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150 multiple-choice questions and 85 flashcards, organised into 5 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 6: Ratios and Proportional Relationships (6.RP.A.1, 6.RP.A.2, 6.RP.A.3a-d). Public standards from corestandards.org.
CoStudy's 6th Math: Ratios & Proportional Relationships bank holds 235 items organised into 5 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.
A 20% tip on a $35 meal is:
Answer: B — $7
B) 0.20 · 35 = 7. A/C/D) Each is incorrect.
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.
Which is NOT a way to write a ratio of 5 to 8?
Answer: D — 5 − 8
D) Ratio is NOT subtraction. A), B), C) are the three standard forms.
The ratio 18:24 in simplest form is:
Answer: C — 3:4
GCF(18,24) = 6; 18÷6:24÷6 = 3:4. (A), (B) are still reducible; (D) is incorrect arithmetic.
A $24 shirt has 7% sales tax. The total cost is:
Answer: C — $25.68
C) Tax = $24 × 0.07 = $1.68; total = 24 + 1.68 = $25.68. A) Only the tax. B) Added 7 cents (wrong place value). D) Added $7.
Ratio 3:5 of boys to girls. Total 16 students. Boys =
Answer: B — 6
B) Total parts 8; 3/8 × 16 = 6. A/C/D) Each is incorrect.
Tip 20% on $25 bill:
Answer: B — $5
B) 0.20·25. A/C/D) Each is incorrect.
"Best buy" — compare $4 for 8 oz vs $5 for 16 oz:
Answer: B — 16 oz is cheaper per oz
B) $0.50 vs $0.3125 per oz. A/C/D) Each is incorrect.
A jacket originally costs $80. It is on sale for 25% off. What is the sale price?
Answer: A — $60
Discount = 25% × 80 = $20. Sale price = 80 − 20 = $60. (B) is the discount, not the sale price; (C), (D) misapply.
A 6% sales tax on $50 item adds:
Answer: A — $3
A) 0.06 · 50 = 3. B/C/D) Each is incorrect.
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.
If the ratio of cats to dogs is 4:3 and there are 12 cats, how many dogs are there?
Answer: A — 9
A) Scale by 3: 12 cats means 4 → 12 (× 3), so dogs = 3 · 3 = 9. B) Added 4 to the cat count. C) Used the sum 4 + 3. D) Reused the cat count.
6 sample cards from the 85 in the bank.
At 60 mph, how far in 3 hours?
180 miles. (60 × 3.)
What percent of 200 is 50?
25%.
If the ratio of A:B = 5:3 and total = 40, how many of each?
A = 25, B = 15. (5+3=8 parts; 40÷8=5; A=5×5=25, B=3×5=15.)
Going from $50 to $60: percent increase?
20%. (10/50 × 100 = 20.)
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 ✓
Word: A test has 50 questions. You got 40 right. What percent?
80%.
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 6th Math: Ratios & Proportional Relationships →
The 6th 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 5 chapters that follow the published exam blueprint: Understanding Ratios; Unit Rates and Rate Reasoning; Equivalent Ratios: Tables, Tape Diagrams, Double Number Lines; Percent as a Ratio per Hundred; Real-World Ratio Reasoning and Measurement Conversions. 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 6: Ratios and Proportional Relationships (6.RP.A.1, 6.RP.A.2, 6.RP.A.3a-d). 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.