Write the following as an algebraic expression.
one half of the difference between $y$ and $4$

• A. $\frac{1}{2}y-4$
• B. $y-2$
• C. $\frac{1}{2}(y-4)$
• D. $\frac{1}{2}(y+4)$

Answer: (C)

Verified step by step guidance

1. Identify the phrase "one half of the difference between y and 4." The key parts are "one half" and "difference between y and 4."
2. Recall that "difference between y and 4" means subtracting 4 from y, which can be written as \(\left(y - 4\right)\).
3. Since the phrase says "one half of" this difference, you multiply the difference by \(\frac{1}{2}\).
4. Combine these parts to write the algebraic expression as \(\frac{1}{2} \times \left(y - 4\right)\).
5. Write the final expression neatly as \(\frac{1}{2}\left(y - 4\right)\), which correctly represents "one half of the difference between y and 4."