Chapter 7.2, Problem 52IP

To determine

Simplify and name of the property used in the statement $22\cdot \left(-18\right)-22\cdot \left(24\right)$ .

Answer to Problem 52IP

  $-924$

Distributive property

Explanation of Solution

Given information:

The statement, $22\cdot \left(-18\right)-22\cdot \left(24\right)$

Concept Used:

Commutative property:

• $a+b=b+a$
• $a\cdot b=b\cdot a$

Associative property:

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

Distributive property:

• $a\left(b+c\right)=ab+ac$
• $\left(b+c\right)a=ba+ca$

Additive identity:

• $a+0=0+a=a$

Multiplicative identity:

• $a\cdot 1=1\cdot a=a$

Zero property of Multiplication:

• $a\cdot 0=0\cdot a=0$

Calculation:

Here in the given statement, observe that sequence of the addition of first two numbers is change in the right side. It is of the form $a\left(b+c\right)=ab+ac$ . So, the property shown by the given statement is distributive property of addition as below

  $\begin{array}{c}22(-18)-22(24)\\ =22(-18-24)\\ \text{ (distributive property)}\\ =22(-42)\end{array}$

Simplify $22(-42)$ as below

  $\begin{array}{c}22(-42)\\ =-924\end{array}$

Thus, the given statement shows the distributive property.