# Reciprocal Formula

Reciprocal means an inverse of a number or value. If x is any real number, then the reciprocal of this number will be 1/x. For example, the reciprocal of 8 is 1 divided by 8, i.e. 1/8.

Also, if we multiply a number by its reciprocal, it gives one (1) as a result.

Let us learn about the reciprocal formula with a few examples in the end.

## What Is Reciprocal Formula?

The Reciprocal Formula of a given number can be expressed as,

\(\dfrac{1}{x} \,\,\text{or}\,\, {x^-1}\)

## Solved Examples Using Reciprocal Formula.

**Example 1:** What number would give the product as 1 when multiplied by14?

**Solution:**

To find: We need to determine the reciprocal of 14

14 is a natural number. (given)

Using Reciprocal Formula,

the reciprocal of 14 = \(\dfrac{1}{14}\)

\(\dfrac{1}{14}\) on multiplying with 14 gives 1:

\(\dfrac{1}{14} \times 14 = 1\)

**Answer:** \(\dfrac{1}{14}\) when multiplied by 14 gives 1.

**Example 2**: Daniel bought 4 apples from the market. He ate \(1\dfrac{1}{2}\) apples from the 4 he bought. Determine the reciprocal of \(1\dfrac{1}{2}\).

**Solution:**

Firstly, let's convert the mixed fraction into an improper fraction.

\(1\dfrac12 = \dfrac32\)

To find: The reciprocal of \(\dfrac{3}{2}\)

Using Reciprocal Formula,

Reciprocal of \(\dfrac{3}{2}\) is \(\dfrac{2}{3}\)

**Answer: **\(\dfrac{2}{3}\) is the reciprocal of \(\dfrac{3}{2}\).