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Finding the Reciprocal of an Algebraic Fraction
(KS3, Year 8)
The Lesson
To find the reciprocal of an algebraic fraction, turn the fraction upside down.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?StepbyStep:
1
Make the numerator of the fraction the denominator of the reciprocal. In our example, the numerator of the fraction is x.
2
Make the denominator of the fraction the numerator of the reciprocal. In our example, the denominator of the fraction is y.
Answer:
We have found the reciprocal of the fraction: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:

When an algebraic fraction has a term, we can find the reciprocal:

When an algebraic fraction has a expression, we can find the reciprocal:
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:By finding the reciprocal, the denominator becomes 1:
But a letter divided by 1 is itself:
The reciprocal of a fraction with a numerator of 1 is simply the denominator.
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