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8/11/2019 Shortcut for Tricks & Calculations - Shortcut & Tricks for Calculations2

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Multiplication Techniques

Example

Find 42 x 48 ?

Solution

Both the numbers here start with 4 and the unit digits (2 and 8) add up to 10.

Steps:

1. First multiply the unit digit of the number: 2 8 = 16

2. Then multiply 4 by 5 (the succeeding number) to get 20 for the first part of

the answer.

3. So, Required answer is 2016.

Example

Find 44 64?

Solution

1. Here tens digit are 4 and 6 and their sum is 10 and unit digits of both

numbers are same. Multiplying the unit digits, we get 4 4 = 16. Put it

at right hand side.

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Multiplication Techniques

Multiplying 2-digit numbers where the Tens digit add up to 10 and Unit digits

are same:

Suppose, we want to find the multiplication of two numbers AB & CB (where A,

B, C represent various digits of the numbers) and these two numbers satisfy a

condition which says A + C = 10, then we can follow the following steps to find

the answers.

First find the multiplication of last two digit of both the numbers ie.

Find B x B. It will give us last 2 digits of the answer.

Multiply the Tens digits and Add the common digit to the

multiplication ie. find AxC + B. It will give us the initial digits of the

multiplication.
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Comment

2. Again multiplying the tens digits of numbers and adding common

digit, we get (4 6) + 4 = 24 + 4 = 28. Put it at the left hand side. So, we

get required answer as 2816.

Multiplying numbers just over / below 100.

Example

108 109?

Solution

108 109 = 11772. The answer is in two parts: 117 and 72, 117 is just 108 + 9

(or 109 + 8), and 72 is just 8 9.

Now, check for 107 106 = 11342. As before, the surpluses above the base

of 100 are set down on the right.

100 + 15 + 7 = 122 or 115 + 07 = 122 or 115 + 7 = 122 or 107 + 15 = 122

7 15 = 105, but since the right-hand portion has only two digits we must

carry the 1 of 105 to the left. So, the answer is 12305.

Special Multiplication Technique for 5, 25, 125 & 625

Number Method Example

Multiplication by 5

Put one 0 at the end of

the number and devide

by 2 512x5 = 5120/2=2560

Multiplication by 25

Put two 0 at the end of


by 4

512x25 =

51200/4=12800


Put three 0 at the end of


by 8

512x125 =

512000/8=64000


Put Four 0 at the end of


by 16

512x625 =

5120000/16=320000

Multiplication of digits near 100

Our approach should be this:

Note: The above method can be applied to numbers which are just above

10000 as well, by changing the base to 1000 instead of 100.


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Comment

Whenever we have more than 100 on the right hand side we add the digits at the

100 place to the left hand side (as shown above). In the above case the digit at

the 100 place is 1 so we will be required to add 1 to the left and side of the

digit, thus our answer comes to 7743 which is same as obtained by conventionalmethod.

Multiplication of digit near 50

We can state 50 = 100/2

Therefore, we will divide the number obtained after crosswise operation by 2.

Example

33/39 = 3339 or 66 50 (Base) + 39 = 3300 + 39 = 3339

Example

Cross wise operation (47 + 14) or (64 3) given us 61.

To get 3050, you can simply multiply the left-hand (61) side by 100 and divide by

2 to get the desired result.

Multiplication of a 2-digit number by a 2-digit number

Example

th

th


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12 13?

Solution

Steps:

1. Multiply the right-hand digits of multiplicand and multiplier (unit-digit

of multiplicand with unit-digit of the multiplier).

2. Now, do cross-multiplication, i.e., multiply 3 by 1 and 1 by 2. And the

two products and write down the left of 6.

3. In the last step we multiply the left-hand figures of both multiplicand

and multiplier (tens digit of multiplicand with tens digit of

multiplier).

So, the answer is 156.

Example

325 17 = ?

Solution

Steps:

Step 1

(5 7 = 35, put down 5 and carry over 3)

Step 2


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Comment

(2 7 + 5 1 + 3 = 22, put down 2 and carry over 2)

Step 3

(3 7 + 2 1 + 2 = 25, put down 5 and carry over 2)

Step 4

So, answer is 5525

Three digit number multiplied by three digit number

Now let us try to see the Magical method. We will explain this method using our

old friends a, b, c and x, y, z.

Example

How to gain speed?

The key to speed is to do away with the intermediate steps:

This is being explained with the help of the following example.

To get better results, you should try to do all intermediate steps mentally and

directly write down the answers in each step.


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Comment

Comment

Multiplying any number with 11

With a little practice method can be applied without writing but some care must

be taken when carry overs are involved.

Squaring Any 2 Digit Number Boundary Method

1. Look for the nearest 10 boundary. Eg. 3 from 47 to 50

2. Since we went up 3 to 50, now go down 3 from 47 to 44.

3. Now mentally multiply 44 x 50 = 2200 - 1st answer.

4. 47 is 3 away from the 10 boundary 50, Square 3 as 9 - 2nd answer.

5. Add the first and second answer, 2200 + 9

Answer: 2209

Multiplied with 12

Example: 13,423 11

Write down the number, as shown on the right, with a zero placed at both ends. This is

a zero sandwich.

0134230

Add the last two digits, 3 + 0 = 3, and write the answer below the 0.

For the tens digit, add the hundred place digit and tens digit, that is 2 + 3 = 5.

Continue to add adjacent digits, that is, 4 + 2 = 6, 3 + 4 = 7 and 1 + 3 = 4, 0 + 1 = 1. The

answer is 147,653.

0134230 11

147653

Example:6

5214 12

Again we start with the zero sandwich. 0652140.

The ultimate digit is 0 and the penultimate digit is 4. Adding the ultimate

digit and twice the penultimate digit, we get 0 + 8 = 8.

For the tens column, the ultimate digit is 4 and the penultimate digit is 1, so

4 + 2 = 6.


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Likewise, 1 + 4 = 5 and 2 + 10 = 12. With 12 we set down 2 and carry 1.

5 + 12 + carry 1 = 18 and again we carry 1.

The final step is 6 + 0 + carry 1 = 7. So, the answer is 782568.

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