We all know the trick when multiplying by ten - add 0 to the end of the number, but did you know there is an equally easy trick for multiplying a two digit number by 11? This is it:

Take the original number and imagine a space between the two digits (for example we will use 52:

5_2

Now add the two numbers together and put them in the middle:

5_(5+2)_2

That is it - you have the answer: 572.

If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first:

9_(9+9)_9

(9+1)_8_9

10_8_9

1089 - It works every time.

 

Most people memorize the 5 times tables very easily, but when you get in to larger numbers it gets more complex - or does it? This trick is super easy.

Take any number, then divide it by 2 (in other words, halve the number). If the result is whole, add a 0 at the end. If it is not, ignore the remainder and add a 5 at the end. It works everytime:

2682 x 5 = (2682 / 2) & 5 or 0

2682 / 2 = 1341 (whole number so add 0)

13410

Let?s try another:

5887 x 5

2943.5 (fractional number (ignore remainder, add 5)

29435

 

If you have a large number to multiply and one of the numbers is even, you can easily subdivide to get to the answer:

32 x 125, is the same as:
16 x 250 is the same as:
8 x 500 is the same as:
4 x 1000 = 4,000

 

Dividing a large number by five is actually very simple. All you do is multiply by 2 and move the decimal point:

195 / 5

Step1: 195 * 2 = 390
Step2: Move the decimal: 39.0 or just 39

2978 / 5

step 1: 2978 * 2 = 5956
Step2: 595.6

 

To subtract a large number from 1,000 you can use this basic rule: subtract all but the last number from 9, then subtract the last number from 10:

1000
-648

step1: subtract 6 from 9 = 3
step2: subtract 4 from 9 = 5
step3: subtract 8 from 10 = 2

answer: 352

 

Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 6: Sometimes multiplying by 3 and then 2 is easy.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number (which is obvious from the first step).
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).
Multiply by 45: Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number.

 

Twisting the trick a bit, we can generate ALL Pythagorean Triplets

Most people will recall a 3,4,5 triangle
Some remember the 5,12,13 triangle
Few remember the 7,24,25 triangle
Most don?t know the 121,7320,7321 triangle

Note that the smallest side is odd.

Simply square an odd number such as 9^2 = 81
Divide in half (not evenly)
An uneven split of 81 is 40,41

So 9,40,41 is a pythagorean triplet

It also works for even numbers, but they have to have at least one odd factor.

Lets try 10. Find the pythagorean triplet for 5.
5,12,13 and then muliply by the other factor of 10 (namely 2) to get 10,24,26.

For powers of 2 we must be really sneaky.
Take 2^6 = 64.
Divide the number by 4 to get 16.

We know 3,4,5 is a pythagorean triplet.

Multiply the triplet by 16 to get 48,64,80.

 

Like:

12 x 734

can be broken into ((10×700) + (2×700) + (10×34) + (2×34)) = 7068

or

8 x 6846

can be broken into ((8×6000) + (8×800) + (8×40) + (8×6)) = 54768

basically you break the number into tens, hundreds, thousands, etc and mulitply each group. with some larger numbers it can get hard to remember each ?sub-number? but if you?re trying to estimate, its a good way to get a rough idea.

 

e.g 57

take 7's square i.e 49 (here only 9 is taken while 4 is carried on)

multiply d two numbers and double d product and add 4 to them

again square d 1st digit and add if any carry on 7 in this example

therefore d square is 3249

 

guys i know some of them may not be useful to you but u can tell them to ur young brothers and sister it will help them.