Multiply and divide fractions and mixed numbers and interpret the result in context.
Check fraction-division reasoning
Problem
A student writes \(3/4~\div~1/2~=~4/3~\times~1/2~=~2/3\). Classify the work and give the correct quotient.
Big Picture
What this problem is really about
We’ll check first which fraction the student inverted, because fraction division keeps the dividend and takes the reciprocal of only the divisor. Then we’ll rewrite the division correctly, multiply, simplify, and convert if needed. Multiplying the quotient by one half should return three fourths and confirm the correction.
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