Difficulty: Easy
Correct Answer: 73
Explanation:
Introduction:
This question combines decimal to fraction conversion with a small follow up calculation. Instead of asking directly for the simplified fraction, it asks for the sum of the numerator and denominator of that fraction, which is a common style in aptitude tests.
Given Data / Assumptions:
Concept / Approach:
To convert 0.46 to a fraction, note that there are two decimal places, so you can write 0.46 as 46/100. Then reduce the fraction by dividing numerator and denominator by their greatest common divisor. Once in lowest terms, simply sum the numerator and denominator.
Step-by-Step Solution:
Step 1: Write the decimal as a fraction: 0.46 = 46/100.Step 2: Find the greatest common divisor of 46 and 100.Step 3: Both 46 and 100 are divisible by 2: 46 = 2 * 23 and 100 = 2 * 50.Step 4: Divide numerator and denominator by 2: 46/100 = 23/50.Step 5: Check if 23 and 50 have any common factors greater than 1. They do not, since 23 is prime and does not divide 50.Step 6: So the simplest form is 23/50.Step 7: Compute the sum of numerator and denominator: 23 + 50 = 73.
Verification / Alternative check:
Convert 23/50 back to a decimal: 23 ÷ 50 = 0.46. This confirms that the simplified fraction is correct. The sum 73 therefore corresponds to the correct reduced fraction.
Why Other Options Are Wrong:
69, 96, 41, and 59 correspond to sums of other possible numerator and denominator pairs, but those fractions would not simplify to 0.46. Only 73 results from the correct fraction 23/50 that exactly equals 0.46.
Common Pitfalls:
A common mistake is to reduce 46/100 incorrectly, for example to 11.5/25 or to stop at 23/100. Others may attempt to simplify further by dividing numerator and denominator by 5 or 10 even when not possible. Carefully finding and applying the greatest common divisor avoids such errors.
Final Answer:
The sum of the numerator and denominator of the fraction representing 0.46 in simplest form is 73.
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