Question 9 of 29intermediate🔍 AnalyzeShort Answer2 marks

In which of the following multiplications is the product less than 1? Can you find the answer without actually doing the multiplications? (a) 7×0.67 \times 0.6 (b) 0.7×0.60.7 \times 0.6 (c) 0.7×60.7 \times 6 (d) 0.07×0.060.07 \times 0.06

Correct Answer

The product is less than 1 in cases (b) and (d).

Rule: When both numbers being multiplied are between 0 and 1, the product is less than both numbers and therefore less than 1. When one number is greater than 1 and one is between 0 and 1, the product is between the two numbers.

(a) 7×0.67 \times 0.6: One number is greater than 1 and one is between 0 and 1 Product is greater than the smaller number but could be greater than 1 ∴ Product greater than 1

(b) 0.7×0.60.7 \times 0.6: Both 0.7 and 0.6 are between 0 and 1 Product is less than both numbers and definitely less than 1 ∴ Product less than 1

(c) 0.7×60.7 \times 6: One number is greater than 1 and one is between 0 and 1 Product is greater than the smaller number but could be greater than 1 ∴ Product greater than 1

(d) 0.07×0.060.07 \times 0.06: Both 0.07 and 0.06 are between 0 and 1 Product is less than 1 ∴ Product less than 1

Exercise: Figure it Out (Section 1) | Q: 9 | (Page Page 7)
For More Understanding

Explanation

As explained in the chapter, when both numbers being multiplied are between 0 and 1, the product is less than both numbers and therefore less than 1. When one number is greater than 1 and one is between 0 and 1, the product is between the two numbers.

Solution Steps

  1. Apply the rule: when both numbers being multiplied are between 0 and 1, the product is less than both numbers and therefore less than 1.

  2. When one number is greater than 1 and one is between 0 and 1, the product is between the two numbers.

  3. For (a) 7×0.67 \times 0.6: one number (7) is greater than 1, one (0.6) is between 0 and 1, so product is greater than 1.

  4. For (b) 0.7×0.60.7 \times 0.6: both numbers are between 0 and 1, so product is less than 1.

  5. For (c) 0.7×60.7 \times 6: one number (6) is greater than 1, one (0.7) is between 0 and 1, so product is greater than 1.

  6. For (d) 0.07×0.060.07 \times 0.06: both numbers are between 0 and 1, so product is less than 1.

  7. Conclusion: Products less than 1 are in cases (b) and (d).

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