Today, we will learn about the magic numbers or the magic of numbers.

In this module, we will learn about the beauty of numbers and their usage in various fields, like various competitive exams.

Number magic, or the magical numbers tricks, is one of the topics which is not taught in detail in schools, colleges and other institutions,

Firstly, we will know how magical the numbers are. With some of the examples.

The beautiful examples will enable students to develop an interest in numbers and mathematics.

So, let us start with our first example: –

Table of Contents

**Eg-1 – Addition of same Numbers in a Sequence**

7+77+777+7777

**Step 1 **= Consider the largest digit number and mark it 1 if it’s 1 digit, 12 if it’s 2 digit, 123 if it’s 3 digit and so on…

In this example, the largest number is 7777 which has 4 digits, so write it as 1234

**Step 2** = Now, multiply the 1234 by the digit itself.

**Step 3 =** 7+77+777+7777

= 1 2 3 4 X 7

= 2638

**88888+8888+888+88+8**

Here the most significant number is 88888, which has 5 digits, so: –

= 1 2 3 4 5 X 8

= 9 8 7 6 0

**3+33+333**

= 1 2 3 X 3

=3 6 9

- 666666+66666+6666+666+66+6

= 12 3 4 5 6 X 6

= 740736

I hope, you must be enjoying the magic of numbers; let us proceed to our second example:

**Let’s Practice: –**

- 2222222+222222+22222+2222+222+22+2
- 9999+999+99+9
- 55555+5555+555+55+5

**Eg-2 – Multiplication by 5**

**23 X 5**

**Step 1 **= Divide the number by 2 or simply half the number to be multiplied by 5. = 23/2 = 11.5

**Step 2 **= Now, multiply the answer by 10

= 11.5 X 10

= 115

**2. 28 X 5 **

Half of 28 = 14

= 14 X 10

= 140

**3. 2468 X 5**

Half of 2468 = 2468/2 = 1234

= 1234 X 10

=12340

**4. 15694 X 5 **

= 15694/2 = 7847

= 7847 X 10

= 78470

### Let’s Practice: –

- 4568 X 5
- 78965 X 5
- 12345678 X 5

## Eg-3 – Multiply any Number by 15

**16*15**

Step 1 = (16 + half of 16) * 10

= (16+8) *10 *

Step 2 = 24 X 10

= 240

**2. 52*15**

= (52+ half of 52) X 10

= (52+26)X *10 *

*= 78* X 10

= 780

**3. 764*15**

= ( 7 6 4 + 3 8 2 ) X 1 0

= 1 1 4 6 X 10

= 11460

4. 1 5 4 6 2 X 1 5

= ( 1 5 4 6 2 + 7 7 3 ) X 1 0

= 2 3 1 9 3 X 1 0

= 23 1 9 3 0

**Let’s Practice: –**

- 3456*15
- 398764*15
- 989898*15

## Eg-4 – Multiplication of Two Digit Numbers if the Tenth Place is same (Only Applicable if the Sum of the Ones is 10)

- 2 2 X 2 8

Step 1 = multiply the ones

= 28 = 16

Step 2 = multiply the tens number by its next number

= 2 X 3 = 6

**Step 3** = write the answer to multiplication of tens number and then the ones

= 616

**Step 4 **= 616 is the answer.

**2. 3 4 X 3 6 **

= 4 X 6 = 24

= 3 X 4 = 12

Write together

= 1224

= 1224 is the answer.

**3. 5 7 X 5 3 **

= 7 X 3 = 21

= 5 X 6 = 30

Write together

= 3021

= 3021 is the answer

**4. 89 X 81 **

*= 9* X 1 = 09

= 8 X9 = 72

= 7209

= 7209 is the answer

**Let’s Practice: –**

- 45*45
- 41*49
- 37*33
- 74*76

So, those are a few examples that show the magical nature of numbers