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 \( 0 \).

Source: Rice University, https://openstax.org/books/prealgebra/pages/7-4-properties-of-identity-inverses-and-zero
This work is licensed under a Creative Commons Attribution 4.0 License.

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:

ⓐ \( (1.95) \cdot 0 \)

ⓑ \( 0(−17)  \)

ⓒ \( 0 \cdot \frac {5}{4} \)

EXAMPLE 7.36

TRY IT 7.71

TRY IT 7.72