MATHS SHORTCUTS
 

SHORTCUTS, PUZZLES..

 

ADDITION SHORTCUTS.....

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People think adding big numbers in mind is difficult.

Read this and practice this to do add numbers in mind easily.

Let's take an example,

     7133 + 498 + 6192 + 520 = ????

Looks difficult??

Generally what we do in our traditional method is write down the numbers one below another and add them, this is difficult to do.

But use the following method,

     7  1  3  3 

+      4  9   8

+   6  1  9  2 

+       5  2  0

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Take a column and add the numbers say, 3 plus 8 plus 2 plus 0

    Note: While adding don't take a number greater than '10', while adding when you get more than '10', make a mark(*) and subtract the number from '10'

In our case, 3+8 = 11, so make a mark in 8 and subtract 11 from 10, so 11 - 10 = 1, then continue 1 plus 2 = 3, then 3 plus 0 = 3.

Write down 3. 

Count the number of marks made, here it is 1.

Write down 1.

    7  1   3  3 

+      4  9  8 *

+   6  1  9  2 

+       5  2  0

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                 3
               1

Take the second column, 3 plus 9 plus 9 plus 2.

3 + 9 = 12, so mark one (*) and 12 - 10 = 2, then 2 plus 9 = 11, so mark two, 11 - 10 = 1, 1 plus 2 = 3.

Write down 3.

Count the number of marks made, here it is 2.

Write down 2.

    7  1   3    3  

+      4  9*  8

+   6  1  9    2 

+       5  2 * 0

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               3   3
             2   1

Repeat the same for each column and you will get as,

    7  1   3  3 

+      4  9  8 

+   6  1  9  2 

+       5  2  0

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      3  1  3  3
      1  1 2  1


Take these two numbers and add as shown below, add zero in front of first row and then add zero to the end of second row,

      0 3  1  3 3
      1  1  2 1 0

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      1 4 3 4 3

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Answer is 

    7  1   3  3 

+      4  9  8 

+   6  1  9  2 

+       5  2  0

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       1 4 3 4 3  
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ADDITION OF CONSECUTIVE NUMBERS SHORTCUTS.....

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Adding consecutive numbers in mind will be easy. But needs continuous practice.

First what is consecutive numbers, 

Consecutive numbers are continuous numbers from one start to end,

Let's take an example,

Numbers from 1 to 10, 1,2,3,4,5,6,7,8,9,10.

Numbers from 24 to 31, 24,25,26,27,28,29,30,31.

This shortcuts is to add consecutive numbers (or) find sum of consecutive numbers.

Example1:

Lets find sum of consecutive numbers from 24 to 31.

Step1: Take first number and last number and add them,

            24 + 31 = 55

Step2: Count the number of digit between 24 and 31, it is 8 digits. (31 - 24) + 1 = 8

Step3: Multily the answer of Step1 and Step2 and then divide by 2, 

             55 x 8 = 440 ,  440 / 2 = 220. 

Answer to sum of consecutive numbers from 24 to 31 = 220.


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PERCENTAGE SHORTCUTS.....

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Doing percentage in mind will be easy. But needs continuous practice.

Let's take an example,
60% of 800.

100% of 800 = 800

   50% of 800 = 400

    10% of 800 = 80

       5%  of 80 = 40

Thats it,  60% = 50% + 10% = 400 + 80 = 480.

Answer: 60% of 800 =480. (in mind in few secs...)


15% of 800. 

10% + 5% = 80+40 = 120

Answer: 15% of 800 = 120. (in mind in few secs...)

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SQUARE OF ANY NUMBER ENDING IN 9 .....

Square any number ending in 9 very easily,

Let's take an example,
Finding the square of 19

Step1: Firstly add 1 to the number. The number now ends in zero and is easy to square.
20^2 = 400. 
Step2: Add 20 plus 19 (the number we squared plus the number we want to square)
20 + 19 = 39
Step3: Subtract 39 from 400, answer is 400 - 39 =361.


Another Example finding the square of 99,

99 + 1 = 100

100^2 = 10000
100 + 99 = 199
10000 – 199 = 9801.

So, square of 99 is 9801.  

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MULTIPLY ANY TWO NUMBERS FROM 11 TO 20 IN FEW SECS.. 

With this shortcuts, in secs you can multiply any two numbers from 11 to 19.
You must know tables till 10.

Let's take an example,

  Take 17 x 16,
   
Out of these two numbers, keep the big number fully and from small number,take the last number
Add these two numbers, add 17 + 6 = 23
Add a zero at last, to get 230.
Multiply the last digit of both the numbers, (7x6= 42)
Add 230 + 42 = 272.
So answer of 17 x 16 = 272 (in very few secs.)

Few more examples,
19 x 18,
19 + 8 = 27,
add zero 270,
9 x 8 =72,
add 270 + 72 = 342.......

Try more examples, practice this and enjoy...

 
 

DECIMAL FRACTIONS 

Just have a look, practice and do fast!! 

First we will start with easy one, 

Fraction by 10,
Just add decimal to numerator.

1/10 = .12/10 = .23/10 = .3
4/10 = .4
5/10 = .5
6/10 = .6
7/10 = .7
8/10 = .8
9/10 = .9

Fraction by 2,

1/2 = .5

Fraction by 3,

1/3 = .333...
2/3 = .666...

 

Fraction by 4, Just add .25,

1/4 = .25
2/4 = .50
3/4 = .75

Fraction by 8, Just add .125,

1/8 = .125
2/8 = .250
3/8 = .375
4/8 = .500
5/8 = .625
6/8 = .750
7/8 = .875

Fraction by 5,  
Just even numbers (or) double the numerator,

1/5 = .2
2/5 = .4
3/5 = .6
4/5 = .8

Fraction by 6,
No way,

1/6 = .1666...
2/6 = 1/3 = .333...
3/6 = 1/2 = .5
4/6 = 2/3 = .666...
5/6 = .8333...

 

Fraction by 9, Most easy to remember,
Just keep a decimal & repeat the numerator...

1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888... 

Fraction by 11,
The next easy one,
Take numerator x9 (multiples of 9)
 
1/11 = .090909...
2/11 = .181818...
3/11 = .272727...
4/11 = .363636...
5/11 = .454545...
6/11 = .545454...
7/11 = .636363...
8/11 = .727272...
9/11 = .818181...
10/11 = .909090...

Fraction by 7,

1/7 = .142857142857142857...
2/7 = .285714285714285714...

See the pattern ".142857", for each fraction this moves in circular way,

1/7 = .142857...    
for starting (1*14 =14)
2/7 = .285714...   
for starting (2*14 =28)
3/7 = .428571...   for starting (3*14 =42)
4/7 = .571428... for starting (4*14+1 =57)
5/7 = .714285... for starting (5*14+1 =71)
6/7 = .857142... for starting (6*14+1 =85)

CALCULATE TIME USING ROPE 

You have two ropes of equal size which can burn for 1 hour each. You have only rope, lighter/match box with you and you don't have any other things.

How will you calculate 30 minutes & 90 minutes?

Answer:

To calculate 30 minutes:

First light up the two ends of the first rope (30 min).


To calculate 90 minutes:

First light up one end of the first rope (60min). When it will burn out light up the two ends of the second candle (30 min).   Total 30+60=90.


3 SWITCH 1 LIGHT PUZZLE 

A room without window has 1 light.  Outside the room there are 3 switches. You are outside the room and the door of the room is closed. The light is connected with one switch out of the three. You can go into the room - one time only - to see the light. 

Find out which out of the three light switches controls the light inside the room?

Answer:

First switch on the first switch for about 5 - 10 min and then switch off the first switch and switch on the second switch; and then enter the room.

Inside the room, there are three cases are possible

1. If Bulb is on => 2nd switch is the answer.

2. If Bulb is off and on touching the bulb, if it is hot => 1st switch is the answer.

3. If Bulb is off and on touching the bulb, if it is normal => 3rd bulb is the answer.


SHORTCUT# NUMBER DIVISIBLE BY 7

From the given number,  Take the last digit, multiply by 2 and  subtract it from the truncated original number, repeat this until only one digit remains. 

If unit digit is 0 or 7, then the original number is divisible by 7

Example: 

Consider the number 147, 

14(7), take 7, multiply by 2 which is 14.

So 14 -14 = 0, So we can say 147 is divisible by 7, lets try one more example.


Consider the number 1603, 

160(3), take 3, multiply by 2 which is 6.

So 160 - 6 = 154, 

again, 15(4), 15-(4 x 2) = 15 - 8 = 7, 

So we can say 1603 is divisible by 7, lets try one more example.


Consider the number 2842, 

284(2), take 2, multiply by 2 which is 4.

So 284 - 4 = 280, 

again, 28(0), 28-(0 x 2) = 28, 28 is divisible by 7

So we can say 2842 is divisible by 7.

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