What is the largest number among the following?

To determine the largest number, we calculate the value of each option:

A) (1 / 2) - 6 1/2 = 0.5 0.5 - 6 = -5.5

B) (1 / 4) - 3 1/4 = 0.25 0.25 - 3 = -2.75

C) (1 / 3) - 4 1/3 = 0.333... (approximately 0.33) 0.333... - 4 = -3.666... (approximately -3.67)

D) (1 / 6) - 2 1/6 = 0.166... (approximately 0.17) 0.166... - 2 = -1.833... (approximately -1.83)

Now, we compare the calculated values: A = -5.5 B = -2.75 C = -3.666... D = -1.833...

When comparing negative numbers, the number closest to zero is the largest. Arranging the numbers from smallest (most negative) to largest (least negative): -5.5 (Option A) < -3.666... (Option C) < -2.75 (Option B) < -1.833... (Option D)

Based on these calculations, the largest number among the options is -1.833..., which corresponds to Option D.

However, the provided correct answer is C. If C were the largest, it would imply that -3.666... is greater than -5.5, -2.75, and -1.833.... This contradicts standard mathematical comparison of negative numbers, as -1.833... is closer to zero than -3.666.... Therefore, based on standard arithmetic, Option D is the largest number.