The Lesson
To find the reciprocal of a fraction, turn the fraction upside down.Make the numerator the denominator, and the denominator the numerator.
How to Find the Reciprocal of a Fraction
Question
What is the reciprocal of the fraction below?StepbyStep:
1
Make the numerator of the fraction the denominator of the reciprocal. In our example, the numerator of the fraction is 3.
2
Make the denominator of the fraction the numerator of the reciprocal. In our example, the denominator of the fraction is 5.
Answer:
We have found the reciprocal of the fraction:Finding the Reciprocal of a Mixed Fraction
The method above can be used to find the reciprocal of proper and improper fractions, but can not immediately be applied to mixed fractions. Mixed fractions must first be converted to improper fractions before the method can be applied.Question
What is the reciprocal of the mixed fraction below?StepbyStep:
Add a preliminary step. The method then continues as before.1
Make the numerator of the fraction the denominator of the reciprocal. In our example, the numerator of the fraction is 11.
2
Make the denominator of the fraction the numerator of the reciprocal. In our example, the denominator of the fraction is 3.
Answer:
We have found the reciprocal of the fraction:What Is a Reciprocal?
The reciprocal of a quantity is the result of dividing 1 by that quantity.Why Is Finding the Reciprocal of a Fraction Useful?
The reciprocal of a fraction is useful for:
the laws of exponents.
For example, when the base is a fraction and the exponent is negative.
This is equivalent to replacing the fraction with its reciprocal and using the positive exponent.

dividing by a fraction.
Dividing by a fraction is equivalent to multiplying by its reciprocal.
Reciprocal When the Numerator Is 1
Consider a fraction where the numerator is 1:By finding the reciprocal, the denominator becomes 1:
But a number divided by 1 is itself:
The reciprocal of a fraction with a numerator of 1 is simply the denominator.