Question

enter the result of applying the distributive property in the equation \\(\frac{2}{5}(5w + 10) = 2\frac{7}{10}\\).

Explanation:

Step1: Recall Distributive Property

The distributive property is \( a(b + c)=ab + ac \). Here, \( a=\frac{2}{5} \), \( b = 5w \), and \( c=10 \).

Step2: Apply Distributive Property

Multiply \(\frac{2}{5}\) with \(5w\) and \(\frac{2}{5}\) with \(10\) separately.

• For \(\frac{2}{5}\times5w\): \(\frac{2}{5}\times5w = 2w\) (since \(\frac{2}{5}\times5 = 2\)).
• For \(\frac{2}{5}\times10\): \(\frac{2}{5}\times10=\frac{20}{5}=4\).

So the left - hand side of the equation \(\frac{2}{5}(5w + 10)\) becomes \(2w+4\) after applying the distributive property. The right - hand side remains \(2\frac{7}{10}\) (or \(\frac{27}{10}\)). So the equation is \(2w + 4=2\frac{7}{10}\).

Answer:

\(2w + 4=2\frac{7}{10}\)