Inverse property of multiplication

Definition

The inverse property of multiplication states that any nonzero number multiplied by its reciprocal equals 1. Mathematically, for a number $a$, where $a \neq 0$, $a \cdot \frac{1}{a} = 1$.

5 Must Know Facts For Your Next Test

1. The inverse property of multiplication is valid only for nonzero numbers.
2. The reciprocal of a number $a$ is given by $\frac{1}{a}$.
3. Multiplying a number by its reciprocal yields the multiplicative identity, which is 1.
4. The inverse property is essential in solving equations and simplifying expressions involving fractions.
5. This property helps in understanding and working with rational numbers.

Review Questions

• What is the multiplicative inverse of the number 7?
• Using the inverse property of multiplication, what is $5 \cdot \frac{1}{5}$?
• Why can't zero have a multiplicative inverse?

Related terms

Multiplicative Identity: The number 1, because any number multiplied by 1 remains unchanged.

Reciprocal: For a nonzero number $a$, its reciprocal is $\frac{1}{a}$.

Real Numbers: All numbers on the continuous number line, including rational and irrational numbers.