Chapter 1.4, Problem 22IP

To determine

The name of the property used in the statement $14\times 0\times 3=0$ .

Answer to Problem 22IP

  $\text{Zero Property of Multiplication}$

Explanation of Solution

Given information:

The statement, $14\times 0\times 3=0$

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 two numbers 14 and 3 are multiplied with 0 and the result of the product is 0 as well. It implies that anything multiplied to 0 is equal to 0. It is of the form $a\cdot 0=0\cdot a=0$ . So, the property shown by the given statement is zero property of multiplication.

Thus, the given statement shows the zero property of multiplication.