Multiplication Techniques
Find 42 Ã— 48 ?
 First multiply the unit digit of the number: 2 Ã— 8 = 16
 Then multiply 4 by 5 (the succeeding number) to get 20 for the first part of the answer.
 So, Required answer is 2016.
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 â€“
 First find the multiplication of last two digits of both the numbers ie. Find B Ã— B. It will give us last 2 digits of the answer.
 Multiply the Tenâ€™s digits and Add the common digit to the multiplication ie. find A Ã— C + B. It will give us the initial digits of the multiplication
 Here tenâ€™s 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 Ã— 4 = 16. Put it at right hand side.
 Again multiplying the tenâ€™s digits of numbers and adding common digit, we get (4 Ã— 6) + 4 = 24 + 4 = 28. Put it at the left hand side. So, we get required answer as 2816.
108 Ã— 109 ?
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.
Special Multiplication Technique for 5, 25, 125 & 625
Number  Method  Example: 

Multiplication by 5  Put one 0 at the end of the number and divide by 2  512 Ã— 5 = 5120/2 = 2560 
Multiplication by 25  Put two 0 at the end of the number and divide by 4  512 Ã— 25 = 51200/4 = 12800 
Multiplication by 125  Put three 0 at the end of the number and divide by 8  512 Ã— 125 = 512000/8 = 64000 
Multiplication by 625  Put Four 0 at the end of the number and divide by 16  512 Ã— 625 = 5120000/16 = 320000 
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33/39 = 3339 or 66 Ã— 50 (Base) + 39 = 3300 + 39 = 3339
Cross wise operation (47 + 14) or (64 â€“ 3) given us 61
To get 3050, you can simply multiply the lefthand (61) side by 100 and divide by 2 to get the desired result.
Special Technique for multiplying any two/three digit number with a two/three digit number
Multiplication of a 2digit number by a 2digit number
12 Ã— 13?
Steps:
 Multiply the righthand digits of multiplicand and multiplier (unitdigit of multiplicand with unitdigit of the multiplier).
 Now, do crossmultiplication, i.e., multiply 3 by 1 and 1 by 2. And the two products and write down the left of 6.
 In the last step we multiply the lefthand figures of both multiplicand and multiplier (tenâ€™s digit of multiplicand with tenâ€™s digit of multiplier).
So, the answer is 156.
325 Ã— 17 = ?
Steps:
Step 1
(5 Ã— 7 = 35, put down 5 and carry over 3)
Step 2
(2 Ã— 7 + 5 Ã— 1 + 3 = 22, put down 2 and carry over 2)
Step 3
(3 Ã— 7 + 2 Ã— 1 + 2 = 25, put down 5 and carry over 2)
Step 4
So, answer is 5525
Multiplication of a 3digit number by a 3digit number
321 Ã— 132 = ?



 (3 Ã— 3 ++ 1 Ã— 2 + 1 = 12, write down 2 and carry over 1)

How to gain speed?
 Let us say, we have to multiply AB with 11 (where AB is the two digit number)
 Separate AB and create one digit space between them ie. A_B
 Add A & B and put the result in the above space created.
 If the addition of A & B is a two digit number, then put the unit digit in the space created in step 2 and add the carry digit to A.
Multiply 43 Ã— 11
We can do the multiplication in the following steps:
 Create a one digit space between 4 and 3 ie we get 4_3
 We add 4 & 3 to get 7 and put the 7 in the space created above
 We get 473 as answer.
Multiplying a two digit number with 11
 Let us say, we have to multiply AB with 11 (where AB is the two digit number)
 Separate AB and create one digit space between them ie. A_B
 Add A & B and put the result in the above space created.
 If the addition of A & B is a two digit number, then put the unit digit in the space created in step 2 and add the carry digit to A.
Multiply 43 Ã— 11
 Create a one digit space between 4 and 3 ie we get 4_3
 We add 4 & 3 to get 7 and put the 7 in the space created above
 We get 473 as answer.
13,423 Ã— 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 tenâ€™s digit, add the hundred place digit and tenâ€™s 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 Ã— 11
147653
With a little practice method can be applied without writing but some care must be taken when carry overs are involved.
 Look for the nearest 10 boundary. Eg. 3 from 47 to 50
 Since we went up 3 to 50, now go down 3 from 47 to 44.
 Now mentally multiply 44 Ã— 50 = 2200  1st answer.
 47 is 3 away from the 10 boundary 50, Square 3 as 9  2nd answer.
 Add the first and second answer, 2200 + 9
Multiplied with 12
65214 Ã— 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 tenâ€™s column, the ultimate digit is 4 and the penultimate digit is 1, so 4 + 2 = 6.
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.