Difficulty: Easy
Correct Answer: 1/8
Explanation:
Introduction:
This question checks your understanding of how to reduce a fraction to its simplest or lowest terms. Simplifying fractions is a fundamental skill in arithmetic and is used frequently in higher mathematics, data interpretation, and everyday calculations.
Given Data / Assumptions:
Concept / Approach:
To simplify a fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest positive integer that divides both numbers exactly. After dividing by the GCD, the resulting fraction is in lowest terms. The value of the fraction does not change, only its representation becomes simpler.
Step-by-Step Solution:
Step 1: Identify the fraction: 125/1000.Step 2: Find the greatest common divisor of 125 and 1000.Step 3: Recognize that 125 is a factor of 1000, because 125 * 8 = 1000.Step 4: Therefore, GCD(125, 1000) = 125.Step 5: Divide numerator and denominator by 125.Step 6: Numerator: 125 / 125 = 1.Step 7: Denominator: 1000 / 125 = 8.Step 8: The simplified fraction is 1/8.
Verification / Alternative check:
You can convert both 125/1000 and 1/8 to decimals. 125/1000 = 0.125. Also, 1/8 = 0.125. Since the decimal values are the same, the fractions are equivalent, confirming that 1/8 is the correct simplified form of 125/1000.
Why Other Options Are Wrong:
2/9, 3/8, and 4/7 all represent different decimal values (approximately 0.222..., 0.375, and 0.5714 respectively), none of which equal 0.125. They are included as plausible looking fractions but do not match the given value when simplified or converted to decimals.
Common Pitfalls:
One common mistake is to divide only by a small common factor instead of the greatest one, for example dividing 125/1000 by 5 or 25 and stopping too early. While repeated simplification works, using the greatest common divisor is faster and ensures the fraction is fully simplified in one step.
Final Answer:
The fraction 125/1000 in simplest form is 1/8.
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