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# Reciprocal of Rational Numbers

Rational numbers are the numbers expressed as the Ratio of the two integers. The basic rational number is expressed in the form of (p/q), where 'p' and 'q' are two integers. Let us see some example of Rational Numbers:-

2/3,

1/2,

11/17.

Reciprocal of the rational numbers can be defined as the reverse of the rational numbers, which means the numerator is placed in place of denominator and vice-versa. The main difference between rational number and reciprocal of rational number is that the numerator of rational number becomes the denominator of reciprocal and the denominator of the rational number becomes the numerator of the reciprocal.

To get a reciprocal of a rational number just divide the original number by '1'. Let 'p/q' be any rational number then 1/ (p/q) is the reciprocal that is 'q/p' is the reciprocal of given rational number.

Let us take some examples:

2/3 = 1/ (2/3) = 3/2,

7/2 = 1/ (7/2) = 2/7.

So, the reciprocal of any rational number is just the opposite of that rational number.

## Determine the reciprocal of 2/5?

The reciprocal of 2/5 is 5/2, as in reciprocal we interchange the value of numerator with denominator and vice-versa.

## Find reciprocal of 2?

2 can be written as 2/1 as a rational number, now its reciprocal is 1/2.

Multiplying rational number 2 with it’s reciprocal.

2/1*1/2 = 1,

Dividing rational number 2 with it’s reciprocal.
2/1÷1/2 = 2/1*2/1 = 4,

Adding rational number 2 with its reciprocal.
2/1+1/2 = (4+1)/2 = 5/2,

Subtracting rational number 2 with its reciprocal.
2/1-1/2 = (4-1)/2 = 3/2

## Determine the reciprocal of 2/3?

Reciprocal of 2/3 is 3/2,

Multiplying rational number '2/3' with it’s reciprocal we get,

2/3*3/2 = 1.

Dividing rational number 2/3 with it’s reciprocal we get,
=> 2/3÷3/2,
=> 2/3*2/3,
=> 4/9.

Adding rational number 2/3 with its reciprocal, we get:
=> 2/3+3/2,
=> (4+9)/6,
=> 13/6.

Subtracting rational number 2/3 with its reciprocal, we get:
=> 2/3-3/2,
=> (4-9)/6,
=> -5/6.

## Determine the reciprocal of 10/3?

Reciprocal of 10/3 = 3/10,

If we Multiply Rational Number '10/3' with it’s reciprocal, we get:
=> 10/3*3/10,

=> 1.

If we perform division operation on the given rational number and its reciprocal then we get:       => 10/3÷3/10,
=> 10/3*10/3,

=> 100/9.

If we do addition of  both rational number and its reciprocal then we get:

=> 10/3+3/10,

=> (100+9)/30,

=> 109/30.

On subtracting reciprocal of given rational number we get:
=> 10/3-3/10,

=> (100-9)/6,

=> 91/30.

## Find reciprocal of 8/9?

Solution:
Reciprocal of 8/9 is 9/8

If we Multiply Rational Number '8/9' with it’s reciprocal, we get:
=> 8/9*9/8,
=> 1.

If we perform division operation on the given rational number and its reciprocal, we get:
=> 8/9÷9/8,
=> 8/9*8/9,
=> 64/81.

If we do addition of  both rational number and its reciprocal then we get:
=> 8/9+9/8,
=> (64+81)/72,
=> 145/72.

On subtracting reciprocal of given rational number we get:
=>8/9–9/8,
=> (64-81)/72,
=> -17/72.

## Find reciprocal of 15/5?

Reciprocal of 15/5 is 5/15

If we Multiply Rational Number '15/5' with it’s reciprocal, we get:
=> 15/5*5/15,
=> 1.

If we perform division operation on the given rational number and its reciprocal, we get:
=> 15/5÷5/15,
=> 15/5*15/5,
=> 225/25.

If we do addition of  both rational number and its reciprocal then we get:
=> 15/5+5/15,
=> (45+5)/15,
=> 50/15.

On subtracting reciprocal of given rational number we get:
=> 15/5–5/15,
=> (45-5)/15,
=> 40/15.