Question

Your friend factors the expression. Is your friend correct? Explain your reasoning.

$$\begin{gathered} \frac{2}{3}y-\frac{14}{3}=\frac{2}{3}.y-\frac{2}{3}.7 \\ =\frac{2}{3}(y-7) \end{gathered}$$

Answer 1

We have expression $\frac{2}{3}y-\frac{14}{3}$

This expression has two terms

$$\begin{gathered} \frac{2}{3}y=\frac{1}{3}\times 2\times y \\ \frac{14}{3}=2\times 7\times \frac{1}{3} \end{gathered}$$

Using the distributive property to factor out the common term $\frac{2}{3}$

$$\begin{gathered} \frac{2}{3}y-\frac{14}{3}=\left(\frac{1}{3}\times 2\times y-2\times 7\times \frac{1}{3}\right)\{Rewritetheexpression\} \\ =\frac{2}{3}(y-7)\{Distributionproperty\} \end{gathered}$$

Yes friend factor the expression correctly.

Final Answer: Yes friend is correct.