Question

write the expanded form of the expression.
$-\frac{1}{2}(y - x)$
$-\frac{1}{2}(y - x)=\square$
(use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Apply Distributive Property

The distributive property states that \( a(b - c)=ab - ac \). Here, \( a = -\frac{1}{2} \), \( b = y \), and \( c = x \). So we distribute \( -\frac{1}{2} \) to both \( y \) and \( -x \):
\( -\frac{1}{2}(y - x)=-\frac{1}{2}\times y+(-\frac{1}{2})\times(-x) \)

Step2: Simplify Each Term

Simplify \( -\frac{1}{2}\times y = -\frac{1}{2}y \) and \( (-\frac{1}{2})\times(-x)=\frac{1}{2}x \) (since multiplying two negative numbers gives a positive result). Combining these terms, we get:
\( -\frac{1}{2}y+\frac{1}{2}x \) or we can rearrange the terms as \( \frac{1}{2}x-\frac{1}{2}y \)

Answer:

\(\frac{1}{2}x - \frac{1}{2}y\) (or \(-\frac{1}{2}y+\frac{1}{2}x\))