Home › Certifications › 6th Math: The Number System
150 multiple-choice questions and 85 flashcards, organised into 6 chapters, written to the Common Core State Standards blueprint. Every question carries a full rationale.
Study 6th Math: The Number System in CoStudy →
Common Core State Standards (CCSS) — Mathematics, Grade 6: The Number System (6.NS.A.1, 6.NS.B.2-4, 6.NS.C.5-8). Public standards from corestandards.org.
CoStudy's 6th Math: The Number System bank holds 235 items organised into 6 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.
|−7| equals:
Answer: C — 7
C) Absolute value is distance from 0. A/B/D) Each is incorrect.
Compute 0.08 × 0.5.
Answer: D — 0.04
C) 8 × 5 = 40; three decimal places: 0.040 = 0.04. A/B) Off-by-one shift. C) Off-by-one too small.
LCM of 4 and 6:
Answer: B — 12
B) Smallest multiple of both. A/C/D) Each is incorrect.
What is the GCF of 12 and 18?
Answer: C — 6
Factors of 12: 1,2,3,4,6,12. Factors of 18: 1,2,3,6,9,18. GCF = 6. (A), (B), (D) miscalculate.
Convert 0.75 to fraction:
Answer: D — 3/4
D) 75/100 = 3/4. A/B/C) Each is incorrect.
Greatest Common Factor (GCF) of 12 and 18:
Answer: C — 6
C) Largest common factor. A/B/D) Each is incorrect.
What is the opposite of −8?
Answer: B — 8
The opposite of a number reflects across 0. (A), (C), (D) misread.
Point (−3, 4) is in which quadrant?
Answer: C — II
B) Negative x, positive y. A) +,+. B) −,−. D) +,−.
0.7 + 0.25 =
Answer: B — 0.95
B) Align decimals. A/C/D) Each is incorrect.
Reflection of (5, −2) across the x-axis is:
Answer: A — (5, 2)
A) Keep x, negate y. B) Reflection across y-axis. C) Reflection through origin. D) Swap.
A point at (−6, 0) is located:
Answer: B — On the x-axis, 6 units to the left of the origin
y = 0 means on the x-axis. (A), (C), (D) misread.
What is the distance between (−3, 4) and (5, 4)?
Answer: D — 8
Same y, distance = |5 − (−3)| = 8. (A), (C), (B) miscalculate.
6 sample cards from the 85 in the bank.
What is 2.5 × 4.2?
10.5.
What is 0.5 × 0.5?
0.25.
What is 4 ÷ 1/4?
16.
What does a negative number represent?
A value LESS than zero. Below zero on a number line, in the opposite direction of positive.
What's the opposite of 5?
−5.
Worked example: Find the LCM of 6 and 8.
Step 1: Prime-factor each number. 6 = 2 × 3 8 = 2 × 2 × 2 = 2³ Step 2: Take the HIGHEST power of every prime that appears: 2: max(1, 3) = 3 → 2³ = 8 3: max(1, 0) = 1 → 3 Step 3: Multiply: 8 × 3 = 24. Check: Multiples of 6 → 6, 12, 18, 24. Multiples of 8 → 8, 16, 24. ✓ Answer: LCM = 24.
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: The Number System →
The 6th Math: The Number System 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 6 chapters that follow the published exam blueprint: Dividing Fractions by Fractions; Multi-Digit Decimal and Whole-Number Operations; Greatest Common Factor and Least Common Multiple; Positive and Negative Numbers (Integers); Rational Numbers on the Number Line; The Coordinate Plane (Four Quadrants). 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: The Number System (6.NS.A.1, 6.NS.B.2-4, 6.NS.C.5-8). 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.