Multiplying by 11

We can use an easy trick for multiplying a two digit number by 11.

Such as,

we try to multiplying 23 by 11.

Generally its ,
              23
            *11 
              23
          +230
            253

by we can use a tricks to solve this multiplying 23 by 11.
23 is the original number here , we imagine a space between two digits ( in this example 2 and 3). 

like , 2___3

Now add the two number and put in the middle .
here (2+3=5),so we put additional number 5 in the middle .

like,  2 5 3 ..

we generally get it and , by using tricks it solve a few second.


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

Suppose we multiplying 56*11

Generally,
                56
              *11
               56
           +560  
             616 

by using tricks  we apply ,

5___6

add two digit ,(5+6=11)
we put 1 in middle and another 1 add to 1st number .
like ,

  5 (11) 6
=616
Its same as general multiplying.

Asset Allocation by Age

This one really isn't a math trick, so much as it is a rule of thumb ...

The Trick: Don't have a financial planner to walk you through asset allocation? A simple way to find out is to subtract your age from the number 120; the number remaining is the percentage of your portfolio that should be in stocks.

Example: For instance, if you're 50, you should be keeping 70% of your holdings in stocks with the remaining 30 percent in fixed income products.

The basic idea here is that younger investors who have decades of working ahead of them can take on more risk than people closer to retirement.

Multiplying by 11

The Trick: When multiplying a figure by 11, follow this pattern: leave the last and first digits alone, then sum each and every pair of digits next to each other (this makes the most sense when seen in example):

Examples: 4,281 x 11 becomes the following digits: (4)(4+2),(2+8)(8+1)(1) or 47,091.

When the sum of a pair is greater than 10, carry that digit to the next left pair (as seen above, where 2+8 was 10).

Let's try something harder. 9,621,576,521 x 11 becomes: (9)(9+6),(6+2)(2+1)(1+5),(5+7)(7+6)(6+5),(5+2)(2+1)(1) or 105,837,341,731.

This is a neat trick of our base 10 place value system. Because 11 = 10 + 1, multiplying a number by 11 is the same as multiplying that number by 10 and then adding it back to itself. Multiplying a number by 10 means we shift all our digits one place over to the left and stick a zero on the end, so when we add this to the original number, we get exactly the paring up of digits that we saw.

Squaring numbers in your head

The Trick: Say you have a number, x, that you want to square.

First, find the difference between x and the nearest multiple of 10, and call that difference d.

Then, multiply (x-d) and (x+d). This should be much easier, because one of the numbers will be a multiple of 10 (based on how we defined d). After multiplying (x-d) and (x+d), just add d2, and you have your square. 

Example: Say you want to find the square of 77. The closest multiple of 10 is 80, so d will be 80 - 77 = 3. Then 77 + 3 = 80, and 77 - 3 = 74.

Multiplying these together is pretty straightforward: 74 x 80 = 70 x 80 + 4 x 80 = 5,600 + 320 = 5920. Add in the 32 = 9, and we get 5929 as our square of 77.

Once you get the hang of this method, it's a good bit quicker and easier than trying to attack 772head on.

How long it'll take to triple your investment

The Rule of 115: If you're more inclined to triple your investment, because you're not as risk averse (or perhaps your time horizon is just a tad bit further out), simply divide 115 or 110 by your growth rate. This will give you the amount of time it will take to triple your investment.

Example: So, if you're getting a return of 10% per year, it will take about 11 1/2 years for your investment to triple in size.

This works for basically the same reason the Rule of 72 works, except that we're aiming to triple rather than double our initial investment.

How long it'll take to double your investment

The Rule of 72: Need an easy way to determine how long it will take to double your investment? Simply divide the number 72 by your projected growth rate.

Example: So, if you're getting a return of 9% per year, it will take about eight years for your investment to double in size, because 72/9 = 8.

The rule of 72 comes from manipulating the basic mathematical formula for calculating compound interest. The exact number you need to divide your growth rate by is actually closer to 69, but 70 or 72 are frequently used for quick mental estimates, because most common single-digit rates of return will divide evenly into one of these.

Figuring out sales tax and tips

The Trick: Assuming an approximately 9% sales tax, as in New York, if you take your pre-tax part of the bill, divide by four, and add this amount to the pre-tax part, you'll be leaving about a 16% tip. If you're feeling more generous, divide by three and add that amount instead, leaving about a 24% tip.

Example: Say your part of the pre-tax bill comes to $18. If you want to leave a 16% tip, divide $18 by four to get $4.50. Add that to your $18 pre-tax cost, and leave a total of $22.50. If you want to leave a larger tip, divide $18 by three to get $6, and combine that with the pre-tax cost to leave a total of $24.

Here's why this works: Dividing the pre-tax bill by four is the same as taking 25% of that amount. That's enough money to cover the 9% sales tax, with 16% leftover for the tip, because 25 - 9 = 16. Similarly, dividing by three gives about 33% of the pre-tax bill, covering the 9% sales tax and a 24% tip, because 33 - 9 = 24.

Business Insider's Sarah Schmalbruch also recently wrote about a few other nice tricks to calculate tips, like moving the decimal point one place to the left and multiplying by two to find 20% of the bill.

So, if the bill is $18, the moving the decimal points gets you $1.80. And multiplying it by two gets you $3.60.

Converting your salary to an hourly figure

The Trick: Take your salary, drop the last three zeros, and then divide by two.

Example: So if you earn $40,000, you're left with $20 an hour.

Maybe you're a salaried employee trying to figure out whether you should take that job that pays by the hour. This trick would certainly help.

This comes from making a couple of assumptions about your working hours and some quick observations about time. There are 52 weeks in a year, and so if you're working a 40 hour week for 50 of those weeks, you'll be working 40 x 50 = 2,000 hours in a year. Take your annual salary and divide by those 2,000 hours (equivalently, drop the last three zeros and divide by two), and voila, you get your hourly rate.

EVOLUTION OF + AND - SIGN

The + symbol came from Latin word et meaning and. The two symbols were used in the fifteenth century to show that boxes of merchandise were overweight or underweight.

EXAMPLE.

For overweight they used the sign + and for underweight the sign -.

Within about 40 years accountants and mathematicians started using them.

FAMILIARITY WITH CARDINAL AND ORDINAL NUMBER

 An ordinal number given us the rank or order of a particular object and the cardinal number states how many objects are in the group of collection.

EXAMPLE.

Fourth - an ordinal number
Four - a cardinal number

LARGEST CALCULATION (9^9)^9

Ninth power of the ninth power of nine is the largest in the world of number that can be expressed with just 3 digit. No one has been able to compute this yet. The very task is staggering to the mind.

EXAMPLE.

The answer to this number will contain 369 million digits. And to read it normally it would take more than a year. To write down the answer, you would require 1164 miles of paper.

AWESOME DIVISION RULE FOR 11

If a number is divisible by eleven the difference between the sum of the digits in the even places and the sum of the digits in the odd places is 11 or 0.

EXAMPLE.

23485 is shown to be divisible by 11 because

2 + 4 + 5 = 11
3 + 8 = 11
11 - 11 = 0
and

and 60852 is shown to be divisible by 11 because
6 + 8 + 2 = 16
0 + 5 = 5
16 - 5 = 11

STUPENDOUS DIVISION RULE FOR 10

If a number is divisible by ten it ends with a 0.

EXAMPLE.

45683750
last digit is 0
then number 45683750 is divisible by 10.

ASTONISHING DIVISION RULE FOR 9

If a number is divisible by nine the sum of its digits is divisible by 9.

EXAMPLE.

8916345
Sum of the digit 
8+9+1+6+3+4+5 = 36
36/9 = 4

number 8916345 is divisible by 9

EXCLUSIVE DIVISION RULE FOR 8

If a number is divisible by eight the last three digits are divisible by 8.

EXAMPLE.

4857248
last three digits are 248
248/8 = 31
Then 4857248 is divisible by 8

PHENOMENAL DIVISION RULE FOR 6

If a number is divisible by six the last digit will be even and the sum of the digit divisible by 3.

EXAMPLE.

46536
last digit is 6 (even) and
sum of digit
4+6+5+3+6 = 24
24 is divisible by 3
then 46536 is divisible by 6.

INCREDIBLE DIVISION RULE FOR 5

If a number is divisible by five the last digit will be 5 or 0.

EXAMPLE.

48905
last digit is 5 then 48905 is divisible by 5
and
56890
last digit is 0 then 56890 is also divisible by 5

EXCEPTIONAL DIVISION RULE FOR 4

If a number is divisible by four the last two digit are divisible by 4 (or are zeros).

EXAMPLE.

45624
last two digit is 24
24 is divisible by 4 then 45624 is divisible by 4.

GOLDEN DIVISION RULE FOR 3

If a number is divisible by three the sum of its digits will be divisible by 3

EXAMPLE.

372 = 3 + 7 + 2 = 12

A corollary of this is that any number made by rearranging the digits of a number divisible by 3 will also be divisible by 3

MAGICAL DIVISION RULE FOR 2

If a number is divisible by two it will end in an even number or a 0.

EXAMPLE.

For example 
28964
given number end with 2 then it will be divisible by 2.
and
89450
given number end with 0 it will also be divisible by 2.