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Assertion (A): Dividing 6 by gives 12. Reason (R): Dividing by a fraction is the same as multiplying by its reciprocal. Which is correct?

Class 7Fractions and DecimalsFractions and Decimals
  • ABoth A and R are true, and R is the correct explanation of A
  • BBoth A and R are true, but R is not the correct explanation of A
  • CA is true but R is false
  • DA is false but R is true

Step-by-Step Solution

, so A is true. R is the rule used, so R correctly explains A.
Answer: A) Both A and R are true, and R is the correct explanation of A

Key idea: Dividing fractions: multiply by the reciprocal

Dividing by a fraction is the **same as multiplying by its reciprocal**. To divide, flip the second fraction (the divisor) and multiply.

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c).

Example: (2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6.

Why? Dividing by 1/4 is the same as asking 'how many quarters fit in this?' — which is the same as multiplying by 4. The reciprocal trick generalises that idea.

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