# Multiplication by Zero

 Site: Saylor Academy Course: RWM101: Foundations of Real World Math Book: Multiplication by Zero
 Printed by: Guest user Date: Saturday, April 13, 2024, 3:00 AM

## Description

Read this text to see this definition written formally. Complete the practice questions and check your answers.

## Multiplication by Zero

#### Use the Properties of Zero

We have already learned that zero is the additive identity, since it can be added to any number without changing the number's identity. But zero also has some special properties when it comes to multiplication and division.

#### Multiplication by Zero

What happens when you multiply a number by $0$? Multiplying by $0$ makes the product equal zero. The product of any real number and $0$ is $0$.

For any real number $a$,

$a \cdot 0 = 0$            $0 \cdot a = 0$

Source: Rice University, https://openstax.org/books/prealgebra/pages/7-4-properties-of-identity-inverses-and-zero

## Example

#### EXAMPLE 7.36

##### Simplify:

$-8 \cdot 0$

$\frac {5}{12} \cdot 0$

$0(2.94)$

##### TRY IT 7.71

Simplify:

$-14 \cdot 0$

$0 \cdot \frac {2}{3}$

$(16.5) \cdot 0$

##### TRY IT 7.72

Simplify:

$(1.95) \cdot 0$

$0(−17)$

$0 \cdot \frac {5}{4}$

### Solution

 ⓐ $-8 \cdot 0$ The product of any real number and 0 is 0. $0$

 ⓑ $\frac {5}{12} \cdot 0$ The product of any real number and 0 is 0. $0$

 ⓒ $0(2.94)$ The product of any real number and 0 is 0. $0$