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19 multiple-choice questions and 24 flashcards on Unit Rates and Rate Reasoning, about 13% of the 6th Math: Ratios & Proportional Relationships bank. Every one carries a written rationale.
Unit Rates and Rate Reasoning is one of 5 chapters in CoStudy's 6th Math: Ratios & Proportional Relationships bank, and it holds 19 of the bank's 150 multiple-choice questions — roughly 13% 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.
Brand X: 16 oz for $4.00. Brand Y: 20 oz for $4.50. Which has the lower unit price?
Answer: B — Brand Y
B) X = $0.25/oz, Y = $0.225/oz — Y is cheaper per ounce. A) Lower TOTAL price but not lower per ounce — common misconception. C) Not equal. D) Determinable from given data.
A car travels 240 miles in 4 hours. What is its unit rate in miles per hour?
Answer: C — 60
C) 240 ÷ 4 = 60 mph. A) Total miles, not the rate. B) Used a wrong divisor. D) The time, not the rate.
Mia walks 1.5 miles in 30 minutes. Her walking rate in miles per hour is:
Answer: B — 3 mph
B) 30 minutes is 0.5 hour; 1.5 ÷ 0.5 = 3 mph. A) Used 1.5 mi over 1 hour by mistake. C) Used minutes as hours. D) Inverse: hours per mile.
If 8 oranges cost $6, the unit price per orange is:
Answer: B — $0.75
6 ÷ 8 = $0.75 per orange. (A) is half; (C) inverts (oranges per dollar); (D) multiplies.
Maria runs 3 miles in 24 minutes. How many minutes does she take per mile?
Answer: B — 8 minutes
24 ÷ 3 = 8 minutes/mile. (A), (C), (D) misread.
If 5 apples cost $4.00, the unit price per apple is:
Answer: D — $0.80
D) $4.00 ÷ 5 = $0.80. A) Used apple count as dollars. B) Total cost, not per-apple. C) Used a wrong divisor.
Brand A: 12 oz for $3. Brand B: 8 oz for $2. Which is the better buy (cheaper per ounce)?
Answer: C — They are equal
A: 3/12 = $0.25/oz. B: 2/8 = $0.25/oz. Equal per-ounce price. (A), (B), (D) misread the unit rates.
If a worker earns $84 in 7 hours, what is the hourly wage?
Answer: A — $12
84 ÷ 7 = $12/hour. (B), (C) are arithmetic errors; (D) is subtraction.
A factory produces 240 widgets in 4 hours. The rate per hour is:
Answer: A — 60 widgets/hour
240 ÷ 4 = 60/hour. (B), (C), (D) misread.
3 pounds of grapes cost $9. What is the cost per pound?
Answer: A — $3
9 ÷ 3 = $3 per pound. (B), (C), (D) misapply the unit rate.
3 cards from the 24 in this chapter.
Speed = distance ÷ time. If distance = 150 mi and time = 3 hr, speed?
50 mph.
Compare: 12 oz for $2 vs. 18 oz for $3. Which has lower unit price?
They're equal! Both are $0.167/oz (or 6 oz/$1).
What is a 'unit rate'?
A rate where the second quantity is 1. Like 60 miles per HOUR (1), or $5 per POUND (1).
These are a sample. The full Unit Rates and Rate Reasoning chapter runs 43 items with per-chapter progress tracking, on the web and in the iOS app.
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