# Tips for Calculations (Part 2)

## TIP 6: Multiply a number by 9

In this case just add a zero to the end of the number and subtract it from the beginning number. Let's do the following multiplication: 44 x 9.

Adding a zero to the end of number 44 gives us 440.
Then we subtract from this value the initial value: 440-44 = 396.
So 44 x 9 = 396.

Another examples:
27 x 9 = 270-27 = 243.
56 x 9 = 560-56 = 504.
33 x 9 = 330-33 = 297.

## TIP 7: Multiply a number by 99

In this case just add 2 zeros to the end of the number and subtract it from the beginning number. Let's do the following multiplication: 44 x 99.

Adding 2 zeros at the end of number 44 gives us 4400.
Then we subtract from this value the initial value: 4400-44 = 4356.
Therefore 44 x 99 = 4356.

Another examples:
27x99 = 2700-27 = 2673
56x99 = 5600-56 = 5544
33x99 = 3300-33 = 3267

## TIP 8: Multiply a number by 101

When a 2-digit number AB multiplied by 101, the result will be ABAB. Some examples:

43 x 101 = 4343
32x101 = 3232
14 x 101 = 1414

## TIP 9: Multiply 2 numbers (2 digits) that have the same number as the tens, and the sum of their unit digits is 10

Examples of multiplications that can be done with this method: 42x48, 53x57, 21x29, 35x35, 87x83, 94x96, etc.

The following steps must be followed:
1) We multiply the digit of tens (which is equal to the 2 numbers) by the number following it;
2) We multiply unit numbers normally;
3) We put the two parts together.

Let's do the following multiplication: 53 x 57:
Step 1:
5x6 = 30
Step 2:
3x7 = 21
Step 3:
We put the two numbers together: 3021.
So 53 x 57 = 3021. Bearded!

Another example: 94x96:
Step 1:
9x10 = 90
Step 2:
4x6 = 24
Step 3:
We put the two numbers together: 9024.
So 94 x 96 = 9024. Bearded!

## TIP 10: Sum of n first odd natural numbers

The sum of no first odd natural numbers equals no2. Examples:

1) Sum of the first 5 odd natural numbers (1 + 3 + 5 + 7 + 9):
The sum is equal to 52 = 25.

2) Sum of the first 15 odd natural numbers:
The sum is equal to 152 = 225.

## TIP 11: Multiply a number by 15

Add the number with its half, and multiply the result by 10.
Examples:
14×15 =(14+7)×10=210
10,4×15=(10,4+5,2)×10=15,6×10=156

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