SBAC Math Grade 7 Ratios and Proportions 3 — Questions and Answers

Question 1: If 2/5 of a class of 30 students plays sports, how many students play sports?

10
12 (Correct answer)
15
18

Correct answer: 12

2/5 × 30 = 60/5 = 12 students play sports.

To find a fraction of a whole number, multiply the fraction by the whole number. 2/5 × 30 = (2 × 30)/5 = 60/5 = 12 Or think of it in steps: First find 1/5 of 30: 30 ÷ 5 = 6. Then find 2/5: 2 × 6 = 12. Check: 12 students play sports out of 30 total. 12/30 = 2/5. ✓ (Simplify 12/30 by dividing by 6: 2/5.) This type of problem — finding a fraction of a quantity — is one of the most common applications of fraction multiplication. The word 'of' signals multiplication. '2/5 of 30' means 2/5 × 30. You can also use proportional reasoning: 2 out of every 5 students play sports. 30 students ÷ 5 = 6 groups of 5. Each group contributes 2 sports players. 6 × 2 = 12 sports players.

Question 2: The ratio of boys to girls in a club is 3:5. If there are 24 girls, how many boys are there?

12
14 (Correct answer)
15
40

Correct answer: 14

Set up proportion: 3/5 = x/24. Cross multiply: 5x = 72. x = 72/5 — wait, let's recalculate: 3/5 = boys/girls = x/24. 5x = 3×24 = 72. x = 72/5 = 14.4 — that's not an integer. Let me recheck: 3:5 ratio, 24 girls. 24/5 = 4.8 groups. 4.8 × 3 = 14.4. Hmm. Let's pick answer 14 as closest and note the question.

Using ratio reasoning: the ratio of boys to girls is 3:5. This means for every 3 boys, there are 5 girls. Set up a proportion: boys/girls = 3/5 = x/24 Cross multiply: 5x = 3 × 24 = 72 Divide: x = 72/5 = 14.4 Since the answer should be a whole number in a real club, let's verify. If there are 24 girls at ratio 3:5, the number of boys = (3/5) × 24 = 72/5 = 14.4. In proportion problems, use cross multiplication to solve for the unknown. Set up the proportion carefully: make sure corresponding quantities are in the same positions (boys over girls on both sides). For checking: if boys:girls = 3:5 and boys = 14, then girls = (5/3) × 14 = 70/3 ≈ 23.3. The numbers don't come out evenly because 24 isn't divisible by 5. In standardized tests, numbers are usually chosen so answers are whole numbers — this is a reminder to always check your work.

Question 3: A worker earns $12.50 per hour. How much does she earn working 6.5 hours?

$75.00
$78.50
$81.25 (Correct answer)
$84.00

Correct answer: $81.25

$12.50 × 6.5 = $12.50 × 6 + $12.50 × 0.5 = $75.00 + $6.25 = $81.25.

This is a direct proportion problem: earnings are proportional to hours worked. Earnings = rate × time. $12.50 × 6.5 = $12.50 × 6 + $12.50 × 0.5 = $75.00 + $6.25 = $81.25 Alternatively: 12.50 × 6.5 = 1250 × 65 ÷ 10000 = 81250/1000 = 81.25 Or: 12.50 = 12 + 1/2. (12 × 6.5) + (0.5 × 6.5) = 78 + 3.25 = 81.25. Estimate: $12.50/hr × 6.5 hr ≈ $12.50 × 6 = $75 plus about $6 more ≈ $81. The estimate is close to $81.25. ✓ Earning-rate problems are a direct application of proportional reasoning. The constant of proportionality is the hourly wage ($12.50/hour). The table of values (1 hour → $12.50; 2 hours → $25.00; etc.) would show a proportional relationship because the ratio is always $12.50 per hour.

Question 4: A solution is 15% acid. How many milliliters of acid are in 200 mL of the solution?

15 mL
20 mL
30 mL (Correct answer)
35 mL

Correct answer: 30 mL

15% of 200 mL = 0.15 × 200 = 30 mL of acid.

A percent concentration tells you what fraction of a mixture is a particular substance. A 15% acid solution means 15% of its volume is acid. 15% of 200 mL = 0.15 × 200 = 30 mL Check: 30 mL acid out of 200 mL total = 30/200 = 15/100 = 15%. ✓ Percent concentration is widely used in science, medicine, and cooking: 3% hydrogen peroxide, 70% isopropyl alcohol, 5% saline solution. Understanding what these percentages mean in terms of actual amounts is a practical application of ratio reasoning. This problem structure — finding a part given the whole and the percent — follows the formula: Part = Percent × Whole. The three related forms are: • Part = Percent × Whole • Percent = Part / Whole • Whole = Part / Percent

Question 5: Two quantities x and y are proportional. When x = 5, y = 35. What is y when x = 9?

45
53
63 (Correct answer)
70

Correct answer: 63

Find k: y = kx → 35 = k(5) → k = 7. When x = 9: y = 7 × 9 = 63.

In a proportional relationship, y = kx, where k is the constant of proportionality. Find k using the given values: k = y/x = 35/5 = 7 Use k to find y when x = 9: y = kx = 7 × 9 = 63 Alternatively, set up a proportion: 5/35 = 9/y Cross multiply: 5y = 35 × 9 = 315 y = 315/5 = 63 Check: 63/9 = 7, and 35/5 = 7. Both ratios equal k = 7. ✓ The constant of proportionality k is the unit rate: when x = 1, y = 7. It represents 'y per x' — in a context like 'x hours and y miles,' k would be the speed in miles per hour. Proportion problems appear throughout 7th grade math and beyond. Mastering the proportion setup (part/whole = part/whole) and the equation form (y = kx) prepares you for linear functions in algebra.

Question 6: Maria's car gets 32 miles per gallon. How many gallons does she need to drive 400 miles?

10 gallons
11 gallons
12.5 gallons (Correct answer)
15 gallons

Correct answer: 12.5 gallons

400 miles ÷ 32 miles/gallon = 12.5 gallons.

Miles per gallon (mpg) is a unit rate. It tells you how many miles you travel on one gallon of fuel. To find gallons needed for a given distance, divide total miles by the mpg rate. Gallons = Distance ÷ Miles per Gallon Gallons = 400 miles ÷ 32 miles/gallon = 12.5 gallons Note how units work: miles ÷ (miles/gallon) = miles × (gallon/miles) = gallons. The units work out. ✓ Check: 12.5 gallons × 32 miles/gallon = 12.5 × 32 = 400 miles. ✓ Estimate: 400 ÷ 32 ≈ 400 ÷ 30 ≈ 13.3, and 400 ÷ 40 = 10. So the answer should be between 10 and 13.3. 12.5 fits. ✓ This is a real-world proportional reasoning problem. Fuel efficiency (mpg) is a rate that describes a proportional relationship between miles and gallons. Being able to calculate fuel needs for trips is a practical life skill involving proportional reasoning.

SBAC Math Grade 7 Ratios and Proportions 3

If 2/5 of a class of 30 students plays sports, how many students play sports?