Question

alex rewrote the expression \\(\frac{1}{3}(12t - 5)\\) as \\(4t - 1\frac{2}{3}\\). which prop
choose the correct answer below.
\\(\bigcirc\\) distributive property
\\(\bigcirc\\) commutative property
\\(\bigcirc\\) associative property
\\(\bigcirc\\) multiplication property

Explanation:

Step1: Recall Distributive Property

The distributive property states that \( a(b + c)=ab+ac \) (or \( a(b - c)=ab - ac \)). Here, we have \( \frac{1}{3}(12t - 5) \).

Step2: Apply Distributive Property

Using the distributive property, we distribute \( \frac{1}{3} \) to both terms inside the parentheses: \( \frac{1}{3}\times12t-\frac{1}{3}\times5 \).

Step3: Calculate Each Term

Calculate \( \frac{1}{3}\times12t = 4t \) and \( \frac{1}{3}\times5=\frac{5}{3}=1\frac{2}{3} \). So, \( \frac{1}{3}(12t - 5)=4t - 1\frac{2}{3} \), which matches Alex's rewrite. The commutative property is about order (\( a + b=b + a \)), associative about grouping (\( (a + b)+c=a+(b + c) \)), and "multiplication property" is not a standard property here. So the correct property is distributive.

Answer:

A. Distributive Property