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# What Does Reciprocal Mean in math?

July 30, 2022
written by Azhar Ejaz

Reciprocal mean in math is simply defined as the inverse of a value or a number. if m is a natural number then the reciprocal of m is equal to 1/m. for example, the reciprocal of 8 is 1 divided by 8 reciprocal of 8 is 1/8.

The word reciprocal came from the Latin word

â€˜Reciprocusâ€™meaning â€˜â€™returning .in this article learn the definition of reciprocal and .how to find the reciprocal of numbers.

## What is reciprocal?

Reciprocal mean in math is simply defined as the inverse of a value or a number.if m is a natural number then the reciprocal of m is equal to 1/m. for example, the reciprocal of 8 is 1 divided by 8 reciprocal of 8 is 1/8.

The word reciprocal came from the Latin word

â€˜Reciprocusâ€™meaning â€˜â€™returning.

Example:

• The reciprocal of 4 and 5 are 1/4 and 1/5
• The reciprocal of 1/6 and 2 are 6 and 1/2

## Not for zero

The reciprocal condition can not apply on zero, it will return an indefinite value.

1/0=undefined

Therefore, all real numbers have a reciprocal but not for zero (0)

## Â Reciprocal of a number?

The reciprocal of a number is defined as divided by the one by the given number

Example:

Find the reciprocal of 7

Solution:

We will use

x=1/x

X=7

7=1/7

## Reciprocal of a negative number?

Reciprocal can be a negative number (-x) the inverse of the given number with a negative sign along with that (-1/x)

For example, the reciprocal of -5x2 is writing 1/-5x2

The following step is to find the reciprocal of a negative number.

Step1: For any given negative number write the form of an improper fraction by writing the number 1 in the denominator.

Step2: interchange the numerator and denominator

Step3: add a negative sign (-) to the resultant number.

Example: find the reciprocal of a negative number.

Considered a negative number -18

Step 1: convert the number 18 into the improper fractionÂ Â Â Â Â Â Â Â Â Â Â Â Â Â  (18/1)

Step2: interchange numerator and denominator values we get

1/18

Step 3: add a negative sign to the resultant number

We get

-1/18

Therefore, the reciprocal of negative number -18 is -1/18

## Reciprocal of a mixed fraction?

In order to find the same for a mixed fraction. Convert into improper fractions.

For example: find the reciprocal of a mixed fraction

Considered a mixed fraction, 4(1/2).

Step1: convert a mixed fraction into an improper fraction.

4(1/2)=9/2

Step 2: interchange nominator and denominator values.

We get,

9/2=2/9

Therefore, the reciprocal of mixed fraction 4(1/2) is 2/9.

## Reciprocal of decimal?

The reciprocal of a decimal is the same defined for the reciprocal of a number.

For example: Find the reciprocal of a decimal

Considered, decimal fraction0.75

Solution:

0.75 is written as3/4

Reciprocal of 3/4 is 4/3

## Finding unity?

Reciprocal of number multiply by itself number is equal to unity (1).let see some example

• 2X1/2=1
• 15×1/15=1
• 23×1/23=1

## Rules for reciprocal?

Two important rules for reciprocal are.

• Any number y the reciprocal will be 1/y

Are also can be written as x-1

• For any fraction y/x, the reciprocal will be x/y.
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