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150 multiple-choice questions and 85 flashcards, organised into 4 chapters, written to the Common Core State Standards blueprint. Every question carries a full rationale.
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Common Core State Standards (CCSS) — Mathematics, Grade 7: Ratios and Proportional Relationships (7.RP.A.1-3). Public standards from corestandards.org.
CoStudy's 7th Math: Ratios & Proportional Relationships bank holds 235 items organised into 4 chapters that follow the published blueprint. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.
Each chapter follows a domain of the published exam outline. Practise one on its own:
A sample of 12 multiple-choice questions from the bank, with the full rationale shown.
Find the unit rate: 1/4 mile in 1/8 hour.
Answer: A — 2 mph
A) (1/4) ÷ (1/8) = (1/4)·8 = 2 mph. B) Reciprocated. C) Multiplied instead of dividing. D) Doubled the time, not divided.
A 20% discount on a $75 item saves:
Answer: C — $15
C) 0.20 · 75 = $15. A) Used 33%. B) Used remaining price minus 20. D) Used the 20% as $20.
In a proportional relationship, doubling x:
Answer: B — Doubles y
B) In y = kx, replacing x with 2x gives y = k(2x) = 2(kx). A) Wrong; y depends on x. C) Inverse relationship, not proportional. D) Quadratic relationship, not proportional.
Convert 60 mph to km/h (1 mi ≈ 1.6 km):
Answer: C — 96 km/h
C) 60·1.6. A/B/D) Each is incorrect.
A salesperson earns a 6% commission on $4,500 in sales. The commission is:
Answer: A — $270.00
A) 0.06 × $4,500 = $270. B) Decimal misplaced. C) Used 1/6, not 6%. D) Decimal misplaced upward.
If 4 books cost $20, the cost per book (constant of proportionality) is:
Answer: A — $5
A) $20 / 4 = $5. B) Used the count. C) Took the reciprocal. D) Used the total.
If 8 ounces of juice cost $1.60, the unit price per ounce is:
Answer: A — $0.20
A) $1.60 ÷ 8 = $0.20. B) Off by a factor of 4. C) Misplaced decimal. D) Total cost.
A 6-pack of soda costs $4.20. The cost of one can is:
Answer: A — $0.70
A) $4.20 ÷ 6 = $0.70. B) Decimal shifted. C) Used 5 cans. D) Used 4 cans.
A blueprint scale is 1/4 inch = 1 foot. A wall measuring 3 inches on the blueprint is how many feet long in reality?
Answer: C — 12 ft
C) 3 ÷ (1/4) = 3 × 4 = 12 feet. A) Multiplied 3 × 1/4. B) Used scale numerator. D) Doubled.
Map scale 1 inch = 50 miles. 2.5 inches represents:
Answer: B — 125 miles
B) 2.5 · 50. A/C/D) Each is incorrect.
Convert 2 km to meters:
Answer: C — 2,000
C) 1 km = 1000 m. A/B/D) Each is incorrect.
If 6 oranges cost $3, how much will 10 oranges cost (proportional pricing)?
Answer: B — $5
Unit price = $0.50/orange. 10 × $0.50 = $5. (A), (C), (D) miscalculate.
6 sample cards from the 85 in the bank.
In y = 0.75x, if y = 6, what's x?
8. (x = y/k = 6/0.75 = 8.)
Calculate 18% tip on a $35 dinner.
$6.30.
How do you calculate sales tax?
Tax = price × tax rate (as decimal). Total = price + tax.
A jacket marked up 20% over a $40 cost — final price?
$48.
What is the 'constant of proportionality' (k)?
The ratio between two proportional quantities. y/x = k. For y = 5x, k = 5.
5% of $20 is what?
$1.
These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.
Open 7th Math: Ratios & Proportional Relationships →
The 7th Math: Ratios & Proportional Relationships bank holds 235 items: 150 multiple-choice questions, 85 flashcards. 18 of them are on this page to read free, with no signup.
Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.
It is organised into 4 chapters that follow the published exam blueprint: Computing Unit Rates with Complex Fractions; Recognizing Proportional Relationships; Constant of Proportionality (Equations and Graphs); Percent Problems: Discount, Tax, Markup, Interest. The number of questions in each chapter is proportional to that domain's published weight, so working through the bank exposes you to roughly the mix the real exam uses.
Common Core State Standards (CCSS) — Mathematics, Grade 7: Ratios and Proportional Relationships (7.RP.A.1-3). Public standards from corestandards.org.
The samples on this page are free to read in full, rationales included, with no account. The complete 235-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.
Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.