Find the value of the fraction 1/2 − 1/8.

Introduction / Context:
This question is a basic example of subtracting fractions with different denominators. Being able to find a common denominator, convert fractions and then subtract them correctly is an essential arithmetic skill that appears frequently in many exams and everyday calculations.

Given Data / Assumptions:

• Expression: 1/2 − 1/8.
• Both fractions are positive.
• We perform exact arithmetic and express the result in simplest form.

Concept / Approach:
To subtract 1/2 and 1/8, we need a common denominator. The least common denominator of 2 and 8 is 8. We convert 1/2 into an equivalent fraction with denominator 8, then subtract 1/8. Finally, we simplify the result if possible.

Step-by-Step Solution:
Identify the least common denominator of 2 and 8, which is 8.Convert 1/2 to a fraction with denominator 8: 1/2 = 4/8.Now the expression becomes 4/8 − 1/8.Subtract the numerators while keeping the denominator the same: 4/8 − 1/8 = (4 − 1)/8 = 3/8.The fraction 3/8 is already in simplest form, since 3 and 8 have no common factor greater than 1.

Verification / Alternative check:
Convert the fractions to decimals for a quick check: 1/2 = 0.5 and 1/8 = 0.125.Compute 0.5 − 0.125 = 0.375.The decimal 0.375 is exactly equal to 3/8, confirming our fraction arithmetic.

Why Other Options Are Wrong:
1/2 is the original value of the first fraction and would result only if we incorrectly ignore the subtraction of 1/8.2/3 and 3/2 are both larger than 1/2 and cannot represent the difference of two positive fractions that are less than or equal to 1/2.

Common Pitfalls:
A frequent mistake is to subtract denominators as well as numerators, giving something like (1 − 1)/(2 − 8) = 0/(−6), which is not a valid method.Another pitfall is to choose an incorrect common denominator or to miscalculate the equivalent fraction for 1/2.

Final Answer:
The correct value of 1/2 − 1/8 is 3/8.