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19 multiple-choice questions and 19 flashcards on Dividing Fractions by Fractions, about 13% of the 6th Math: The Number System bank. Every one carries a written rationale.
Dividing Fractions by Fractions is one of 6 chapters in CoStudy's 6th Math: The Number System bank, and it holds 19 of the bank's 150 multiple-choice questions — roughly 13% 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 5/6 ÷ 10.
Answer: A — 1/12
A) 5/6 × 1/10 = 5/60 = 1/12. B) Multiplied by 10 instead. C) Used 10 as numerator. D) Flipped the first fraction.
What is 3/4 ÷ 1/2?
Answer: B — 3/2
B) Multiply by the reciprocal: 3/4 × 2/1 = 6/4 = 3/2. A) Used multiplication only. C) Used a wrong operation. D) Dropped the denominator.
A ribbon is 9/10 m long. Pieces are 3/10 m each. How many pieces?
Answer: D — 3
B) 9/10 ÷ 3/10 = 9/10 × 10/3 = 90/30 = 3. A) Multiplied. C) Inverted the result. B) Shifted decimal one place.
3/8 ÷ 3/8 equals:
Answer: D — 1
C) Any non-zero value divided by itself is 1. A) Confused with subtraction. B) Multiplied. C) Added numerators.
The reciprocal of 3/7 is:
Answer: A — 7/3
Reciprocal flips numerator and denominator. (B) is the same number; (C), (D) misread.
What is 3/4 ÷ 1/2?
Answer: B — 1.5
3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1.5. (A) multiplies; (C), (D) miscalculate.
Compute 2 1/4 ÷ 3/8.
Answer: D — 6
B) 9/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6. A) Multiplied directly. C) Took reciprocal of answer. B) Multiplied numerators, ignored divisor.
What is 4/5 ÷ 2?
Answer: A — 2/5
4/5 ÷ 2 = 4/5 × 1/2 = 4/10 = 2/5. (B), (C), (D) misread.
Dividing by a fraction less than 1 results in:
Answer: C — A larger number — because dividing by a value < 1 is multiplying by a reciprocal > 1
e.g., 6 ÷ 1/2 = 12 > 6. (A), (B), (D) misread.
What is 5 ÷ 1/3?
Answer: B — 15
5 ÷ 1/3 = 5 × 3 = 15. (A) multiplies; (C), (D) miscalculate.
4 cards from the 19 in this chapter.
Find the GCF of 24 and 36.
12.
What is the LCM (Least Common Multiple)?
The smallest positive number that is a multiple of two or more numbers.
Find the LCM of 6 and 8.
24.
What is 3/4 ÷ 1/2?
3/2 = 1 1/2. (3/4 × 2/1 = 6/4 = 3/2.)
These are a sample. The full Dividing Fractions by Fractions chapter runs 38 items with per-chapter progress tracking, on the web and in the iOS app.
Open 6th Math: The Number System in CoStudy →