Reciprocal of Fraction

The reciprocal of a fraction can be found by turning a fraction upside down. In other words, it is found by interchanging the positions of numerator and denominator in a fraction. For example, the reciprocal of fraction 2/3 is 3/2. The reciprocal of a fraction is also known as its multiplicative inverse.

To find the reciprocal of a fraction, we just need to interchange or swap numerator and denominator. For example, the reciprocal of fraction 7/9 is 9/7. Look at the image given below showing the reciprocal of fractions.

Some interesting facts about the reciprocal of fractions are given below:

• Reciprocal of a proper fraction is always turned out to be an improper fraction.
• The reciprocal of a unit fraction is always a whole number.
• The reciprocal of an improper fraction is always a proper fraction.

Use Cuemath's free online reciprocal calculator to verify your answers.

Now let us look at the reciprocal of mixed fractions and negative fractions in detail.

Reciprocal of Mixed Fraction

The reciprocal of mixed fractions can be found by converting mixed numbers to improper fractions first, and then we can simply interchange numerator and denominator values. For example, the reciprocal of \(2\dfrac{3}{5}\) can be found by first converting it to an improper fraction. \(2\dfrac{3}{5}\) is the same as 13/5. Now, the reciprocal of 13/5 is 5/13. This is how the reciprocal of a mixed fraction is found out.

Reciprocal of a Negative Fraction

If a negative fraction is given, let's say -8/9, then its reciprocal or multiplicative inverse is -9/8. The negative sign will remain with the numerator. We just need to swap numerator and denominator values. So, the reciprocal of a negative fraction -a/b is -b/a.

Fractions with exponents are in the form of (a/b)^p, where a and b are any whole numbers (b ≠ 0), and p is any rational number. The reciprocal of fraction with negative exponents is the same as the given fraction raised to the same exponent without the negative sign. It is because the value of a fraction with a negative exponent is its reciprocal without the negative sign. So, (2/3)^-2 is the same as (3/2)². And now we can easily find its reciprocal by turning the fraction upside down which is (2/3)². So, we can say that the reciprocal of the fraction with a negative exponent is the same fraction with the same exponent without the negative sign.

In general, if we have to find the reciprocal of fraction with exponents, then first we have to separate numerator and denominator with exponents. For example, we write (a/b)⁵ = a⁵/b⁵. Now, we can interchange the values of numerator and denominator along with their respective exponents. So, the reciprocal of a⁵/b⁵ is b⁵/a⁵.

Reciprocal of Fraction Related Articles

Check these interesting articles related to the concept of reciprocal of fractions in math.

• Reciprocal Definition
• Reciprocal Function
• Division of Fractions
• Multiplicative Inverse

What is Reciprocal of Fraction?

The reciprocal of a fraction is the number whose product with the given fraction is 1. It is also known as the multiplicative inverse of the fraction. It is found by swapping the numerator and denominator of the fraction. In other words, the numerator of the fraction is the denominator of its reciprocal and the denominator of the fraction is the numerator of its reciprocal.

What is the Reciprocal of a Negative Fraction?

The reciprocal of a negative fraction is found by interchanging the numerator and denominator of the fraction. The negative sign will still be there with the numerator of the reciprocal. For example, the reciprocal of -x/y is -y/x.

How to Find Reciprocal of Fraction?

The reciprocal of a fraction can be found by turning a fraction upside down. For example, the reciprocal of 1/5 is 5/1 or 5, the reciprocal of 5/9 is 9/5, etc.

How to Find the Reciprocal of a Mixed Fraction?

The reciprocal of a mixed fraction is found by converting it to an improper fraction. Then, we can simply interchange the numerator and denominator. For example, the reciprocal of \(1\dfrac{1}{2}\) can be found by first converting it to an improper fraction, which is 3/2. Now the reciprocal of fraction 3/2 is 2/3.

What is a Reciprocal of Fraction Example?

The reciprocal of a fraction p/q is q/p. Let us take an example of the reciprocal of the fraction. The reciprocal of 4/5 is 5/4, the reciprocal of -9/5 is -5/9, etc.

What is a Reciprocal of Fraction 3/10?

The reciprocal of fraction 3/10 is 10/3.

What is a Reciprocal of Fraction 8 1/11?

\(8\dfrac{1}{11}\) is a mixed number. So its reciprocal can be found by converting it to an improper fraction first. \(8\dfrac{1}{11}\) is the same as 89/11. Its reciprocal is 11/89. Therefore, the reciprocal of 8 1/11 is 11/89.

What is a Reciprocal of Fraction 7/9?

The reciprocal of fraction 7/9 is 9/7.