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6th Math: The Number System practice questions and exam guide

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.

Last reviewed 2026-10-26 · CoStudy · how we write and review questions

  • 235 total items
  • 150 multiple choice
  • 85 flashcards
  • 6 chapters

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About the 6th Math: The Number System exam

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.

What the 6th Math: The Number System bank covers

Each chapter follows a domain of the published exam outline. Practise one on its own (chapter URLs are in the app and on this page for navigation; they are not sitemap targets):

Free 6th Math: The Number System practice questions

A sample of 12 multiple-choice questions from the bank, with the full rationale shown.

|−7| equals:

  1. −7
  2. 0
  3. 7
  4. 14

Answer: C — 7

C) Absolute value is distance from 0. A/B/D) Each is incorrect.

Compute 0.08 × 0.5.

  1. 0.40
  2. 0.4
  3. 0.004
  4. 0.04

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:

  1. 2
  2. 12
  3. 24
  4. 10

Answer: B — 12

B) Smallest multiple of both. A/C/D) Each is incorrect.

What is the GCF of 12 and 18?

  1. 2
  2. 3
  3. 6
  4. 36

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:

  1. 7/5
  2. 3/40
  3. 75/10
  4. 3/4

Answer: D — 3/4

D) 75/100 = 3/4. A/B/C) Each is incorrect.

Greatest Common Factor (GCF) of 12 and 18:

  1. 2
  2. 3
  3. 6
  4. 36

Answer: C — 6

C) Largest common factor. A/B/D) Each is incorrect.

What is the opposite of −8?

  1. −8
  2. 8
  3. 0
  4. 1/8

Answer: B — 8

The opposite of a number reflects across 0. (A), (C), (D) misread.

Point (−3, 4) is in which quadrant?

  1. I
  2. III
  3. II
  4. IV

Answer: C — II

B) Negative x, positive y. A) +,+. B) −,−. D) +,−.

0.7 + 0.25 =

  1. 0.32
  2. 0.95
  3. 0.92
  4. 0.75

Answer: B — 0.95

B) Align decimals. A/C/D) Each is incorrect.

Reflection of (5, −2) across the x-axis is:

  1. (5, 2)
  2. (−5, −2)
  3. (−5, 2)
  4. (−2, 5)

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:

  1. On the y-axis
  2. On the x-axis, 6 units to the left of the origin
  3. In Quadrant III
  4. At the origin

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)?

  1. 2
  2. 1
  3. 4
  4. 8

Answer: D — 8

Same y, distance = |5 − (−3)| = 8. (A), (C), (B) miscalculate.

6th Math: The Number System flashcards

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.

Practise the full 6th Math: The Number System bank

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 →

6th Math: The Number System — frequently asked

What is the 6th Math: The Number System exam?

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.

How is CoStudy’s 6th Math: The Number System bank organised?

It holds 235 items across 6 chapters: 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). Free samples on this page include the full rationale, with no account. Chapter counts in the bank are our mix; they are not a promise that the live exam uses the same item counts.

Does CoStudy replace the certifying body?

No. the certifying body owns the outline, the badge, and the sitting rules. This is independent practice with written rationales. We do not sell live items and we do not guarantee a pass.

Where do 6th Math: The Number System fees, cut scores, and pass rates live?

On the certifying body’s site. CoStudy will not invent a sitting fee or a pass rate. If a table on this page lacks a citation, treat it as unverified.

Are these real 6th Math: The Number System exam questions?

No. CoStudy does not have live items. The samples below are original practice written to the published outline, with rationales. Anyone selling “real exam dumps” is describing something you should not buy.

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