Chapter 1.4, Problem 58STP

To determine

To simplify the expression $10\cdot \left(x\cdot 3\right)$ .

Answer to Problem 58STP

  $30x$

Explanation of Solution

Given information:

The expression: $10\cdot \left(x\cdot 3\right)$ .

Concept Used:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Associative Property of multiplication: $\left(a\cdot b\right)\cdot c=a\cdot \left(b\cdot c\right)$

Calculation:

In order to simplify the expression $10\cdot \left(x\cdot 3\right)$ , use the associative property of multiplication and then multiply the like terms to simplify further as shown below,

  $\begin{array}{c}10\cdot \left(x\cdot 3\right)=10\cdot \left(3\cdot x\right)\text{Commutative property}\\ =\left(10\cdot 3\right)\cdot x\text{Associative property}\\ =\left(30\right)\cdot x\\ =30x\end{array}$

Thus, the given expression simplifies to $30x$ .