Chapter 1.4, Problem 19IP

To determine

The name of the property used in the statement $8\cdot 1=8$ .

Answer to Problem 19IP

  $\text{Multiplicative Identity}$

Explanation of Solution

Given information:

The statement, $8\cdot 1=8$

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 8 is multiplied to 1 and the result itself is 8. It is of the form $a\cdot 1=a$ . So, the property shown by the given statement is multiplicative identity.

Thus, the given statement shows the multiplicative identity.