In Exercises 1–3, evaluate the expression. Justify each of your steps.

$8(-3)\left(5\right)$

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

Suppose a, b, and c is three real numbers.

Associative property of Multiplication

Property:$\text{(a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}b)\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c}=\text{a\hspace{0.17em}\hspace{0.17em}}·(\text{\hspace{0.17em}b\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}})$

If you are multiplying three real numbers, the product is always the same regardless of their grouping.

Example:$\text{(6\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}4)\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}3}=\text{6\hspace{0.17em}\hspace{0.17em}}·(\text{\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}3\hspace{0.17em}})=72$

Associative property of Multiplication states thatif you are multiplying three real numbers, the product is always the same regardless of their grouping.

Property:$\text{(a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}b)\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c}=\text{a\hspace{0.17em}\hspace{0.17em}}·(\text{\hspace{0.17em}b\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}})$

Example:$\text{(6\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}4)\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}3}=\text{6\hspace{0.17em}\hspace{0.17em}}·(\text{\hspace{0.17em}4\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}3\hspace{0.17em}})=72$

Associative Property of Multiplication:$\text{(a\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}b)\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c}=\text{a\hspace{0.17em}\hspace{0.17em}}·(\text{\hspace{0.17em}b\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}c\hspace{0.17em}})$

So, we can multiply the numbers in any ord

$\begin{array}{l}8(-3)5\\ (8·-3)5(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Multiplication)}\\ 8(-3·5)(\text{Associative\hspace{0.17em}\hspace{0.17em}Property\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}Multiplication)}\\ 8·-15=-120\end{array}$

$8(-3)5=-120$