Multiplication by Zero
| Site: | Saylor Academy |
| Course: | RWM101: Foundations of Real World Math copy 1 |
| Book: | Multiplication by Zero |
| Printed by: | Guest user |
| Date: | Tuesday, May 13, 2025, 11:32 PM |
Description
buttons.Multiplication by Zero
Zero is the easiest number to multiply by because the answer is always zero. Read this text to see how this fact is written formally. Complete the practice questions and check your answers.
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 \( 0 \).
Multiplication by Zero
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
This work is licensed under a Creative Commons Attribution 4.0 License.
Examples and Exercises
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:
ⓐ \( (1.95) \cdot 0 \)
ⓑ \( 0(−17) \)
ⓒ \( 0 \cdot \frac {5}{4} \)
Answers
EXAMPLE 7.36
| ⓐ | |
| \( -8 \cdot 0 \) | |
| The product of any real number and 0 is 0. | \( 0 \) |
TRY IT 7.71
| ⓑ | |
| \( \frac {5}{12} \cdot 0 \) | |
| The product of any real number and 0 is 0. | \( 0 \) |
TRY IT 7.72
| ⓒ | |
| \( 0(2.94) \) | |
| The product of any real number and 0 is 0. | \( 0 \) |