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Inverse property of multiplication

from class:

Algebra and Trigonometry

Definition

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

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5 Must Know Facts For Your Next Test

  1. The reciprocal of a number $a$ is $\frac{1}{a}$.
  2. The property only applies to nonzero numbers, as dividing by zero is undefined.
  3. This property helps simplify equations and solve for variables in algebraic expressions.
  4. Multiplying a number by its inverse yields the multiplicative identity, which is 1.
  5. In practical applications, this property is used to isolate variables and solve equations.

Review Questions

  • What is the inverse property of multiplication?
  • Why can't the inverse property be applied to zero?
  • How does the inverse property of multiplication help in solving equations?

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