Chapter 1.4, Problem 24IP

To determine

The name of the property used in the statement $7+x+11=x+7+11$ .

Answer to Problem 24IP

  $\text{Commutative Property}$

Explanation of Solution

Given information:

The statement, $7+x+11=x+7+11$

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 and the expressions both sides are equal. It is of the form $a+b=b+a$ . So, the property shown by the given statement is commutative property of addition.

Thus, the given statement shows the commutative property.