Unleash Your Mental Math Potential:Become a Human Calculator

Regular way is called as Right to Left Arithmetic which we have learnt in our schools. But the technique is utilizing the Left to Right Arithmetic. In order to use this techniques we have to divide the number as 1's, 10's, 100's, etc. Then we have to add the corresponding digits. If we use this method we can solve adding problems by our mind without using a pen and a paper. Thus, it is highly recommended for you to practice this Left to Right Arithmetic Technique to solve addition by mind.

If we are going to subtract a 2 digit number from an original number. We have to identify that particular number whether it is more than 5 or less than 5.

Rounding Up Method

If the number is higher than 5 we have to round the number for the next 10's. And then, we have to find the difference which is between the number and the rounded 10's. Then finally, We have to add the difference and the original number to find out the final answer.

As an example: 32 - 19. Consider 19 as the subtracting number  and 32 is the original number. Thus we have to round up 19 as to the next 10's. Thus, it will be changed as 20. Then we have to find the difference between 20 and 19. It is equal to 1. If we obtain the next 10's (Called as round up) the difference will be added with the original number.

This is how the technique works mathematically.

What is 32 - 19 = ?

32 - 19 =

=  32 - (20 - 1)

= 32 - 20 + 1

= (32 - 20) + 1               This is very easy to solve the bracket by our mind

= 12 + 1

= 13.

Rounding Down Method

If the number is less than 5 we have to round down the number for the earlier 10's. And then, we have to find the difference which is between the number and the rounded 10's. Then finally, We have to subtract the difference from the original number to find out the final answer.

As an example: 64 - 31. Consider 11 as the subtracting number  and 32 is the original number. Thus we have to round down 31 as to the earlier 10's. Thus, it will be changed as 30. Then we have to find the difference between 30 and 31. It is equal to 1. If we obtain the earlier 10's (Called as round down) the difference will be subtracted form the original number.

This is how the technique works mathematically.

What is 64 - 31 = ?

64 - 31

=  64 - (30 + 1)

= 64 - 30 - 1

= (64 - 30) - 1               This is very easy to solve the bracket by our mind

= 34 - 1

= 33.

Multiplying by  ( 0 - 9 ) is very simple. We have to divide the numbers as 1's, 10's, 100's, etc. Then we have to do the LEFT TO RIGHT Arithmetic to find the answer. So that we have to multiply, in an order of higher digits to lower digits. Then we can use the LEFT TO RIGHT ADDITION Technique to add these numbers together.

Multiplying by 10

Multiplying by 10 is very easy as we add a zero after the number. Example : 45 X 10 = 450. Similarly

Multiplying by 11

This is also very easy. Copy and paste the last digit and the first digits. Add the digits together to find the between numbers. But the in a place only one digit should be placed in the answer. If it becomes as a 2 digit we have to set the 10's as a reminder and add when calculating the next stuffs. Watch the video to know how easy it is.

Example: 23 X 11 =

The last digit is 3 will come 3 as the last digit in the answer.

in the middle digit in the answer we have to add the 2 digits together. Such as add 2 + 3 = 5. Thus, 5 is the middle digit.

Finally for the first digit in the answer 2 will become as 2.

Thus, the answer is = 253. Simple!!!

NOTE: Multiplying (12 - 19) : A new trick to quickly multiply. But, both the numbers should be within this range in order to pursue this method.

In this lecture we learn how to multiply any 2 digit number. Basically we will calculate in the range of (21 - 89).

However, it will be difficult to calculate 91 - 99 by using this technique even though they lie in this range. Thus, we have a separate technique to solve the arithmetic problems in the range of  (91 - 99) given in the next lecture.

99 - 100 : Simple obtain the difference between hundred and multiply the differences. Place the multiplied answer of the differences as two digits in the answer. Then subtract the the first difference from the second number or subtract the the second difference from the first number. Both will give the same answer.

NOTE: In this method we have to write down the multiplications of the differences as two digits even it comes as a single digit answer.

Example:

98 X 96 = ?

Difference between 98 and 100 = 2 >>>>>First difference

Difference between 96 and 100 = 4 >>>>>Second difference

Now multiply the differences together.

then it will come as 2 X 4 = 8 >>>>>But this 8 should be written as 08 in the answer. Thus, the final 2 digits of the answer is 08.

Now finding the first two digits of the answer. This is very simple.

Subtract the First Difference from the second number of vice versa.

So, it will become as 96 - 2 = 94. OR VISE VERSA, 98 - 4 = 94. Both are same answers as 94.

Thus, we found the first two digits of the final answer as 94.

Finally, the answer is 9408.

i.e. 98 X 96 = 9408.

101-119: Simple obtain the difference between hundred and multiply the differences. Place the multiplied answer of the differences as two digits in the answer. Then ADD the the first difference from the second number or ADD the the second difference from the first number. Both will give the same answer.

NOTE: In this method we have to write down the multiplications of the differences as two digits even it comes as a single digit answer.

Example:

103 X 102 = ?

Difference between 103 and 100 = 3 >>>>>First difference

Difference between 102 and 100 = 2 >>>>>Second difference

Now multiply the differences together.

then it will come as 3 X 2= 6 >>>>>But this 8 should be written as 06 in the answer. Thus, the final 2 digits of the answer is 06.

Now finding the first three digits of the answer. This is very simple.

ADD the First Difference from the second number of vice versa.

So, it will become as 3 + 102 = 105. OR VISE VERSA, 2 + 103 = 105. Both are same answers as 105.

Thus, we found the first three digits of the final answer as 105.

Finally, the answer is 10506.

i.e. 103 X 102 = 10506.

When multiplying numbers in this case we have to combine the techniques learnt from 11, 12 - 19, 21 - 89 multiplication and 101 - 109 multiplication techniques.

Obtain the difference between hundred and multiply the differences. Place the multiplied answer of the differences as two digits in the answer. When finding the answer of the multiplication of the differences we have to use the techniques learnt in previous multiplications such as 11, 12 - 19, 21 - 89 multiplication techniques.

Then ADD the the first difference from the second number or ADD the the second difference from the first number. Both will give the same answer. In addition also we have to use the technique learnt in our addition technique. Then only we can find the answer from our mind. That is why the course is started with the basic addition technique. So if you have omitted the Addition Technique please revisit the Lecture No. 02.

NOTE: In this method we have to write down the multiplications of the differences as two digits even it comes as a single digit answer.

Example:

113 X 112 = ?

Difference between 113 and 100 = 13 >>>>>First difference

Difference between 112 and 100 = 12 >>>>>Second difference

Now multiply the differences together.

then it will come as 13 X 12= 156 >>>>> This is in 3 digits. We only have to write them in two digits. Thus the first digit '1' is a reminder.  Thus, the answer's last 2 digits will become as 56.

Now finding the first three digits of the answer.

ADD the First Difference from the second number of vice versa.

So, it will become as 13 + 112 = 125. OR VISE VERSA, 12 + 113 = 125. Both are same answers as 125.

Then we have to add the remainder with 125.

Thus, we found the first three digits of the final answer as 126.

Finally, the answer is 12656.

i.e. 113 X 112 = 12656.

In this category, the course will provide techniques about how to divide any numbers by 2, 4, 5, 8 and 25. These divisions can be done very easily.

Division by 2

If we are going to divide any number by 2 we have to half the given number once.

Division by 4

If we are going to divide any number by 4 we have to half the given number twice.

Division by 8

If we are going to divide any number by 8 we have to half the given number thrice.

Division by 5

If we are going to divide any number by 5 we have to multiply the number by 2. To do that, we can use the technique learnt in Multiplication of (0 - 9) Numbers in this course. Or simply we can double the number.

After multiplying by 2 or doubling the given number we have to take a decimal point towards left or divide by 10 to obtain the final answer.

Example: 34 / 5 = ?

Double 34.

34 X 2 = 68

Then, take a decimal point towards left or divide by 10.

Thus, the  answer will become as 68/10 = 6.8

Division by 25

If we are going to divide any number by 25 we have to multiply the number by 4. To do that, we can use the technique learnt in Multiplication of (0 - 9) Numbers in this course. Or simply we can double the number twice.

After multiplying by 4 or doubling the given number twice we have to take 2 decimal points towards left or divide by 100 to obtain the final answer.

Example: 34 / 25 = ?

Double 34.

34 X 2 = 68.

Double 68.

68 X 2 =136.

Then, take 2 decimal points towards left or divide by 100.

Thus, the  answer will become as 136/100 =1.36

A5 Square Technique

If we are going to find the square of a number which is ending with 5, it will be very easy. Always 25 will become as the last two digits. Then we have to find the first digit/s. In order to find the find the first digit/s we have to obtain A. Then we have to add 1 from A. Then we have to multiply A by (A+1). Then the first digit will become as the answer of A(A+1).

Example: 35 ^2

Here, A is 3

This 35 is ending with 5. Thus we can use this A5 square technique.

If we find A = 3. Then > A + 1 = 3 + 1 = 4.

After that find A x (A + 1)  = 3 X 4 = 12.

Final digits will become as 25 for always.

Thus the final answer for the square of 35 is = 1225.

Further quick examples:

45 ^ 2 = 2025

55 ^ 2 = 3025

65 ^ 2 = 4225

Near a Known Number Technique

If we are going to find the square of a number which is near to a square known number, it is very easy. 

A ^ 2 - B ^ 2 = (A - B) (A+B)

Thus if we arrange components for finding A ^ 2,

A ^ 2 = ( A - B )  (A + B ) + B ^ 2  .............................(1)

Example:

21 ^ 2 = ?

In this example A =21 and B = 1

From (1) >>>>>>>

A ^ 2 = ( A - B )  (A + B ) + B ^ 2

21 ^ 2 = ( 21 - 1 ) ( 21 + 1 ) + 1 ^ 2

21 ^ 2 = (20 ) ( 22 ) + 1

21 ^ 2 = 440 + 1

21 ^ 2 = 441

Mirror Technique

This is an special case of multiplications. If two numbers are multiplied together and they are mirror to a 3rd number, we can use the Mirror Technique.

Example ,

If 18 and 22 are multiplied together,

we can easily find the answer.

Because these two numbers are mirror to a third number which is 20.

18 is obtained from 20 by subtracting 2 and 22 is obtained from 20 by adding 2. That is why we call 20 as a mirror to these numbers.

To find the answer,

Step 1 : Obtain the square of the mirror.

20 ^ 2 = 400

Step 2 : Obtain the difference from the mirror.

The difference between 20 and 18 is = 2

Step 3 : Obtain the square of the difference.

2 ^ 2 = 4

Step 3 : Subtract the square of the difference from the square of the mirror.

Calculate 20 ^ 2 - 2 ^ 2 = 400 - 4 = 396.

Example 2

If 34 and 36 are multiplied together,

we can easily find the answer.

Because these two numbers are mirror to a third number which is 35.

34 is obtained from 35 by subtracting 1 and 36 is obtained from 35 by adding 1. That is why we call 35 as a mirror to these numbers.

To find the answer,

Step 1 : Obtain the square of the mirror.

35 ^ 2 =   1225 >>>>>>>>>RECALL THE A5 SQUARING TECHNIQUE. >>>>>{3} X {3+1} 25

Step 2 : Obtain the difference from the mirror.

The difference between 35 and 34 is = 1.

Step 3 : Obtain the square of the difference.

1 ^ 2 = 1

Step 3 : Subtract the square of the difference from the square of the mirror.

Calculate 35 ^ 2 - 1 ^ 2 = 1225 - 1 = 1224.

How cool is that!!!

Practice - Practice - Practice. Think 10 examples from your mind and solve them without obtaining a paper or a calculator. When you are free you can think about the techniques and do arithmetic according to the techniques. Then these techniques will be familiarized. So you can use them in your examinations and save more time in exams. 

ALL THE BEST!!!

This is a downloadable exercise. You can download this and Solve the problems by using your mind when you are free.