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47 multiple-choice questions and 14 flashcards on Operations with Rational Numbers in Real-World Problems, about 31% of the 7th Math: The Number System bank. Every one carries a written rationale.
Operations with Rational Numbers in Real-World Problems is one of 4 chapters in CoStudy's 7th Math: The Number System bank, and it holds 47 of the bank's 150 multiple-choice questions — roughly 31% 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.
The 'additive inverse' of a number:
Answer: D — Is the number with opposite sign — adding a number and its additive inverse gives 0 (e.g., 5 + (−5) = 0)
Additive inverse + original = 0. (A), (C), (B) misread.
A football team gains 8 yards on one play and loses 3 on the next. Net yards gained:
Answer: D — 5
8 + (−3) = 5. (A), (C), (B) miscalculate.
A bank account starts at $50. Owner withdraws $80. The balance:
Answer: D — −$30
50 − 80 = −30 (overdrawn). (A), (C), (B) misread.
What is (−4) × (−7)?
Answer: B — 28
Negative × negative = positive. (A), (C), (D) misread.
Word: Spend 1/3 of $42 on lunch. Lunch cost:
Answer: C — $14
C) 42/3 = 14. A) Off by 2. B) 1/6 instead. D) That's the remainder.
What is −3 − 5?
Answer: C — −8
−3 − 5 = −3 + (−5) = −8. (A), (B), (D) misread.
Word: A hiker descends 250 ft, then climbs 90 ft. Net elevation change:
Answer: D — −160 ft
D) −250 + 90 = −160 ft. A/B) Sign error. C) Added.
What is 3.2 − (−1.8) + (−2.0)?
Answer: A — 3.0
3.2 + 1.8 − 2.0 = 3.0. (B), (C), (D) miscalculate.
What is −5 + 8?
Answer: D — 3
−5 + 8 = 3 (positive movement larger). (A), (C), (B) misread signs.
Distance between −4 and 9 on the number line:
Answer: B — 13
B) |9 − (−4)| = 13. A) Subtracted magnitudes. C) Distance is non-negative. D) Endpoint only.
4 cards from the 14 in this chapter.
Word: Mt. Everest is 8,849 m above sea level. Mariana Trench is −10,994 m. Distance?
19,843 m. (8849 − (−10994) = 19,843.)
Word: You owe $50 (so balance −$50). You pay $30. New balance?
−$20.
Worked example: Distance between −3 and 7 on the number line
Step 1: Distance formula: |a − b|. Step 2: |−3 − 7| = |−10| = 10. Step 3: (Check: from −3 up to 0 is 3 units; 0 up to 7 is 7 units; 3 + 7 = 10.) Answer: 10 units.
Word: A diver at −20 ft descends 15 ft more. New depth?
−35 ft.
These are a sample. The full Operations with Rational Numbers in Real-World Problems chapter runs 61 items with per-chapter progress tracking, on the web and in the iOS app.
Open 7th Math: The Number System in CoStudy →