Use the distributive property to help simplify the expression. $\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }$
A) $\frac { 5 \sqrt { 3 } } { 12 }$
B) $- \frac { 5 \sqrt { 7 } } { 12 }$
C) $\frac { 12 \sqrt { 3 } } { 5 }$
D) $- \frac { 5 \sqrt { 3 } } { 12 }$

Question

Quizplus · Accepted Answer

Using the distributive property, we get:
\begin{align*}
\frac{1}{3}\sqrt{3}-\frac{1}{4}\sqrt{27} &= \frac{1}{3}\sqrt{3}-\frac{1}{4}\sqrt{3}\sqrt{9} \
&= \frac{1}{3}\sqrt{3}-\frac{1}{4}\sqrt{3}\sqrt{3^2} \
&= \frac{1}{3}\sqrt{3}-\frac{1}{4}\cdot3\sqrt{3} \
&= \frac{1}{3}\sqrt{3}-\frac{3}{4}\sqrt{3} \
&= -\frac{5}{12}\sqrt{3}
\end{align*}
Therefore, the answer is D.

Use the Distributive Property to Help Simplify the Expression 133−1427\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }31​3​−41​27​

Use the Distributive Property to Help Simplify the Expression $\frac { 1 } { 3 } \sqrt { 3 } - \frac { 1 } { 4 } \sqrt { 27 }$