Guide
What Is the Reciprocal of a Fraction?
The reciprocal is just a fraction flipped over — but it's the secret behind dividing fractions.
The reciprocal is just a fraction flipped over — but it's the secret behind dividing fractions.
What a reciprocal is
The reciprocal of a fraction is that fraction turned upside down — the numerator and denominator swap places. The reciprocal of 3/4 is 4/3, and the reciprocal of 2/5 is 5/2.
Finding the reciprocal
Just swap the top and bottom. For a whole number, write it over 1 first: the reciprocal of 5 (which is 5/1) is 1/5.
A number times its reciprocal equals 1
Any fraction multiplied by its reciprocal gives 1. For example 3/4 x 4/3 = 12/12 = 1. This is the defining property of a reciprocal.
Why reciprocals matter for dividing
Dividing by a fraction is the same as multiplying by its reciprocal. That's the 'flip' in 'keep, change, flip' — to compute 1/2 ÷ 1/4 you multiply 1/2 by the reciprocal of 1/4, which is 4/1.
Related tools & guides
Frequently asked
What is the reciprocal of a fraction?
It's the fraction flipped upside down, with the numerator and denominator swapped. The reciprocal of 3/4 is 4/3.
What is the reciprocal of a whole number?
Write the whole number over 1, then flip it. The reciprocal of 6 is 1/6.
Why do you use the reciprocal to divide fractions?
Because dividing by a fraction is the same as multiplying by its reciprocal — that's the 'flip and multiply' rule.