# The Reciprocal of a Number

The reciprocal of a number is 1 divided by the number.

• The reciprocal of a number is also called its multiplicative inverse.
• The product of a number and its reciprocal is 1.
• All numbers except 0 have a reciprocal.
• The reciprocal of a fraction is found by flipping its numerator and denominator.

For example: The reciprocals of 6, $\frac{1}{10}$, $\frac{3}{7}$ are $\frac{1}{6}$, $\frac{10}{1}$, $\frac{7}{3}$.

Example

Find the reciprocal of 3

Solution

Step 1:

To find the reciprocal of 3, we write 1 over 3 i.e., $\frac{1}{3}$.

Step 2:

So the reciprocal of 3 is $\frac{1}{3}$

Find the reciprocal of $\frac{1}{4}$

### Solution

Step 1:

To find the reciprocal of $\frac{1}{4}$, its numerator and denominator are flipped

Step 2:

The reciprocal of $\frac{1}{4}$ = $\frac{4}{1}$ or 4.

So, the reciprocal of $\frac{1}{4}$= 4.

Find the reciprocal of 7

### Solution

Step 1:

To find the reciprocal of 7, first it is re-written as $\frac{7}{1}$. Then its numerator and denominator are flipped and the reciprocal = $\frac{1}{7}$.

Step 2:

So the reciprocal of 7 is $\frac{1}{7}$