11 x 11 = 121 (there are 2 ones in 11 and the largest digit in the product is 2)

111 x 111 = 12321 (there are 3 ones in 111 and the largest digit in the product is 3)

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

pretty cool huh (ahh bucky quote!)

now

12,345,679 (skip the 8) x 9 = 111,111,111

12,345,679 x 18 = 222,222,222 (its 9 * 2 so its all 2's get it?)

12,345,679 x 27 = 333,333,333 (again 9 * 3 all 3's)

12,345,679 x 36 = 444,444,444

12,345,679 x 45 = 555,555,555

12,345,679 x 54 = 666,666,666

12,345,679 x 63 = 777,777,777

12,345,679 x 72 = 888,888,888

12,345,679 x 81 = 999,999,999

12,345,679 x 999,999,999 = 12,345,678,987,654,321 (FINALLY THE 8'S)

a few simpler tricks

6 x 2

there is a trick for 2 digit numbers (for one digits it's just the repeat 44,55 etc)

for 2 digit numbers: add the digits (of the other number) and insert that between the number you are multiply by 11

for example: 15 x 11 = 1(1+5)5 = 165

eventually you will have to carry the one so:

55 x 11 = 5(5+5)5 = 5 (10) 5 = 605

For larger numbers it's basically the same concept:

For example, we'll take a seven digit number, 1415926, and multiply it by eleven.

Start with the rightmost digit, 6, that is the last digit.

Add the 6 to the 2 preceding it, equaling eight.

Add the two and the nine preceding it, equaling 11, keep the one.

Add the nine and the five preceding it, equaling 14, keep the four, add the 1 left over from the previous operation.

Add the five and the one preceding it, equaling 6, and add the one left over from the previous operation.

Add the one and the four preceding it, equaling 5.

Add the four and the one preceding it, equaling 5.

And finally, put the first digit, 1, as the first digit of the new number.

giving you 15575186.

Add one to the first digit and multiply it by the first digit, this will be the first two digits of the answer.

Multiply the last digits and this will be the last two digits.

For example 42 x 48.

4+1 = 5. 5 x 4 = 20

2 * 8 = 16.

so the answer is just 2016.

How to multiple:

not really a trick this time but it's just how to multiply faster

Let's start with just 2 digits:

how about 47 x 53

multiply the first digits: 20

multiply the last digits: 21

Now (draw lines if you need to) multiply the first digit of the first number with the 2nd digit of the 2nd number AND the 2nd digit of the first number and the 1st digit of the 2nd number (making like 2 umbrella things). ADD these two numbers. 12 + 35 = 47

Now the 47 goes in the middle but obviously u can only put 1 digit in the middle.

Carry the 4 over to the 20 (from multiplying the first digits) to get 24.

Do the same with the 21 from the last digits but this time carry the 2 to the 47 to get 49.

The answer will be 2491 (24 = 20 + 4; the 9 from 47 + 2; and the 1 from 21).

This does also apply for larger numbers; you just move the umbrellas more.

Okay so 341 x 854 = 291214 (don't worry I'll make a slideshow for this)

first 1 * 4 = 4

Then you move that umbrella so that 1 is matched with the next digit 5, and now the 4 in 341 will match to the 4 in 854. Add those and you get 5 + 16 = 21.

Then you "move the umbrella" left one unit to get (oh you can put invisible 0's if you wish): 3 * 4 + 4 * 5 + 1 * 8 = 12 + 20 + 8 = 40.

Now the one has multiplied to all 3 digits in 854, it is no longer needed. The 4 in 854 also has multiplied with every digit in 341 so it is also no longer needed. (You can multiply them by 0 if you want)

Now: 3 * 5 + 4 * 8 = 15 + 32 = 47 (or 0 * 4 + 3 * 5 + 4 * 8 + 1 * 0)

The last step is 3 * 8 which is 24.

To put this all together we go back to all the sums:

which were 4, 21, 40, 47 and 24. The last digit will be 4. Put down the 1 carry the 2. 40+2 = 42 carry the 4. 47 + 4 = 51 carry the 5. 24 + 5 = 29. 291214

111 x 111 = 12321 (there are 3 ones in 111 and the largest digit in the product is 3)

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 x 11111111 = 123456787654321

111111111 x 111111111 = 12345678987654321

pretty cool huh (ahh bucky quote!)

now

12,345,679 (skip the 8) x 9 = 111,111,111

12,345,679 x 18 = 222,222,222 (its 9 * 2 so its all 2's get it?)

12,345,679 x 27 = 333,333,333 (again 9 * 3 all 3's)

12,345,679 x 36 = 444,444,444

12,345,679 x 45 = 555,555,555

12,345,679 x 54 = 666,666,666

12,345,679 x 63 = 777,777,777

12,345,679 x 72 = 888,888,888

12,345,679 x 81 = 999,999,999

12,345,679 x 999,999,999 = 12,345,678,987,654,321 (FINALLY THE 8'S)

a few simpler tricks

**has this property: the last digit of the product will be the same as the last digit of the number you're multiplying by 6.**__any multiple of 6__6 x 2

**4**= 14**4****One of my favorites! how to multiply things close to 100,1000 etc.****for example 98 * 97. 98 is 2 away from 100 and 97 is 3 away. You can do 98 -3 or 97 - 2 and get 95. That is the first two digits. no 2 * 3 = 6. Which is the last two digits, the final answer is 9506.**

**first you can just multiply by 10 and add the number however**__for 11:__there is a trick for 2 digit numbers (for one digits it's just the repeat 44,55 etc)

for 2 digit numbers: add the digits (of the other number) and insert that between the number you are multiply by 11

for example: 15 x 11 = 1(1+5)5 = 165

eventually you will have to carry the one so:

55 x 11 = 5(5+5)5 = 5 (10) 5 = 605

For larger numbers it's basically the same concept:

For example, we'll take a seven digit number, 1415926, and multiply it by eleven.

Start with the rightmost digit, 6, that is the last digit.

**6**Add the 6 to the 2 preceding it, equaling eight.

**8**Add the two and the nine preceding it, equaling 11, keep the one.

**1**Add the nine and the five preceding it, equaling 14, keep the four, add the 1 left over from the previous operation.

**5**Add the five and the one preceding it, equaling 6, and add the one left over from the previous operation.

**7**Add the one and the four preceding it, equaling 5.

**5**Add the four and the one preceding it, equaling 5.

**5**And finally, put the first digit, 1, as the first digit of the new number.

**1**giving you 15575186.

__If 2 2-digit numbers, both have the same first digit AND the last digit adds to 10:__Add one to the first digit and multiply it by the first digit, this will be the first two digits of the answer.

Multiply the last digits and this will be the last two digits.

For example 42 x 48.

4+1 = 5. 5 x 4 = 20

2 * 8 = 16.

so the answer is just 2016.

How to multiple:

not really a trick this time but it's just how to multiply faster

Let's start with just 2 digits:

how about 47 x 53

multiply the first digits: 20

multiply the last digits: 21

Now (draw lines if you need to) multiply the first digit of the first number with the 2nd digit of the 2nd number AND the 2nd digit of the first number and the 1st digit of the 2nd number (making like 2 umbrella things). ADD these two numbers. 12 + 35 = 47

Now the 47 goes in the middle but obviously u can only put 1 digit in the middle.

Carry the 4 over to the 20 (from multiplying the first digits) to get 24.

Do the same with the 21 from the last digits but this time carry the 2 to the 47 to get 49.

The answer will be 2491 (24 = 20 + 4; the 9 from 47 + 2; and the 1 from 21).

This does also apply for larger numbers; you just move the umbrellas more.

Okay so 341 x 854 = 291214 (don't worry I'll make a slideshow for this)

first 1 * 4 = 4

Then you move that umbrella so that 1 is matched with the next digit 5, and now the 4 in 341 will match to the 4 in 854. Add those and you get 5 + 16 = 21.

Then you "move the umbrella" left one unit to get (oh you can put invisible 0's if you wish): 3 * 4 + 4 * 5 + 1 * 8 = 12 + 20 + 8 = 40.

Now the one has multiplied to all 3 digits in 854, it is no longer needed. The 4 in 854 also has multiplied with every digit in 341 so it is also no longer needed. (You can multiply them by 0 if you want)

Now: 3 * 5 + 4 * 8 = 15 + 32 = 47 (or 0 * 4 + 3 * 5 + 4 * 8 + 1 * 0)

The last step is 3 * 8 which is 24.

To put this all together we go back to all the sums:

which were 4, 21, 40, 47 and 24. The last digit will be 4. Put down the 1 carry the 2. 40+2 = 42 carry the 4. 47 + 4 = 51 carry the 5. 24 + 5 = 29. 291214