Which of the following expressions represents the statement "half the difference of a and b"?Question 34Answera.(1/2)a - bb.a - b/2c.1/2(a + b)d.(a - b)/2

Break Down the Problem

1. Identify the key components of the expression: "half", "the difference of a and b".
2. Understand what "difference" means in mathematical terms.

Relevant Concepts

1. The difference of $a$ and $b$ can be represented as $a - b$.
2. "Half" of any number means dividing that number by 2.

Analysis and Detail

1. Express the difference of $a$ and $b$: $a - b$
2. Take half of this difference: $\text{Half the difference} = \frac{1}{2}(a - b)$ This can also be written as: $\frac{(a - b)}{2}$

Verify and Summarize

• We have derived that "half the difference of $a$ and $b$" can be represented as $\frac{(a - b)}{2}$.
• Now, we can compare this with the given options:
  • a. $\frac{1}{2}a - b$
  • b. $\frac{a - b}{2}$ (matches our expression)
  • c. $\frac{1}{2}(a + b)$
  • d. $\frac{(a - b)}{2}$ (matches our expression)

Final Answer

The correct expressions that represent "half the difference of $a$ and $b$" are:

• b. $\frac{a - b}{2}$
• d. $\frac{(a - b)}{2}$