## TIP 12: Times tables of 9

If you have difficulty decorating the 9 times tables, you can do the following:

1) Consider the number before which you will multiply 9.

2) See how much he has left to reach 9.

3) Join the two numbers found.

For example:

1) 9 x 2 => the number before two is the **1**.

2) For 1 to reach 9 **8**.

3) Now just join the two numbers: **18**

Therefore, **9 x 2 = 18**.

In the same way it can be done for the other numbers until it reaches 9x9:

1) 9 x 9 => the number before nine is the **8**.

2) For 8 to reach 9 **1**

3) Now just join the two numbers: **81**

Therefore, **9 x 9 = 81**.

## TIP 13: Divide any number by 5

Just multiply the number by 2 and "drag" the comma to the left.

Ex: 345/5 = 345 * 2 = 690. Dragging the comma gives 69.0.

Ex: 1526/5 = 1526 * 2 = 3052. Dragging the comma gives us 305.2.

## TIP 14: How to find out the next square?

Add the previous square twice with the number you want to find the square from, then decrease it by one.

Ex: If 3^{2} = 9, how much is 4^{2}?

Applying the rule we have:

9 + 4 + 4 = 17

17 - 1 = 16

So 4^{2} = 16

Another example: 5^{2} = ?

16 + 5 + 5 - 1 = 25

## TIP 15: Addition: Rounding from 2nd installment to a convenient multiple of 10

The 2nd installment is rounded to the 1st multiple of 10 below this number. Subsequently, the difference between the original number and the rounded number is added.

Examples:

23 + 36 = 23 + 30 + 6 = 53 + 6 = 59

357 + 459 = 357 + 450 + 9 = 807 + 9 = 816

Note: When convenient, round the 2nd installment to the 1st multiple of 10 over this number. Subsequently, the difference between the rounded number and the original number is subtracted.

Example:

357 + 459 = 357 + 460 - 1 = 817 - 1 = 816

## TIP 16: Multiplication by numbers ending in 0

Multiply the parts without the leading zeros and add the amount of trailing zeros.

Examples:

23 x 10 = (23 x 1) 0 = 230

45x20 = (45x2) 0 = 900

15x300 = (15x3) 00 = 4500

30x90 = (3x9) 00 = 2700

## TIP 17: Sum of a group of tens

To find the sum of a group of ten tens (starting at the end 0), just change the number of units by 45. For example, let's consider the number 4260. The sum of ten tens starting with it would be:

4260+4261+4262+4263+4264+4265+4266+4267+4268+4269 = 42645

Using the hint would be easier, just remove the zero and add the 45:

This is because if we added the units separately, we would have 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. *Tip Submitted by Rivonaldo Medeiros Dantas*.

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