The Lesson

To find the reciprocal of an algebraic fraction, turn the fraction upside down. The reciprocal of a over b is b over a Make the numerator the denominator, and the denominator the numerator.

How to Find the Reciprocal of an Algebraic Fraction

Question

What is the reciprocal of the algebraic fraction below?
x over y

Step-by-Step:

1

Make the numerator of the fraction the denominator of the reciprocal. In our example, the numerator of the fraction is x. The numerator of the fraction (x) becomes the denominator of the reciprocal

2

Make the denominator of the fraction the numerator of the reciprocal. In our example, the denominator of the fraction is y. The denominator of the fraction (y) becomes the numerator of the reciprocal

Answer:

We have found the reciprocal of the fraction: y over x

More Examples of Finding the Reciprocal of an Algebraic Fraction

Algebraic fractions do not just contain single letters.
  • When an algebraic fraction has a number, we can find the reciprocal: The reciprocal of x over 2 is 2 over x
  • When an algebraic fraction has a term, we can find the reciprocal: The reciprocal of 3 x squared over y is y over 3 x squared
  • When an algebraic fraction has a expression, we can find the reciprocal: The reciprocal of x plus y over z is z over x plus y

Lesson Slides

The slider below shows another real example of how to find the reciprocal of an algebraic fraction.

What Is an Algebraic Fraction?

An algebraic fraction is a fraction which contains letters.

Reciprocal When the Numerator Is 1

Consider an algebraic fraction where the numerator is 1: 1 over x By finding the reciprocal, the denominator becomes 1: x divided by 1 But a letter divided by 1 is itself: x divided by 1 equals x The reciprocal of a fraction with a numerator of 1 is simply the denominator.