When the fraction 125 over 1000 is reduced to simplest form, what is the resulting fraction?

Introduction / Context:
This question tests your understanding of simplifying fractions to their lowest terms. Simplifying is important because it gives a standard, easiest to read form for a rational number, and many later calculations become more convenient when fractions are reduced first.

Given Data / Assumptions:

• Original fraction: 125/1000.
• We must find its simplest or lowest terms form.
• We assume standard fraction simplification using common factors.

Concept / Approach:
To simplify a fraction, we divide both numerator and denominator by their greatest common divisor. Here, 125 and 1000 are both multiples of 125. Dividing top and bottom by the same non zero number does not change the value of the fraction, it only changes its appearance to a simpler form. This is the central idea of fraction simplification.

Step-by-Step Solution:
Step 1: Start with the fraction 125/1000. Step 2: Find a common factor of 125 and 1000. Clearly 125 divides both numbers. Step 3: Divide the numerator by 125: 125 / 125 = 1. Step 4: Divide the denominator by 125: 1000 / 125 = 8. Step 5: The simplified fraction is 1/8. Step 6: Check whether 1 and 8 have any further common factor greater than 1. They do not, so 1/8 is in simplest form.

Verification / Alternative check:
We can verify with decimal equivalents. 125/1000 equals 0.125, because 125 over 1000 represents 125 thousandths. The fraction 1/8 also equals 0.125 as shown in an earlier question. Since 125/1000 and 1/8 have the same decimal value, they represent the same number, and 1/8 is clearly in lowest terms.

Why Other Options Are Wrong:
2/9 is approximately 0.222 and does not equal 0.125.
3/8 is 0.375, which is three times larger than 1/8.
4/7 is a non terminating decimal around 0.571 and definitely not equal to 125/1000.

Common Pitfalls:
A common error is to divide by a small factor like 5 or 25 and stop too early, leaving the fraction not fully simplified. Another mistake is to miscalculate the division of the denominator, leading to incorrect fractions. Always check whether the resulting numerator and denominator have any further common factor other than 1.

Final Answer:
The simplest form of 125 over 1000 is 1/8.