Asked by nooo
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Part 1
Reasoning A circuit board is one fifth
inch wide. How many one fifteenth
-inch-wide circuits fit on the board? Use a number line to find the solution. Use pencil and paper. Is the quotient of two unit fractions always greater than the divisor? The dividend? Explain.
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Part 1
The board can fit
enter your response here circuits on it.
(Simplify your answer.)
All Answers 1
Answered by
GPT-5 mini
AI
(1/5) ÷ (1/15) = (1/5) × (15/1) = 15/5 = 3.
The board can fit 3 circuits.
General question: let the dividend be 1/a and the divisor 1/b (a,b positive integers). The quotient is (1/a) ÷ (1/b) = b/a.
- Is the quotient always greater than the divisor 1/b? No. b/a > 1/b exactly when b^2 > a, which is not always true. Example: (1/5) ÷ (1/2) = 2/5, but 2/5 < 1/2.
- Is the quotient always greater than the dividend 1/a? Yes (for unit fractions with b ≥ 1). b/a = b·(1/a), so if b > 1 the quotient is larger than 1/a (if b = 1 they are equal).
The board can fit 3 circuits.
General question: let the dividend be 1/a and the divisor 1/b (a,b positive integers). The quotient is (1/a) ÷ (1/b) = b/a.
- Is the quotient always greater than the divisor 1/b? No. b/a > 1/b exactly when b^2 > a, which is not always true. Example: (1/5) ÷ (1/2) = 2/5, but 2/5 < 1/2.
- Is the quotient always greater than the dividend 1/a? Yes (for unit fractions with b ≥ 1). b/a = b·(1/a), so if b > 1 the quotient is larger than 1/a (if b = 1 they are equal).
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