Factor common terms in numerator and denominator: Evaluate (.896 × .752 + .896 × .248) / (.7 × .034 + .7 × .966) by factoring and simplifying before dividing.
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
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A1.28
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B0.976
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C12.8
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D9.76
Answer
Correct Answer: 1.28
Explanation
Introduction / Context:Before multiplying decimals, look for common factors you can pull out. This problem is designed for factoring: both the numerator terms have a common 0.896 and the denominator terms have a common 0.7. Recognizing this pattern turns a messy quotient into a simple ratio.
Given Data / Assumptions:
- Numerator: 0.896 × 0.752 + 0.896 × 0.248.
- Denominator: 0.7 × 0.034 + 0.7 × 0.966.
Concept / Approach:Use distributive factoring a×x + a×y = a(x + y). In both numerator and denominator, the bracketed sums equal 1. This observation reduces the whole fraction to the ratio of the common factors 0.896 to 0.7, which is quick to compute.
Step-by-Step Solution:
Numerator: 0.896(0.752 + 0.248) = 0.896 × 1 = 0.896.Denominator: 0.7(0.034 + 0.966) = 0.7 × 1 = 0.7.Quotient = 0.896 / 0.7 = 1.28.Verification / Alternative check:
Multiply top and bottom by 1000 to clear decimals: 896 / 700 = 128 / 100 = 1.28.Why Other Options Are Wrong:
- 0.976: Comes from dividing 0.896 by 0.918 or other mis-summed bracket.
- 12.8 and 9.76: Lose track of decimal places (×10 or ×100 too much).
Common Pitfalls:
- Multiplying terms directly instead of factoring first.
- Mistallying 0.034 + 0.966 to something other than 1.
Final Answer:
1.28