Question

Which of the following expressions is equivalent to \(\frac{1}{5}(15w - 4)\) after applying the distributive property?

a) \(3w - \frac{4}{5}\)

b) \(3w - \frac{1}{5}\)

c) \(w - \frac{4}{5}\)

d) \(w - \frac{1}{5}\)

Answer 1

The equivalent expression to \(\frac{1}{5}(15w - 4)\) after applying the distributive property is \(3w - \frac{4}{5}\).

Step-by-step explanation:

To apply the distributive property to the expression \(\frac{1}{5}(15w - 4)\), we distribute the \(\frac{1}{5}\) across both terms inside the parentheses. Multiplying \(\frac{1}{5}\) by 15w gives us \(3w\), and multiplying \(\frac{1}{5}\) by -4 gives us \(-\frac{4}{5}\). As a result, the equivalent expression after applying the distributive property is \(3w - \frac{4}{5}\).