**Reciprocal in mathematics :**

Reciprocal of a number is nothing but its multiplicative inverse.

Let us consider the fraction 3/4.

If we want to get its reciprocal, we have write the denominator 4 as numerator and numerator 3 as denominator.

In simple words, we have to flip the fraction.

So, the reciprocal of 3/4 is 4/3. And also the reciprocal of 4/3 is 3/4.

Therefore, 3/4 and 4/3 are reciprocal to each other.

**Important note : **

If two numbers are reciprocal to each other, then their product is 1.

That is,

(3/4) x (4/3) = 1

Let us consider the whole number 8.

If we want to get reciprocal of the whole number 8, first we have write 8 as a fraction with denominator 1.

That is 8/1.

To get reciprocal of 8/1, we have write the denominator 1 as numerator and numerator 8 as denominator.

That is 1/8.

Therefore, the reciprocal of the whole number 8 is 1/8.

And also,

8 x 1/8 = 1

It has been illustrated in the diagram given below.

**Shortcut : **

If we want to get reciprocal of any whole number, we have to write 1 as numerator and the given whole number as denominator.

**The reciprocal of 1 is 1 itself.**

Let us see, how the reciprocal of 1 is 1 itself.

To get the reciprocal of 1, let us write 1 as a fraction with denominator 1.

That is 1/1.

To get reciprocal of 1/1, we have write the denominator 1 as numerator and numerator 1 as denominator.

That is 1/1.

Therefore, the reciprocal of the whole number 1 is 1 itself.

**The reciprocal of zero is undefined. **

Let us see, how the reciprocal of zero is undefined.

To get the reciprocal of 0, let us write 0 as a fraction with denominator 1.

That is 0/1.

To get reciprocal of 0/1, we have to write the denominator 1 as numerator and numerator 0 as denominator.

Then, we have 1/0.

Here, 1 is divided by 0.

In Math, any non zero number divided by zero is undefined.

Therefore, the reciprocal of zero is undefined.

**The reciprocal of ****∞ is zero. **

Let us see, how the reciprocal of infinity is zero.

In Math infinity (∞) is the symbol that we use for the term "Undefined".

To get the reciprocal of ∞, let us write ∞ as a fraction 1/0.

Because, any non zero number divided by zero is undefined or infinity.

To get reciprocal of 1/0, we have write the denominator 0 as numerator and numerator 1 as denominator.

Then, we have 0/1.

Here, 0 is divided by 1.

In Math, zero divided by any non zero number is zero.

Therefore, the reciprocal of infinity (∞) is zero.

Let us consider the mixed number 2 3/4.

To get the reciprocal of 2 3/4, let us convert the given mixed number 2 3/4 into improper fraction.

Then, we have

2 3/4 = 11/4

To get reciprocal of 11/4, we have to write the denominator 4 as numerator and numerator 11 as denominator.

Then, we have 4/11.

Therefore, the reciprocal of 2 3/4 is 4/11.

Let us look at the next stuff on "Reciprocal in mathematics"

**Step 1 :**

When we divide a fraction by another fraction, first we have to change the division sign as multiplication.

**Step 2 :**

Take reciprocal of the second fraction.

**Step 3 :**

Multiply the two fractions. (Numerator times numerator and denominator times denominator).

Let us look at the next stuff on "Reciprocal in mathematics"

**Example 1 : **

Divide 2/5 by 6/7

**Solution : **

Using the method explained above, we have

2/5 ÷ 6/7 = 2/5 x 7/6

2/5 ÷ 6/7 = (2x7) / (5x6)

2/5 ÷ 6/7 = 7/15

**Example 2 :**

Divide 7/5 by 3/2

**Solution : **

Using the method explained above, we have

7/5 ÷ 3/2 = 7/5 x 2/3

7/5 ÷ 3/2 = (7x2) / (5x3)

7/5 ÷ 3/2 = 14/15

**Example 3 :**

Divide 5/12 by 20/13

**Solution : **

Using the method explained above, we have

5/12 ÷ 20/13 = 5/12 ÷ 20/13

5/12 ÷ 20/13 = 5/12 x 13/20

5/12 ÷ 20/13 = (5x13) / (12x20)

5/12 ÷ 20/13 = 13/48

**Example 4 :**

Divide 2/19 by 6 1/2

**Solution : **

First, let us convert the mixed number 6 1/2 in to improper fraction.

6 1/2 = 13/2

Now,m we have 2/19 ÷ 6 1/2 = 2/19 ÷ 13/2

Using the method explained above, we have

2/19 ÷ 13/2 = 2/19 x 13//2

2/19 ÷ 13/2 = (2x13) / (19x2)

2/19 ÷ 13/2 = 13 / 19

**Example 5 :**

One pizza can be made in 1/2 hour. How many pizzas can be made in 5/2 hours ?

**Solution : **

Time taken to make one pizza = 1/2 hour

No. of pizzas made in 5/2 hours = 5/2 ÷ 1/2

No. of pizzas made in 5/2 hours = 5/2 x 2/1

No. of pizzas made in 5/2 hours = (5x2) / (2x1)

No. of pizzas made in 5/2 hours = 5

Let us look at the next stuff on "Reciprocal in mathematics"

**Step 1 :**

When we divide a fraction by a whole number, first we have to write the whole number as fraction with denominator 1.

**Step 2 :**

Change the division sign as multiplication.

**Step 3 :**

Take reciprocal of the second fraction (Whole number with denominator 1).

**Step 4 :**

Multiply the two fractions. (Numerator times numerator and denominator times denominator).

Let us look at the next stuff on "Reciprocal in mathematics"

**Example 1 : **

Simplify : 2/5 ÷ 6

**Solution : **

Using method 1, we have

2/5 ÷ 6 = 2/5 ÷ 6/1

2/5 ÷ 6 = 2/5 x 1/6

2/5 ÷ 6 = (2x1) / (5x6)

2/5 ÷ 6 = 1/15

**Example 2 :**

Simplify : 5/12 ÷ 20

**Solution : **

Using method 2, we have

5/12 ÷ 20 = 5 / (12x20)

5/12 ÷ 20 = 1/48

**Example 3 :**

David eats 1/4 of a pizza and divides the remaining in to two equal parts for his two kids. What is the part of the pizza will each kid receive ?

**Solution : **

Part of the pizza eaten by David = 1/4

Remaining pizza = 3/4

Given : Remaining pizza is divided in to equal parts for his two kids.

So, part of the pizza received by each kid is

= 3/4 ÷ 2

= 3/(4x2)

= 3/8

Hence, each kid will receive 3/8 part of the pizza.

After having gone through the stuff given above, we hope that the students would have understood "Reciprocal in mathematics".

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