Question

In Exercises 23-28, use properties of a real number to write the expression without parentheses.

$\frac{4}{6}\left(-6y\right)$

Short answer

The expression can be written as$-8y$

Step-by-step solution

Step 1. Definition of the Associative property of multiplication.

The associative property of multiplication is the property in which when the three real numbers are multiplied, it doesn’t affect the result of which two numbers we multiply first.

$a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c$

Step 2. Concept of the property.

Either multiply $4/3$ by$\left(-6y\right)$ or$\left(-6y\right)$ by $4/3$, in both cases the result obtained will be the same.

Step 3. Name of the property used.

Using the associative property of multiplication, the given expression can be written as

$\begin{array}{c}\frac{4}{3}\left(-6y\right)=\frac{4}{3}\cdot \left(-6\cdot y\right)\\ =\left(\frac{4}{3}\cdot -6\right)\cdot y\\ =-8\cdot y\\ =-8y\end{array}$