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21 multiple-choice questions and 30 flashcards on Multiplying and Dividing Rational Numbers, about 14% of the 7th Math: The Number System bank. Every one carries a written rationale.
Multiplying and Dividing Rational Numbers is one of 4 chapters in CoStudy's 7th Math: The Number System bank, and it holds 21 of the bank's 150 multiple-choice questions — roughly 14% 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.
Compute: (−1)(−2)(−3)(−4)
Answer: B — 24
B) Even-count negatives → positive 24. A) Sign. C/D) Added.
Compute: (−72) ÷ (−8)
Answer: C — 9
C) Neg ÷ neg = pos; 72/8 = 9. A) Sign error. B/D) Subtracted.
Compute: (−2)⁴
Answer: A — 16
A) Even power of neg → pos. B) Sign. C/D) Used 2·4.
Compute: (−1.5) × 4
Answer: D — −6
D) Different signs; 1.5·4 = 6 → −6. A) Sign. B/C) Subtracted.
(−24) ÷ (−6) =
Answer: B — 4
B) Negative ÷ negative = positive; 24 ÷ 6 = 4. A) Sign error. C/D) Subtracted instead.
Compute: −1/2 × −1/3
Answer: B — 1/6
B) Neg × neg = pos; 1/6. A) Sign. C/D) Added.
Compute: (−2/3) ÷ (−4/9)
Answer: B — 3/2
B) (−2/3)·(−9/4) = 18/12 = 3/2. A) Sign error. C/D) Multiplied without inverting.
(−2) · (−3) · (−4) =
Answer: D — −24
D) Three negatives: net negative; magnitudes multiply to 24. A) Even-count of negatives. B) Added instead. C) Requires a zero factor.
Compute: −2 × −3
Answer: C — 6
C) Two negatives → positive 6. A) Forgot sign rule. B/D) Added instead.
The product of two negative numbers is:
Answer: C — Positive
C) Two negatives multiply to a positive. A) That is positive × negative. B) Only if a factor is 0. D) The operation is defined.
4 cards from the 30 in this chapter.
What is |3 − 10|?
|−7| = 7.
What is 0 ÷ (−7)?
0.
What's the distance between −7 and −2?
5.
What is −4.2 × 3?
−12.6.
These are a sample. The full Multiplying and Dividing Rational Numbers chapter runs 51 items with per-chapter progress tracking, on the web and in the iOS app.
Open 7th Math: The Number System in CoStudy →