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29 multiple-choice questions and 3 flashcards on Real-World Ratio Reasoning and Measurement Conversions, about 19% of the 6th Math: Ratios & Proportional Relationships bank. Every one carries a written rationale.
Real-World Ratio Reasoning and Measurement Conversions is one of 5 chapters in CoStudy's 6th Math: Ratios & Proportional Relationships bank, and it holds 29 of the bank's 150 multiple-choice questions — roughly 19% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
A car travels at 60 mph. How far does it travel in 2.5 hours?
Answer: B — 150 mi
B) d = r · t = 60 · 2.5 = 150 mi. A) Used 1 hour. C) Used 2 hours, ignoring the 0.5. D) Doubled the time instead of multiplying by 2.5.
A printer prints 12 pages per minute. How long to print 360 pages?
Answer: A — 30 minutes
360 ÷ 12 = 30 min. (B), (C), (D) misapply.
How many inches are in 5 feet? (1 foot = 12 inches)
Answer: C — 60
5 × 12 = 60 inches. (A) ignores the conversion; (B) adds; (D) overshoots.
A population of 200 people grows by 15%. The new population is:
Answer: B — 230
Increase = 15% × 200 = 30. New = 200 + 30 = 230. (A) is +15; (C) is +85; (D) subtracts.
A snail moves 30 cm per minute. How many meters does it move in 1 hour?
Answer: C — 18 m
30 cm/min × 60 min = 1800 cm = 18 m. (A), (B), (D) misapply.
In a survey, 36 of 60 students prefer pizza. What percent prefer pizza?
Answer: B — 60%
36 ÷ 60 = 0.60 = 60%. (A), (C), (D) are common errors.
How many minutes are in 3 hours?
Answer: D — 180
3 × 60 = 180 minutes. (A), (B), (C) misapply.
A map scale: 1 inch = 50 miles. The distance between two cities on the map is 3.5 inches. What is the actual distance?
Answer: C — 175 miles
3.5 × 50 = 175 miles. (A), (B), (D) misapply the scale.
A recipe needs 2 cups of broth per liter of water. How many cups for 4 liters of water?
Answer: C — 8 cups
C) Unit rate 2 cups/L × 4 L = 8 cups. A) Reused the unit rate. B) Reused the water amount. D) Added 2 + 4.
A class field trip needs 1 chaperone per 8 students. How many chaperones are needed for 56 students?
Answer: B — 7
56 ÷ 8 = 7 chaperones. (A), (C), (D) miscount.
3 cards from the 3 in this chapter.
Worked example: A 25-cm ribbon is cut in the ratio 2:3. Find the length of each piece.
Step 1: Find total parts. 2 + 3 = 5 parts. Step 2: Find the value of one part. 25 ÷ 5 = 5 cm per part. Step 3: Multiply each ratio term by 5. Short piece = 2 · 5 = 10 cm. Long piece = 3 · 5 = 15 cm. Answer: 10 cm and 15 cm. Check: 10 + 15 = 25 ✓ and 10:15 = 2:3 ✓
Worked example: A recipe calls for 3/4 cup of sugar. You want to double the recipe. How much sugar?
Step 1: Identify the operation. Doubling means multiplying by 2. Step 2: Multiply 3/4 by 2. 3/4 · 2 = 6/4. Step 3: Simplify the result. 6/4 = 3/2 = 1 1/2 cups. Answer: 1 1/2 cups of sugar. Check: half of 1 1/2 = 3/4 ✓
Worked example: Convert 60 mi/h to feet per second using ratio reasoning. (1 mi = 5,280 ft; 1 h = 3,600 s)
Step 1: Start with the given rate. 60 mi/h. Step 2: Multiply by the conversion factor (mi → ft). 60 mi/h × 5,280 ft/mi = 316,800 ft/h. Step 3: Multiply by the conversion factor (h → s). 316,800 ft/h × 1 h / 3,600 s = 316,800 ÷ 3,600 = 88 ft/s. Answer: 88 ft/s. Check: 88 · 3,600 ÷ 5,280 = 60 mph ✓
These are a sample. The full Real-World Ratio Reasoning and Measurement Conversions chapter runs 32 items with per-chapter progress tracking, on the web and in the iOS app.
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