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.
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.
- Convert Mixed numbers into an improper fraction.
- Flip the fraction.
The reciprocal of 14/5 is 5/14.
How to Find the Reciprocal of a Decimal
- 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.
- 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.
- 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.
- 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.