $\dfrac{11}{17}$

Cross-multiplication gives $20x-5y=3x+6y$ , so $17x=11y$ and $x/y=11/17$ .

Practice 66 Ratios, rates, and proportional relationships questions in the app

Ratios, rates, and proportional relationships — ACT practice questions

Sample questions

More ACT topics

Mathematics