What Is Reciprocal Formula? Examples - Cuemath

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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. The reciprocal of 1/8 is 8. Also, if we multiply a number by its reciprocal, the product is 1. 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,

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

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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: One-third of a pie was remaining after the party. Shane decided to divide it among his three friends. How much will each of them get?

Solution:

Firstly, let's understand that this is the division operation involved here.

\(\dfrac{1}{3}\) ÷ 3

We need to convert this operation into multiplication. Thus by using Reciprocal Formula, we convert the divisor into its reciprocal.

Reciprocal of 3 is \(\dfrac{1}{3}\)

\(\dfrac{1}{3} \times \dfrac{1}{3}\)

=\(\dfrac{1}{9}\)

Answer:Thus each of the 3 friends will be getting 1/9 part of the pie.

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