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Assertion (A): is smaller than 0.5. Reason (R): Multiplying a number by a decimal less than 1 gives a result smaller than the number itself. Which option is correct?

Class 7Fractions and DecimalsFractions and Decimals
  • ABoth A and R are true, and R correctly explains A
  • BBoth A and R are true, but R does not explain A
  • CA is true, R is false
  • DA is false, R is true

Step-by-Step Solution

, and 0.25 < 0.5, so A is true. R states the general rule behind it — a factor below 1 shrinks the number — so R is true and is exactly the reason A holds. Students who believe multiplication always makes numbers bigger mark A false.
Answer: A) Both A and R are true, and R correctly explains A

Key idea: Multiplying decimals

Step 1: ignore the decimal points and multiply as whole numbers. Step 2: in the answer, place the decimal point so the **total decimal places equals the sum of the decimal places in the two factors**.

Example: . Whole-number multiply: . Total decimal places: 1 + 1 = 2. Place decimal: 0.24.

Example: . Decimal places: 2 + 1 = 3. Place: 0.375.

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