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How to Find the Multiplicative Inverse of a Rational Number

Any number's multiplicative inverse is concerned with finding the value of only one number, which is the number one. A number's multiplicative inverse, also known as a reciprocal, is a value that when multiplied to the original number produces a value of one. A number is rational if it can be represented either as a common fraction or the decimal product of a common fraction. You can find a number's multiplicative inverse turning the number on its head.

Instructions

- 1
  Find a rational number as an example. In this example, let the rational number be 4/5.
- 2
  Switch the positions of the numerator and denominator to calculate the multiplicative inverse. With this example, 4/5 becomes 5/4.
- 3
  Check your answer by multiplying the multiplicative inverse to the original number. If the product equals 1, then the number calculated in the prior step is the multiplicative inverse. Concluding this example, 4/5 * 5/4 equals 20/20, which is also 1. The multiplicative inverse of 4/5 is 5/4.

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Middle School