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.

So, the answer is 45200.

So, accordingly in the first example

The answer is 2460/2 = 1230

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

Example:

245 X 9

245 X (10 - 1)

(245 X 10) - (245 X 1)

Answer is 2205

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.

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

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

So, the answer is

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

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

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

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

Example:

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

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

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

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

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

- 452 X 100
- 235 X 200
- 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 470

__00__*(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 = 1236

**000***(because there are three zeroes in 3000)*

**2. Multiplication with**

**5**

^{n}**like 5, 25 (=**

**5**

^{2}**), 125 (=**

**5**

^{3}**)**

**, etc**

**Example:**

- 246 X 5
- 479 X 25

**K**by

**5**then you just need to divide that number by

^{n}**2**after writing

^{n }**'n'**zeroes at the end of the number. It goes like this:

*K X*

**5**^{n}= K0000.....n zeroes divided by 2^{n}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 (=5

^{2}) 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:

- 245 X 9
- 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:

- 42 X 48
- 34 X 36
- 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:

- 201 X 299
- 511 X 589
- 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:

- 2002 X 2998
- 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:

- 43 X 63
- 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:

- 22 X 23
- 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**

*You can read the complete Quantitative Aptitude Study Material Here*

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