ACT Math Quiz: Ratios And Proportions

What this quiz covers

This quiz focuses on Ratios And Proportions, giving you a quick way to practice the rules, question types, and explanations that matter most for ACT Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. 27 (correct answer)
2. 24
3. 21
4. 30

Explanation: With a red to blue marbles ratio of 3:4 and 36 blue marbles, we set up the proportion 3/4 = x/36 where x is the number of red marbles. Cross-multiplying gives us 4x = 3 × 36, so 4x = 108. Dividing both sides by 4, we get x = 27 red marbles. We can verify: 27:36 simplifies to 3:4 when divided by 9. A common mistake would be reversing the ratio or incorrectly setting up the proportion.

Question 2

1. 12
2. 24 (correct answer)
3. 48
4. 75

Explanation: This is a ratios and unit conversion question requiring a two-step process. Choice B (24) is correct — first convert quarts to ounces: 5 quarts × 32 oz/quart = 160 oz of water. Then set up the proportion: 3 salt/20 water = x salt/160 water → x = (3 × 160)/20 = 480/20 = 24 oz of salt. Choice A (12) skips the unit conversion: 3/20 = x/5 → x = 0.75... or uses only half of 160: 3/20 × 80 = 12. Choice C (48) doubles the correct answer — perhaps computing 3/10 = x/160 (using 10 instead of 20). Choice D (75) treats 5 quarts as 5 × 5 = 25 units of something: 3/20 × 25 × ... or 5 × 15 = 75. Pro tip: Any problem mixing units requires conversion before setting up proportions. Convert 5 quarts to 160 ounces first, THEN apply the ratio. The ratio is salt:water = 3:20, so for every 20 oz of water, use 3 oz of salt — scale that relationship up to 160 oz.

Question 3

1. $15:9$
2. $21:9$
3. $28:12$
4. $14:6$ (correct answer)

Explanation: To find an equivalent ratio to $7:3$, multiply both terms by the same number. Checking: $14:6 = (7 \times 2):(3 \times 2) = 7:3$ ✓. The other options don't maintain the same proportional relationship when simplified. Students might add instead of multiply or use different multipliers for each term.

Question 4

1. 20
2. 40
3. 60 (correct answer)
4. 80

Explanation: This is a ratios and linear equations question testing parts-to-whole ratio reasoning. Choice C (60) is correct — let the three integers be x, 2x, and 3x. Their sum: x + 2x + 3x = 6x = 120 → x = 20. The largest is 3x = 3 × 20 = 60. Choice A (20) is x, the smallest part — the student finds x but doesn't multiply by 3. Choice B (40) is 2x, the middle part. Choice D (80) likely comes from treating the ratio as 1:2:4 instead of 1:2:3, giving parts of 1+2+4=7 parts, 120/7 ≈ 17... or computing 4x = 80, using the wrong multiplier. Pro tip: When given a ratio a:b:c, let the parts be ax, bx, cx. Sum all parts to find x, then multiply to get each specific value. The ratio 1:2:3 means the three numbers together use 6 "shares" of 120, so each share = 20.

Question 5

1. 20
2. 24 (correct answer)
3. 25
4. 40

Explanation: The ratio of cats to dogs is 4:5, and there are 30 dogs. Set up the proportion: 4/5 = x/30, where x is the number of cats. Cross-multiply: 5x = 120, so x = 24 cats. A common mistake is using the ratio backwards (5:4) which would incorrectly give 37.5 cats.

Question 6

1. $2:3$ (correct answer)
2. $3:2$
3. $12:15$
4. $18:21$

Explanation: To find an equivalent ratio to 6:9, we need to simplify by finding the greatest common factor. The GCF of 6 and 9 is 3. Dividing both parts by 3: 6÷3 : 9÷3 = 2:3. We can verify: 2×3 = 6 and 3×3 = 9, confirming the equivalence. Option C (12:15) is also equivalent but not in simplest form.

Question 7

1. 2 meters
2. 1 meter
3. 0.5 meters (correct answer)
4. 5 meters

Explanation: The scale 1:200 means the model is 1/200 the size of the actual ship. If the ship is 100 meters long, the model length is 100 ÷ 200 = 0.5 meters. Students might confuse scale direction or make division errors.

Question 8

1. 1:4
2. 5:1
3. 1:3
4. 1:5 (correct answer)

Explanation: The scale factor from model to object compares their sizes: model length/object length = 3/15 = 1/5, written as 1:5. This means the model is 1/5 the size of the actual object. Students might reverse the ratio or confuse the direction of comparison.

Question 9

1. 8
2. 9 (correct answer)
3. 10
4. 11

Explanation: This proportion requires solving for x in the denominator. Set up the proportion: $11/x = 22/18$. Cross-multiply: $11 \times 18 = 22x$, so $198 = 22x$, and $x = 198 \div 22 = 9$. Cross-multiplication creates an equation that can be solved using basic algebra. A common error would be incorrectly setting up the cross-multiplication products.

Question 10

1. 5
2. 8 (correct answer)
3. 10
4. 50

Explanation: The ratio of oil to vinegar is 2:5, and the chef uses 20 tablespoons of vinegar. Set up the proportion: 2/5 = x/20, where x is tablespoons of oil. Cross-multiply: 5x = 40, so x = 8 tablespoons of oil. A common error is reversing the ratio setup, which would give 50 tablespoons.

Question 11

1. 42
2. 49 (correct answer)
3. 56
4. 70

Explanation: The ratio of students wearing sneakers to not wearing sneakers is 9:7, with 63 students wearing sneakers. Set up the proportion: 9/7 = 63/x, where x is students not wearing sneakers. Cross-multiply: 9x = 441, so x = 49 students not wearing sneakers. A common error is using 63 as the total instead of just those wearing sneakers.

Question 12

1. 8
2. 9 (correct answer)
3. 18
4. 36

Explanation: The scale is 1:18 (model:real), meaning the model is 1/18 the size of the real car. To find the model length, divide the real car length by 18: 162 inches ÷ 18 = 9 inches. A common mistake is multiplying by 18 instead of dividing, which would give 2,916 inches.

Question 13

1. 30
2. 52.5
3. 105 (correct answer)
4. 210

Explanation: This is a proportions and scale question testing ratio setup. Choice C (105) is correct — establish the unit rate: ½ inch = 15 miles, so 1 inch = 30 miles. Multiply: 3.5 × 30 = 105 miles. Alternatively, set up the proportion: (0.5/15) = (3.5/x) → x = (3.5 × 15) ÷ 0.5 = 105. Choice A (30) correctly finds that 1 inch = 30 miles but then stops there, reporting the unit rate instead of multiplying by 3.5. Choice B (52.5) multiplies 3.5 × 15 = 52.5, treating the scale as "1 inch = 15 miles" rather than "½ inch = 15 miles" — ignoring the half. Choice D (210) doubles the correct answer, possibly treating the scale as "1 inch = 15 miles" AND then doubling somehow, or setting up a flipped proportion. Pro tip: Always convert the scale to a "per 1 inch" rate before multiplying. If ½ inch = 15 miles, then 1 inch = 30 miles — you must account for that doubling before scaling up.

Question 14

1. 88
2. 1,320 (correct answer)
3. 5,280
4. 79,200

Explanation: This is a unit conversion question testing the chain method (dimensional analysis). Choice B (1,320) is correct — convert step by step: 15 miles/hour × 5,280 feet/mile × 1 hour/60 minutes = (15 × 5,280)/60 = 79,200/60 = 1,320 feet per minute. Choice A (88) is feet per second (1,320 ÷ 60 × 4 = 88), likely from an extra division by 60 or from confusing minutes with seconds. Choice C (5,280) gives feet per mile — the student converts the distance unit but forgets to account for the time unit, leaving the answer in "feet per hour ÷ 15." Choice D (79,200) correctly computes 15 × 5,280 = 79,200 but forgets to divide by 60, leaving the answer in feet per hour instead of feet per minute. Pro tip: Write out the conversion as a chain of fractions where unwanted units cancel. Start with 15 miles/1 hour, multiply by 5,280 ft/1 mile (miles cancel), then multiply by 1 hour/60 min (hours cancel), leaving ft/min.

Question 15

1. $\frac{18}{8}$ (correct answer)
2. $\frac{12}{27}$
3. $\frac{36}{20}$
4. $\frac{9}{16}$

Explanation: To find an equivalent ratio to 9:4, we need a fraction that equals $9/4$ when simplified. Check each option: $18/8$ = $9/4$ when simplified (dividing both by 2). The other options don't equal $9/4$: $12/27$ = $4/9$ (the inverse), $36/20$ = $9/5$, and $9/16$ is already in lowest terms. Equivalent ratios must maintain the same proportional value.

Question 16

1. 10
2. 12 (correct answer)
3. 15
4. 20

Explanation: This recipe ratio problem shows flour to sugar as 5:2, meaning for every 5 cups of flour, we need 2 cups of sugar. Set up the proportion: 5/2 = 30/x, where x is the sugar needed. Cross-multiply: 5x = 2 × 30 = 60, so x = 60 ÷ 5 = 12 cups of sugar. A common error would be setting up the ratio backward as 2:5 instead of 5:2.

Question 17

1. 1/3
2. 1/2
3. 3
4. 2 (correct answer)

Explanation: The scale factor is found by comparing corresponding sides of similar triangles. Taking any pair of corresponding sides: 6/3 = 2, 8/4 = 2, and 10/5 = 2. All ratios equal 2, confirming the triangles are similar with a scale factor of 2. This means each side of the larger triangle is 2 times the corresponding side of the smaller triangle. A common mistake would be taking the reciprocal, giving 1/2 instead of 2.

Question 18

1. 20 cups
2. 24 cups
3. 16 cups
4. 32 cups (correct answer)

Explanation: With a butter to sugar ratio of 1:4 and 8 cups of butter, we set up the proportion 1/4 = 8/x where x is cups of sugar needed. Cross-multiplying gives us 1 × x = 4 × 8, so x = 32 cups of sugar. We can verify: 8:32 simplifies to 1:4 when divided by 8. A common error would be reversing the ratio or confusing which quantity corresponds to which part of the ratio.

Question 19

1. 50 (correct answer)
2. 45
3. 40
4. 35

Explanation: The ratio of red to green balls is 2:5, and there are 20 red balls. Set up the proportion: 2/5 = 20/x, where x is the number of green balls. Cross-multiply: 2x = 100, so x = 50. Students might reverse the ratio or make calculation errors.

Question 20

1. $10:8$ (correct answer)
2. $5:6$
3. $8:5$
4. $4:5$

Explanation: To find an equivalent ratio to $5:4$, multiply both terms by the same number. Checking each option: $10:8 = (5 \times 2):(4 \times 2) = 5:4$ ✓. The other ratios don't maintain the same proportional relationship. Students might confuse equivalent ratios with ratios that have the same sum or difference.