3 July 2016

Muliplication Concept: List of Multiplication Short-Cut Methods

I have searched the internet for multiplication shortcuts but I was unable to find the complete list. Some websites say 'top 7 multiplication shortcuts' and some say 'top 10 shortcut methods of multiplication'. So I have done my own research and at the end I have a complete list of shortcut methods which I am giving in this article.

1. Multiplication with the numbers ending with the ZEROES (0000....)

Multiplication Shortcuts
Example:
  1. 452 X 100
  2. 235 X 200
  3. 412 X 3000
Sol. 1: You just have to write as many zeroes as in the 2nd NUMBER (in this 100) at the end of the 2nd NUMBER (in this case 452).

So, the answer is 45200.

Sol. 2: We will first take 235 X 200. You can do multiplication of these numbers like this. 

235 X 200     

235 X 2 = 470 then put the zeroes at the end of this number like 47000 (because there are two zeroes in 200)

It is very simple. Even a child can do this.

Now let's try the next one.

Sol. 2: 412 X 3000

412 X 3 = 1236000 (because there are three zeroes in 3000)

2. Multiplication with 5n like 5, 25 (=52), 125 (=53), etc

Example:
  1. 246 X 5
  2. 479 X 25
If you want to multiply any number K by 5n then you just need to divide that number by 2after writing 'n' zeroes at the end of the number. It goes like this:

K X 5n = K0000.....n zeroes divided by 2n

So, accordingly in the first example

Sol. 1: 246 will become 2460 as 5 have only 1 power and it will be divided by 2 (reason being the same as 5 has only 1 power).

The answer is 2460/2 = 1230

Sol. 2: 479 will become 47900 as 25 (=52) because 5 has power 2.

And this 47900 will be divided by 4 as the power of 2 here will 2 as 5 has power 2.

Answer is 47900/4 = 11975

Pretty Cool...

3. Multiplication with a number near 10, 100, 1000 like 9, 99, 998 etc.

Example:
  1. 245 X 9
  2. 4631 X 99
Sol. 1: Here we will just apply the distributive property of multiplication.

245 X 9
245 X (10 - 1)
(245 X 10) - (245 X 1)
Answer is 2205

Sol. 2: 4631 X 99

4631 X (100 - 1)
Answer is 458469

In other words if you are required to multiply a number with a number nearest to 100, 1000 or 10000 juts split the number in the above manner and it will be easy to find the required number.


4. Multiplication of two numbers whose
  • Unit's digits total to 10 and remaining digits are same 
  • Last two digits total to 100 and remaining digits are same 
  • Last three digits total to 1000 and remaining digits are same
Unit's digits total to 10 and remaining digits are same

Example:
  1. 42 X 48
  2. 34 X 36
  3. 173 X 177
Step 1: Multiply the unit's digits of the numbers to get the last 2 digits of the final solution.
Step 2: And then multiply the common number with next higher number to get the beginning digits of the solution. Let's solve the examples to understand it better.

Sol. 1: 42 X 48

1st Step: 2 X 8 = 16 (last two digits of the final solution)
2nd Step: 4 X 5 = 20 (beginning two digits of the final solution)

So, the answer is 2016

Sol. 2: 34 X 36

1st Step: 4 X 6  = 24 (last two digits of the final solution)
2nd Step: 3 X 4 = 12 (beginning digits of the final solution)

So, the answer is 1224

Sol. 3: 173 X 177

3 X 7 = 21
17 X 18 = 306

So, the answer is 30621

Last two digits total to 100 and remaining digits are same

Example: 
  1. 201 X 299
  2. 511 X 589
  3. 1435 X 1465
Step 1: Multiply the last 2 digits of the numbers to get the last 4 digits of the final solution.
Step 2: And then multiply the common number with next higher number to get the beginning digits of the solution. Let's solve the examples to understand it better.

Sol. 1: 201 X 299

1st Step: 99 X 01 = 0099 (last 4 digits of the final solution)

NOTE: be careful here in putting the zeroes. Although 99 X 01 equals 99 but you have to put here 4 digits for that you should put zeroes to make it a four digits number.

2nd Step: 2 X 3 = 6 (beginning digits of the final solution)

So, the answer is 60099

Sol. 2: 511 X 589

1st Step: 89 X 11 = 0979 (last 4 digits of the final solution)
2nd Step: 5 X 6 = 30 (beginning digits of the final solution)

So, the final answer is 300979

Sol. 3: 1435 X 1465

1st Step: 35 X 65 = 2275 (last 4 digits of the final solution)
2nd Step: 14 X 15 = 210 (beginning digits of the final solution)

So, the answer is 2102275

Last three digits total to 1000 and remaining digits are same

Example: 
  1. 2002 X 2998
  2. 9001 X 9999
Step 1: Multiply the last 3 digits of the numbers to get the last 6 digits of the final solution.
Step 2: And then multiply the common number with next higher number to get the beginning digits of the solution. Let's solve the examples to understand it better.

Sol. 1: 2002 X 2998

1st Step: 002 X 998 = 001996 (last four digits) (write as many zeroes in the beginning so that it becomes as 6 digits number.
2nd Step: 2 X 3 = 6 (beginning digits of the final solution)

So, the answer is 6001996

Sol. 2: 9001 X 9999

1st Step: 001 X 999 = 000999 (last 6 digits of the final solution)
2nd Step: 9 X 10 = 90 (beginning digits of the final solution)

So, the answer is 90000999

5. Multiplication of two numbers whose
  • Ten's digits total to 10 and then unit's digits are same 
  • Unit's digits total to 5 and remaining digits are same 
Ten's digits total to 10 and then unit's digits are same

Example:
  1. 43 X 63 
  2. 27 X 87
Step 1: Multiply the unit's digits of the given numbers to get the last 2 digits of the solution.
Step 2: Multiply the ten's digits of the two numbers and add the common unit's digit to it to get remaining digits of the solution.

Sol. 1: 43 X 73

1st Step: 3 X 3 = 09 (last 2 digits of the final solution)
2nd Step: 4 X 6 + 3 = 27 (beginning digits of the final solution)

So, the answer is 2709

Sol. 2: 27 X 87

1st Step: 7 X 7 = 49 (last 2 digits of the final solution)
2nd Step: 2 X 8 + 7 = 23 (beginning digits of the solution)

So, the answer is 2349

Unit's digits total to 5 and remaining digits are same

Examples:
  1. 22 X 23 
  2. 803 X 802
Step 1: Multiply the unit's digits of the given numbers to get the last 2 digits of the solution.
Step 2: Multiply the ten's digits of the two numbers and add half of the common unit's digit to it to get remaining digits of the solution.

Sol. 1: 22 X 23

1st Step: 2 X 3 = 06 (last 2 digits of the final solution)
2nd Step: 2 X 2 + (1/2 + 2) = 5 (beginning digits of the solution)

So, the answer is 506

Sol. 2: 803 X 802

1st Step: 3 X 2 = 06 (last 2 digits of the solution)
2nd Step: 80 X 80 + (1/2 X 80) = 6440 (beginning digits of the solution)

So, the answer is 644006

Multiplication Series:

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