To divide by a fraction, which method is correct?

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Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

To divide by a fraction, which method is correct?

Explanation:
Dividing by a fraction is done by multiplying by its reciprocal. This works because dividing by a fraction asks how many times that fraction fits into another value, and the reciprocal is the number that undoes multiplying by the original fraction. So for any fractions, (a/b) ÷ (c/d) equals (a/b) × (d/c) = (a d)/(b c). For example, 3 ÷ (2/5) becomes 3 × (5/2) = 15/2. Using this method keeps the operation exact and straightforward. If you tried to multiply the fractions as written, you’d be performing a different operation. Converting to decimals can approximate the result but may lose precision, and adding the fractions has nothing to do with division.

Dividing by a fraction is done by multiplying by its reciprocal. This works because dividing by a fraction asks how many times that fraction fits into another value, and the reciprocal is the number that undoes multiplying by the original fraction.

So for any fractions, (a/b) ÷ (c/d) equals (a/b) × (d/c) = (a d)/(b c). For example, 3 ÷ (2/5) becomes 3 × (5/2) = 15/2.

Using this method keeps the operation exact and straightforward. If you tried to multiply the fractions as written, you’d be performing a different operation. Converting to decimals can approximate the result but may lose precision, and adding the fractions has nothing to do with division.

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