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- Finds the reciprocal (multiplicative inverse) of a whole number, decimal or fraction.
- Shows the answer as a fraction, a decimal and a mixed number.
- Checks that the number times its reciprocal equals 1.
- Explains each step: write it as a fraction, then flip it.
How to use the reciprocal calculator
Choose the number type
A whole number or decimal, or a fraction.
Enter the number
For example 4, 0.2 or −2.5, or a numerator and denominator such as 3 and 4.
Read the reciprocal
See it as a simplified fraction, a decimal and a mixed number.
What is a reciprocal?
The reciprocal of a number is 1 divided by that number. Multiplying a number by its reciprocal always gives 1. To find it, write the number as a fraction and swap the top and bottom. Zero has no reciprocal, because nothing times 0 equals 1.
Reciprocal formula
Reciprocal of x = 1 ÷ x
Reciprocal of a/b = b/a
x × (1 ÷ x) = 1
A negative number has a negative reciprocal.
Example 1: whole numbers and decimals
Write as a fraction, then flip.
- 4 = 4/1 1/4 = 0.25
- 0.2 = 1/5 5
- −2.5 = −5/2 −2/5 = −0.4
Example 2: a fraction
The reciprocal of 3/4.
- Flip 3/4 4/3
- As a decimal 1.333333…
- As a mixed number 1 1/3
Where reciprocals are used
Dividing fractions
Dividing by a fraction is the same as multiplying by its reciprocal.
Solving equations
Multiply both sides by a reciprocal to isolate x.
Perpendicular slopes
A perpendicular line has the negative reciprocal slope.
Rates and units
Turn miles per hour into hours per mile.
Work with fractions using the fraction calculator, convert decimals with the decimal to fraction calculator, or find slopes with the slope calculator.
Reciprocal calculator FAQ
What is the reciprocal of a number?
It is 1 divided by the number. The reciprocal of 4 is 1/4, and the reciprocal of 3/4 is 4/3.
What is the reciprocal of a fraction?
Swap the numerator and denominator. The reciprocal of 2/5 is 5/2.
What is the reciprocal of a decimal?
Write the decimal as a fraction and flip it. 0.2 = 1/5, so its reciprocal is 5.
Does 0 have a reciprocal?
No. 1 ÷ 0 is undefined, so zero has no reciprocal.
Is a reciprocal the same as a multiplicative inverse?
Yes. Both mean the number you multiply by to get 1.
What is the reciprocal of a negative number?
It is also negative. The reciprocal of −2.5 is −2/5, or −0.4.