Maths Tricks

Multiply any two numbers from 11 to 20 in your head.

Take 15 x 13 for example..

Place the larger no. first in your mind and then do something like this Take the larger no on the top and the second digit of the smaller no. in the bottom.

15

3

The rest is quite simple. Add 15+3 = 18 . Then multiply 18 x 10 = 180 ...

Now multiply the second digit of both the no.s (ie; 5 x 3 = 15) Now add 180 + 15

Here is the answer 180 + 15 = 195 .

Think over it. This is a simple trick. It will help you a lot.

 

Multiply any number from 1 to 10 by 9

To multiply by 9,try this:
(1) Spread your two hands out and place them on a desk or table in front of you.
(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.
(3) the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.

This one was really cool wasn't it

 

Multiply any two digit number with 11.

This trick is much simpler than the previous one and it is more useful too. Let the number be 27 . Therefore 27 x 11

Divide the number as 2 _ 7

Add 2+ 7 = 9

Thus the answer is 2 9 7

Wasn't this one simple. But there is one complication. If you take a number like 57 Thus _57 x 11

Divide the number as 5 _ 7

Add 5 + 7 = 12

Now add 1 to 5 and place 2 in the middle so the answer is 5+1_2 _7 = _627

Thus the answer is 627

 

Multiply any number by 11 .

Trick number 2 tells you how to multiply a two digit number by 11 but what if you have a number like 12345678 . Well that is very easy if you our trick as given below . Read it carefully.

Let the number be 12345678 __ thus 12345678 x 11

Write down the number as 012345678 ( Add a 0 in the beginning)

Now starting from the units digit write down the numbers after adding the number to the right

So the answer will be 135802458

This one is simple if you think over it properly all you got to do is to add the number on the right . If you are getting a carry over then add that to the number on the left. So I will tell you how I got the answer . Read carefully.

The number was 12345678 ___ I put a 0 before the number ____ so the new number 012345678

Now I wrote ___ 012345678

Then for the answer

8 + 0 = 8

7 + 8 = 15 (1 gets carry carried over)

6+1+7 = 14 ( 1 gets carried over)

5 + 1 + 6 = 12 ( 1 gets carried over)

4 + 1 + 5 = 10 ( 1 gets carried over)

3 + 1 + 4 = 8

2 + 3 = 5

1 + 2 = 3

0 + 1 = 1

Thus the answer = 135802458

Now I hope you have understood the trick if you want more help please contact me by e-mail using the contact form given below. Please don't fail to mention your e-mail address as it is essential to contact back.

 

Square any two digit number

Suppose the number is 47 . Look for the nearest multiple of 10 . ie; in this case 50 . We will reach 50 if we add 3 to 47. So multiply (47+3) x (47-3) = 50 x 44 = 2200 This is the 1st interim answer.

We had added 3 to reach the nearest multiple of 10 that is 50 thus 3x 3 = 9 This is the second interim answer.

The final answer is 2200 + 9 = 2209 ... Practice This one on paper first.

 

Square a 2 Digit Number, for this example 37:

Look for the nearest 10 boundary
In this case up 3 from 37 to 40.
Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
Now mentally multiply 34x40
The way I do it is 34x10=340;
Double it mentally to 680
Double it again mentally to 1360
This 1360 is the FIRST interim answer.
37 is "3" away from the 10 boundary 40.
Square this "3" distance from 10 boundary.
3x3=9 which is the SECOND interim answer.
Add the two interim answers to get the final answer.
Answer: 1360 + 9 = 1369

With practice this can easily be done in your head.

 

Squaring numbers in the hundreds.

If the number to be squared is 106:
Square the last two digits (no carry): 6 x 6 = 36: _ _ _ 3 6
Add the last two digits (06) to the number: 106 + 6 = 112: 1 1 2 _ _
So 106 x 106 = 11236.
See the pattern?

If the number to be squared is 112:
Square the last two digits (keep carry 1): 12 x 12 = 144: _ _ _ 4 4
Add the last two digits (12) plus the carry (1) to the number:
112 + 12 + 1 = 125: 1 2 5 _ _
So 112 x 112 = 12544.

 

Squaring a number in the three hundreds

Choose a number in the 300s (practice with numbers under 310, then progress to larger ones).
Square the first digit = : 9 _ _ _ _
The next two digits will be 6 times the last 2 digits: _ X X _ _
The last two places will be the square of the last digit: _ _ _ X X
Example:
If the number to be squared is 309:
The first digit is 9: 9 _ _ _ _
The next two digits are 6 times the last digit:
6 x 9 = 54: _ 5 4 _ _
Square the last digit: 9 x 9 = 81: _ _ _ 8 1
So 309 x 309 = 95481.

For larger numbers reverse the steps:

Square the last two digits (keep the carry): _ _ _ X X
6 times the last two digits + carry: _ X X _ _
Square the first digit + carry: X _ _ _ _

See the pattern?


If the number to be squared is 325:
Square last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ 2 5
6 times the last two digits + carry:
6x25 = 150; 150+6 = 156 (keep 1): _ 5 6 _ _
Square the first digit + carry:
3x3 = 9; 9+1 = 10: 1 0 _ _ _ _
So 325 x 325 = 105625.

 

Squaring numbers in the five hundreds

Choose a number in the 500s (start with low numbers at first; then graduate to larger ones).
The first two digits of the square are 25: 2 5 _ _ _ _
The next two digits will be 10 times the last 2 digits: _ _ X X _ _
The last two places will be the square of the last two digits: _ _ _ _ X X
Example:
If the number to be squared is 508:
The first two digits are 25: 2 5 _ _ _ _
The next two digits are 10 times the last 2 digits:
10 x 8 = 80: _ _ 8 0 _ _
Square the last digit: 8 x 8 = 64: _ _ _ 6 4
So 508 x 508 = 258,064.

For larger numbers reverse the steps:

Square the last two digits (keep the carry): _ _ _ _ X X
10 times the last two digits + carry: _ _ X X _ _
25 + carry: X X _ _ _ _

See the pattern?


If the number to be squared is 525:
Square the last two digits (keep the carry):
25 x 25 = 625 (keep 6): _ _ _ _ 2 5
10 times the last two digits + carry:
10 x 25 = 250; 250 + 6 = 256 (keep 2): _ _ 5 6 _ _
25 + carry: 25 + 2 - 27: 2 7 _ _ _ _
So 425 x 425 = 275,625.

 

Square a two digit number ending in five

This one is as easy as the previous ones but you have to pay a little more attention to this one . Read carefully :

Let the number be 35

35 x 35

Multiply the last digits of both the numbers ; thus ___ 5 x 5 = 25

now add 1 to 3 thus 3 + 1 = 4

multiply 4 x 3 = 12

thus answer 1225

You will have to think over this one carefully.As 5 has to come in the end so the last two digits o the answer will be 25 . Add 1 to the first digit and multiply it by the original first digit . Now this answer forms the digits before the 25. Thus we get an answer .

 

Squaring a number in the two hundreds.

Choose a number in the 200s (practice with numbers under 210, then progress to larger ones).
Square the first digit = 4: __4 _ _ _ _
The next two digits will be 4 times the last 2 digits: _ X X _ _
The last two places will be the square of the last digit: _ _ _ X X


Example:
If the number to be squared is 206:
The first digit is 4: 4 _ _ _ _
The next two digits are 4 times the last two digits :
4 x 6 = 24: _ 2 4 _ _
Square the last digit: 6 x 6 = 36: _ _ _ 3 6
So 206 x 206 = 42436.

For larger numbers work right to left:

Square the last two digits (keep the carry): _ _ _ X X
4 times the last two digits + carry: _ X X _ _
Square the first digit + carry: X _ _ _ _

See the pattern?

If the number to be squared is 225:
Square last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ 2 5
4 times the last two digits + carry:
4x25 = 100; 100+6 = 106 (keep 1): _ 0 6 _ _
Square the first digit + carry:
2x2 = 4; 4+1 = 5: 5 _ _ _ _
So 225 x 225 = 50625.

 

Squaring numbers in the four hundreds

Choose a number in the 400s (keep the numbers low at first; then progress to larger ones).
The first two digits of the square are 16: 1 6 _ _ _ _
The next two digits will be 8 times the last 2 digits: _ _ X X _ _
The last two places will be the square of the last two digits: _ _ _ _ X X
Example:
If the number to be squared is 407:
The first two digits are 16: 1 6 _ _ _ _
The next two digits are 8 times the last 2 digits:
8 x 7 = 56: _ _ 5 6 _ _
Square the last digit: 7 x 7 = 49: _ _ _ 4 9
So 407 x 407 = 165,649.

For larger numbers reverse the steps:

Square the last two digits (keep the carry): _ _ _ _ X X
8 times the last two digits + carry: _ _ X X _ _
16 + carry: X X _ _ _ _

See the pattern?


If the number to be squared is 425:
Square the last two digits (keep the carry):
25 x 25 = 625 (keep 6): _ _ _ _ 2 5
8 times the last two digits + carry:
8 x 25 = 200; 200 + 6 = 206 (keep 2): _ _ 0 6 _ _
16 + carry: 16 + 2 = 18: 1 8 _ _ _ _
So 425 x 425 = 180,625.

 

Finding 5 percent of any number

Trick 1 : Finding 5 percent of any number
Choose a large number (or sum of money).
Move the decimal point one place to the left.
Divide by 2 (take half of it).

Example:
If the amount of money selected is Rs. 850:
Move the decimal point one place to the left.: 85
Divide by 2: 85/2 = 42.50
So 5% of Rs.850 = Rs.42.50.
See the pattern?

If the amount of money selected is Rs. 4500:
Move the decimal point one place to the left.: 450
Divide by 2: 450/2 = 225
So 5% of Rs.4500 = Rs. 225

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