How to do Maths Quickly in Mind Without Calculator or Paper-Pencil

Posted BY Admin

Posted Date  26/07/2019


Do we really always need paper-pencil or calculator to solve basic mathematical problems? The answer is No. The following list will improve your general knowledge of mathematical tricks and your speed when you need to do Maths in your head without using a calculator or even paper-pencil.

  

(1). Quick Square

 

If you need to square a 2 digit number ending in 5, you can do so very easily with this trick.

 Multiply the first digit by itself + 1, and put 25 at the end. And that's all.

 

Example 1:

$$(25)^{2} = ?$$

$$= 2\times(2+1) = 6$$

$$\text{Now putting }25\text{ at end gives us}$$

$$= 625\text{ Which is the answer.}$$

 

Example 2:

$$(15)^{2} = ?$$

$$= 1\times(1+1) = 2$$

$$\text{Now putting }25\text{ at end gives us}$$

$$= 225\text{ Which is the answer.}$$

 

(2). Multiply by 5

 

Most people memorize the 5 times tables very easily, but when you get into larger numbers it gets more complex. This trick is super easy. So if you want to multiply any number by 5 then take the number and divide it by 2 (in other words, halve the number). If the result is the whole number, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works every time.

 

Example 1:

$$2682 \times 5 = ?$$

$$(2682 \div 2) = 1341\text{ (half of the number)}$$

As 1341 is a whole number, now just add 0 at the end. So 13410 is the answer.

 

Example 2:

$$5887 \times 5 = ?$$

$$5887 \div 2 = 2943.5\text{ (half of the number)}$$

As 2943.5 is a fractional number so ignore the remainder. And add 5 at the end. 29435 is the answer.

 

(3). Multiply Numbers from 1 to 9 by 9

 

Multiplying numbers from 1 to 9 by 9  is simple. To do so, hold both hands in front of you, drop the finger that corresponds to the number you are multiplying.

 

For example: 

$$9 \times 3 = ?$$

Drop your third finger from any of your hand, then count the fingers before the dropped finger (in the case of 9 x 3 it is 2). Then count the number of fingers after (in this case 7). So the answer is 27.

 

(4). Calculate 10% of a Number

 

If you want to calculate 10% of a number, simply move the decimal point one digit to left. And if the number is whole, then add a point by leaving one digit from the right side.

 

For example:

10% of 1550 =?

By adding a decimal point before the second last digit from the right side we get 155.0 which is 10% of 1550.

 

10% of 100.5 = ?

By moving the decimal point to one digit to left we get 10.05 which is the 10% of 100.5

 

(5). Calculate 15% of a Number

 

If you need to calculate 15% of a number, here is the easy way to do it. Work out 10% as described above then add that number to half that 10% value and you have your answer.

 

For Example

15% of 80 = ?

10% of 80  =  8

$$\text{half of }8 = \frac{8}{2} = 4$$

Now 8 + 4 = 12 is the 15% of 80.

 

(6). Tough Multiplication

 

If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:

 

32 x 125, is the same as:

16 x 250 is the same as:

 8 x 500 is the same as:

4 x 1000 = 4,000

 

(7). Dividing by 5

 

Dividing a large number by 5 is actually very simple. All you do is multiply the number by 2 and move the decimal point one digit to left.

 

Example:

$$195 \div 5 = ?$$ 

Step1: 195 x 2 = 390

Step2: Move the decimal to left: 39.0 or just 39.

 

(8). Assorted Multiplication Rules

 

Multiply by 5: 

Multiply by 10 and divide by 2.

 

Example:

$$96 \times 5 = ?$$

Step 1 (Multiply by 10):   $$96\times10 = 910$$

Step 2 (Divide by 2):        $$960 \div 2 = 480  \text{ (Answer)}$$

 

Multiply by 6: 

Sometimes multiplying by 3 and then 2 is easy.

 

Example:

45 x 6 = ?

Step 1 (Multiply by 3):  45 x 3 = 135

Step 2 (Multiply by 2):  135 x 2 = 270  (Answer)

 

Multiply by 9: 

Multiply by 10 and subtract the original number.

 

Example:

55 x 9 = ?

Step 1 (Multiply by 10):  55 x 10 = 550

Step 2 (Subtract Original Number):  550 - 55 = 495  (Answer)

 

Multiply by 12: 

Multiply by 10 and add twice the original number.

 

Example:

32 x 12 = ?

Step 1 (Multiply by 10):  32 x 10 = 320

Step 2 (Add Twice the Original Number):  320 + 64 = 384  (Answer)

 

Multiply by 13: 

Multiply by 3 and add 10 times the original number.

 

Example:

21 x 13 = ?

Step 1 (Multiply by 3):  21 x 3 = 63

Step 2 (Add 10 times of the Original Number):  63 + 210 = 273  (Answer)

 

Multiply by 14: 

Multiply by 7 and then multiply by 2.

 

Example:

20 x 14 = ?

Step 1 (Multiply by 7):  20 x 7 = 140

Step 2 (Multiply by 2):  140 x 2 = 280  (Answer)

 

Multiply by 15: 

Multiply by 10 and add 5 times the original number.

 

Example:

25 x 15 = ?

Step 1 (Multiply by 10):  25 x 10 = 250

Step 2 (Add 5 times the original number):  250 + 125 = 375  (Answer)

 

Multiply by 16: 

You can double four times if you want to. Or you can multiply by 8 and then by 2.

 

Example:

20 x 16 = ?

Step 1 (Multiply by 8):  20 x 8 = 160

Step 2 (Multiply by 2):  160 x 2 = 320 (Answer)

 

Multiply by 17: 

Multiply by 7 and add 10 times the original number.

 

Example:

15 x 17 = ?

Step 1 (Multiply by 7):  15 x 7 = 105

Step 2 (Add 10 times the original number):  105 + 150 = 255 (Answer)

 

Multiply by 18: 

Multiply by 20 and subtract twice the original number (which is obvious from the first step).

 

Example:

30 x 18 = ?

Step 1 (Multiply by 20):  30 x 20 = 600

Step 2 (Subtract twice the original number):  600 - 60 = 540 (Answer)

 

Multiply by 19: 

Multiply by 20 and subtract the original number.

 

Example:

35 x 19 = ?

Step 1 (Multiply by 20):  35 x 20 = 700

Step 2 (Subtract the original number):  700 - 35 = 665 (Answer)

 

Multiply by 24: 

Multiply by 8 and then multiply by 3.

 

Example:

14 x 24 = ?

Step 1 (Multiply by 8):  14 x 8 = 112

Step 2 (Multiply by 3):  112 x 3 = 336 (Answer)

 

Multiply by 27: 

Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).

 

Example:

14 x 24 = ?

Step 1 (Multiply by 8):  14 x 8 = 112

Step 2 (Multiply by 3):  112 x 3 = 336 (Answer)

  

Multiply by 45: 

Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).

 

Example:

25 x 45 = ?

Step 1 (Multiply by 50):  25 x 50 = 1250

Step 2 (Subtract 5 times of the original number):  1250 - 125 = 1125 (Answer)

 

Multiply by 90: 

Multiply by 9 (as above) and put a zero on the right.

 

Example:

17 x 90 = ?

Step 1 (Multiply by 9):  17 x 9 = 153

Step 2 (Put a zero on the right):  1530 (Answer)

 

Multiply by 98: 

Multiply by 100 and subtract twice the original number.

 

Example:

18 x 98 = ?

Step 1 (Multiply by 100):  18 x 100 = 1800

Step 2 (Subtract twice the original number):  1800 - 36 = 1764 (Answer)

 

Multiply by 99: 

Multiply by 100 and subtract the original number.

 

Example:

49 x 99 = ?

Step 1 (Multiply by 100):  49 x 100 = 4900

Step 2 (Subtract the original number):  4900 - 49 = 4851 (Answer)

 

(9). Bonus: Percentages

 

Finding 7% of 300 sounds Difficult?

First of all, you need to understand the word “Percent”. The first part is PER it means FOR EACH. The second part of the word is CENT, as in 100.

Like Century = 100 years. 100 CENTS in 1 dollar etc.

So

PERCENT = For Each 100. It follows that 7 PERCENT of 100, is 7. (7 for each hundred, of only 1 hundred). 

9 % of 100 = 9

24.52% of 100 = 24.52

 

But how is that useful?

 

Now come back to the problem, 7% of 300. 7% of the first hundred is 7. And 7% of the 2nd hundred is also 7, and yep,7% of the 3rd hundred is also 7. So 7+7+7 = 21. Also, it's useful to know that you can always flip percents. Like 

35% of 100 is the same as 100% of 3. 

35% of 8 is the same as 8% of 35.

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