Sure! To understand which property allows you to compute [tex]\(\frac{1}{3} \times \left[6 \times \frac{4}{3}\right]\)[/tex] as [tex]\(\left[\frac{1}{3} \times 6\right] \times \frac{4}{3}\)[/tex], let's delve into the properties of multiplication.
When working with multiplication, several properties help us to rearrange and simplify expressions. One of these key properties is the Associative Property of Multiplication. This property states that the way in which numbers are grouped in a multiplication problem does not change the product. In mathematical terms, for any real numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex],
[tex]\[ (a \times b) \times c = a \times (b \times c). \][/tex]
Here’s how this applies to your specific example:
1. Start with the original expression:
[tex]\[
\frac{1}{3} \times \left(6 \times \frac{4}{3}\right)
\][/tex]
2. According to the Associative Property of Multiplication, we can change the grouping of the numbers being multiplied without changing the result. Specifically, we can regroup them as follows:
[tex]\[
\left(\frac{1}{3} \times 6\right) \times \frac{4}{3}
\][/tex]
So, by applying the Associative Property of Multiplication, we can see that:
[tex]\[
\frac{1}{3} \times \left(6 \times \frac{4}{3}\right) = \left(\frac{1}{3} \times 6\right) \times \frac{4}{3}.
\][/tex]
Therefore, the property that allows you to compute [tex]\(\frac{1}{3} \times \left[6 \times \frac{4}{3}\right]\)[/tex] as [tex]\(\left[\frac{1}{3} \times 6\right] \times \frac{4}{3}\)[/tex] is the Associative Property of Multiplication.
