How-Tos / Math

How to Find the Reciprocal

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How to Find the Reciprocal

The reciprocal of a number is 1 divided by the number. The reciprocal of a fraction is found by flipping its numerator and denominator. Here is how to find the Reciprocal of a Fraction, Whole Number, Mixed Number, and Decimal. 

How to Find the Reciprocal of a Fraction

Find the reciprocal of a fraction by flipping it. In other words, swap over the Numerator and Denominator.

\\Fraction\ \ \ \ \ Reciprocal \\ \\~\ \ \ \ \ \ \frac{3}{4}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{4}{3} \\ \\~\ \ \ \ \ \ \frac{19}{7}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{7}{19} \\ \\~\ \ \ \ \ \ \frac{1}{2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{2}{1} = 2

How to Find the Reciprocal of a Whole Number

For a whole number, write that as a fraction; there’s no point in calculating it out to a decimal.

  • For instance, the reciprocal of 2 is 1 ÷ 2 = 1/2.

How to Find the Reciprocal of a Mixed Number

A mixed number is a part whole number and part fraction, such as 24/5.

  1. Convert Mixed numbers into an improper fraction.

    2 \ \frac{4}{5} = \frac{2*5}{5}+\frac{4}{5} = \frac{10}{5}+\frac{4}{5} = \frac{14}{5}

  2. Flip the fraction.

    The reciprocal of  14/5  is  5/14. 

How to Find the Reciprocal of a Decimal

  1. Change it to a fraction if possible. For instance, 0.5 = 1/2, and 0.25 = 1/4. Once in fraction form, just flip the fraction to find the reciprocal.

    For instance, the reciprocal of 0.5 is 2/1 = 2.

  2. Write out a division problem. Calculate the reciprocal of that number as a division problem: 1 ÷ (the decimal).

    For example, you can find the reciprocal of 0.4 by calculating 1 ÷ 0.4.

  3. Change the division problem to use whole numbers.

    You can take 1 ÷ 0.4 and rewrite it as 10 ÷ 4. In this case, you’ve moved each decimal place one space to the right, which is the same as multiplying each number by ten.

  4. Solve the problem using long division.

    If you calculate it for 10 ÷ 4, you’ll get the answer 2.5, the reciprocal of 0.4.