Reciprocal of a Fraction

Getting the reciprocal of a fraction is most probably the easiest task you could be asked to do with any fraction.

So, what is the reciprocal of a fraction? It is simply the inverse of the fraction. To get the reciprocal, all you have to do is to flip it over so that the fraction's denominator becomes the numerator, and vice versa.

For instance, the reciprocal of

^{2}?

_{3} is

^{3}?

_{2}. Now, wasn't that easy?

Here are more examples of fractions and their reciprocals:

^{1}?_{4} > ^{4}?_{1}

^{2}?_{5} > ^{5}?_{2}

^{8}?_{3} -> ^{3}?_{8}

^{35}?_{23} -> ^{23}?_{35}

^{102}?_{367} -> ^{367}?_{102}

As you can see, no matter the value, the reciprocal of a fraction is always its upside down version.

Now, finding the reciprocal of a mixed fraction involves one additional step: converting the mixed fraction into an improper fraction.

Here's an example:

### 1^{2}?_{3} = ^{(3 x 1)+2}?_{3}

### 1^{2}?_{3} = ^{(3)+2}?_{3}

### 1^{2}?_{3} = ^{5}?_{3}

^{5}?_{3} > ^{3}?_{5}

Here are more examples of mixed fractions and their reciprocals:

### 2^{1}?_{4} or ^{9}?_{4} > ^{4}?_{9}

### 1^{5}?_{6} or ^{11}?_{6} -> ^{6}?_{11}

^{1}?_{4} or ^{1}?_{4} > ^{1}?_{4}

### 3^{3}?_{4} or ^{15}?_{4} -> ^{4}?_{15}

You might be wondering what about whole numbers, do they have reciprocals? That answer to that question is yes. Whole numbers have an implied denominator of 1. So, the whole number 2 in fraction form is

^{2}/

_{1}.

**This means that the reciprocal of any whole number has a numerator of 1. ** Here are examples of whole numbers and their reciprocals:

### 3 -> ^{1}/_{3}

### 8 -> ^{1}/_{8}

### 300 > ^{1}/_{300}

Easy, right?

While it is very easy to find the reciprocal of a fraction, there is a way to check if you got the reciprocal right.

** Multiply the fraction by its reciprocal and you will get a fraction that equals 1.** Let's take a few of our previous examples and multiply them by their reciprocals:

^{1}?_{4} x ^{4}?_{1} = ^{4}?_{4} or 1

^{2}?_{5} x ^{5}?_{2} = ^{10}?_{10} or 1

^{8}?_{3} x ^{3}?_{8} = ^{24}?_{24} or 1