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How to Find the Reciprocal With Positive and Negative Fractions and Numbers

A reciprocal can be formed from a positive or negative number. The only number that does not have a reciprocal is zero. When a number is multiplied by its reciprocal, the product is equal to 1. Reciprocals are useful, both for dividing fractions and as a way to simplify complex algebraic equations that may contain multiple variables and expressions.

Instructions

    • 1

      Convert whole numbers to fractions. For example, 4 can also be written as 4/1. The 4 on the top is called the numerator, and the 1 on the bottom of the fraction is called the denominator.

    • 2

      Switch the numerator and denominator of the fraction to find the reciprocal. In our example, the reciprocal of 4 is 1/4. In the case of negative numbers, the reciprocal is also negative. For example, the reciprocal of -4 is -1/4

    • 3

      Check your work. When a number or a fraction and its reciprocals are multiplied together, they should equal 1. For example 1/4 x 4/1 = 4/4, which is equal to 1. As for -4, -1/4 x -4/1 = 4/4, which is equal to 1.

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