Question

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

1. $8(-3)\left(5\right)$

Short answer

$8(-3)5 = -120$

Step-by-step solution

Step-1 – What are real numbers? 

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

Step-2 – Associative Property of Multiplication of Real Numbers: 

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

Associative property of Multiplication

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

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

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

Step-3 – Evaluate the expression – 4 (9) (– 5) and justify each of your steps.

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

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

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

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

So, we can multiply the numbers in any order.

$\begin{array}{l}8(-3)5\\ (8·-3)5(\text{AssociativePropertyofMultiplication)}\\ 8(-3·5)(\text{AssociativePropertyofMultiplication)}\\ 8·-15=-120\end{array}$

$8(-3)5 = -120$