Question

$\frac{6.5 \times 0.28 \times 0.5}{0.07 \times 0.13 \times 2.5} =$

• A. 45
• B. 40
• C. 42
• D. 44

Answer 1

Answer:

B. 40

Step-by-Step Calculation

• Step 1: Simplify decimals by removing the decimal point. Count the total decimal places in the numerator and the denominator.
  • Numerator: 6.5 (1), 0.28 (2), 0.5 (1) = Total 4 decimal places.
  • Denominator: 0.07 (2), 0.13 (2), 2.5 (1) = Total 5 decimal places.
• Step 2: Adjust for decimal equivalence. Since the numerator has 4 places and the denominator has 5, multiply the numerator by 10 to balance the decimal count: (65 × 28 × 5 × 10) / (7 × 13 × 25).
• Step 3: Simplify the expression.
  • Divide 65 by 13: 5.
  • Divide 28 by 7: 4.
  • Divide 50 (from 5 × 10) by 25: 2.
  • Multiply the results: 5 × 4 × 2 = 40.

Exam Tips

• Decimal Balancing: Always aim to make the number of decimal places in the numerator and denominator equal by multiplying with powers of 10. This avoids calculation errors involving commas.
• Fraction Cancellation: Look for common factors between the numerator and denominator immediately. For instance, notice that 65 is a multiple of 13 and 28 is a multiple of 7, which significantly simplifies the arithmetic before multiplying.
• Precision: In competitive exams, verifying the count of digits after the decimal point is the most common point of failure. Always double-check this before proceeding to division.