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Reciprocal of a Fraction

Here we will learn reciprocal of a fraction. 

Reciprocal of a Number:

Let us learn reciprocal of a number.

Any natural number can be written as number1

10 = 101;       5 = 51;       23 = 231;      52 = 521 and so on.

Reciprocal of 101 = 110

Reciprocal of 231 = 123

Reciprocal of 521 = 152

Reciprocal of 161 = 116

Reciprocal of 361 = 136, etc.

Reciprocal of a Fraction:

What is the reciprocal of 23?

Reciprocal of a fraction is the fraction inverted.

Therefore, reciprocal of 23 = 32

Reciprocal of 56 = 65, etc.


What is 14 of 4?

We know that 14 of 4 means 14 × 4, let us use the rule of repeated addition to find 14 × 4.

Reciprocal of Fraction

We can say that 14 is the reciprocal of 4 or 4 is the reciprocal or multiplicative inverse of 14.

Now, let us consider the multiplication of the following pairs of fractional numbers.

37 × 73;

58 × 85;

29 × 92 

We observe that

37 × 73 = 2121 = 1;  

58 × 85 = 4040 = 1;   

29 × 92 = 1818 = 1;

Therefore, if the product of two fractions is 1 we call each fraction as the reciprocal of the other. We can get reciprocal of a fraction by interchanging the numerator and the denominator. The reciprocal of 1 is 1 and there is no reciprocal for 0.


Solved Examples on Reciprocal of a Fraction:

1. Find the reciprocal of 1115       

Solution:

By interchanging the numerator and the denominator we get 1511.

1115 × 1511 = 165165 = 1;

Hence, 1511 is the reciprocal of 1115.


2. Find the reciprocal of 1571       

Solution:

By interchanging the numerator and the denominator we get 5711.

1571 × 5711 = 571571 = 1;

Hence, 5711 i.e., 571 is the reciprocal of 1571.



Reciprocal of a Mixed Fraction:

To find the reciprocal of a mixed fraction first we need to convert the mixed fractional number to improper fraction and then interchange the numerator and the denominator of the improper fraction.

Solved Examples on Reciprocal of a mixed fraction:

1. Find the reciprocal of 259       

Solution:

259 is a mixed fraction.

Let's convert the mixed fraction to improper fraction.

259

9×2+59

239

By interchanging the numerator and the denominator we get 923.

239 × 923 = 207207 = 1;

Hence, 923 is the reciprocal of 239 i.e., 259.

Reciprocal of a Fraction


2. Find the reciprocal of 51321       

Solution:

51321 is a mixed fraction.

Let's convert the mixed fraction to improper fraction.

51321  

21×5+1321

11821

By interchanging the numerator and the denominator we get 21118.

11821 × 21118 = 24782478 = 1;

Hence, 21118 is the reciprocal of 11821 i.e., 51321.






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