Question

write the expanded form of the expression.
$(y + 5x)\frac{1}{2}$

$(y + 5x)\frac{1}{2} = \square$
(simplify your answer. 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 \(c = 5x\). So we distribute \(\frac{1}{2}\) to both terms inside the parentheses.
\((y + 5x)\frac{1}{2}=\frac{1}{2}\times y+\frac{1}{2}\times5x\)

Step2: Simplify Each Term

Simplify \(\frac{1}{2}\times y\) to \(\frac{1}{2}y\) and \(\frac{1}{2}\times5x\) to \(\frac{5}{2}x\).
So the expanded form is \(\frac{1}{2}y+\frac{5}{2}x\) (or we can also write it as \(\frac{5}{2}x+\frac{1}{2}y\) since addition is commutative).

Answer:

\(\frac{1}{2}y+\frac{5}{2}x\) (or \(\frac{5}{2}x+\frac{1}{2}y\))