Question

simplify, using the distributive property. enter the number that belongs in the green box \\(\frac{1}{4}(16v + 4w) = 4v + ?w\\)

Explanation:

Step1: Apply distributive property

The distributive property states that \(a(b + c)=ab+ac\). Here, \(a = \frac{1}{4}\), \(b = 16v\) and \(c = 4w\). So we distribute \(\frac{1}{4}\) to both terms inside the parentheses: \(\frac{1}{4}(16v)+\frac{1}{4}(4w)\).

Step2: Simplify each term

For the first term: \(\frac{1}{4}(16v)=\frac{16}{4}v = 4v\) (which matches the given \(4v\) in the equation). For the second term: \(\frac{1}{4}(4w)=\frac{4}{4}w=1w\). So the number in the green box should be \(1\).

Answer:

\(1\)