Difficulty: Medium
Correct Answer: 2
Explanation:
Introduction / Context:
This question involves decimal multiplication and division, and it can be simplified neatly using basic arithmetic and factorisation. It checks comfort with decimal operations and recognition that many decimals can be treated as simple fractions for easier calculation.
Given Data / Assumptions:
We must evaluate:
Concept / Approach:
Decimals can be converted into fractions in order to cancel common factors. For example, 5.6 = 56 / 10, 0.36 = 36 / 100, 0.42 = 42 / 100, 3.2 = 32 / 10, 0.8 = 8 / 10 and 2.1 = 21 / 10. Simplifying with fractions often reveals cancellations that make the computation quick and accurate.
Step-by-Step Solution:
First compute 5.6 × 0.36. As fractions this is (56 / 10) * (36 / 100) = (56 * 36) / 1000.
56 * 36 = 2016, so the product is 2016 / 1000 = 2.016.
Now compute 0.42 × 3.2. This is (42 / 100) * (32 / 10) = (42 * 32) / 1000.
42 * 32 = 1344, so the product is 1344 / 1000 = 1.344.
Add the two products: 2.016 + 1.344 = 3.36.
Now compute the denominator 0.8 × 2.1 = (8 / 10) * (21 / 10) = 168 / 100 = 1.68.
Therefore the required value is 3.36 ÷ 1.68.
Compute 3.36 ÷ 1.68 = 2.
Verification / Alternative check:
We can scale numerator and denominator by 100 to avoid decimals:
3.36 ÷ 1.68 = 336 ÷ 168.
Divide both by 168 to get 336 / 168 = 2.
This confirms the result.
Why Other Options Are Wrong:
1, 3, 3/2 and 5/2 would only be obtained if intermediate products or the final division were computed incorrectly.
For instance, miscalculating 5.6 × 0.36 as 2.016 and then adding a wrong value for 0.42 × 3.2 could lead to a wrong numerator and hence a wrong final result.
Common Pitfalls:
Errors often arise from mishandling decimal places or ignoring that 0.8 × 2.1 is not 1.6 but 1.68. Converting decimals to fractions and simplifying helps avoid such mistakes. Careful alignment of decimal places when multiplying and adding is also critical for accuracy.
Final Answer:
The value of the given expression is 2.
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