This lesson is ten tricks that will help you do any problem quickly and effectively.  Of course as a mathematician you pick up on tons of your own tricks as you go allowing you to skip tedious steps in the math problem that would take a good chunk of your precious time to solve.  Hopefully these ten tricks will help you in saving that time just as it has with me.  And always remember, practice makes perfect.  You will find that not only are you incorrect less the more you practice, but your speed will increase dramatically.

I always listen to math help whenever I can to improve my abilities and skills.  Here are ten tips I have learned:

1: (start with an easy one)
Multiplying or dividing any digit, from 0-10, by 9.
Save time from having to take out the calculator whenever the problem is a simple one involving the number 9.  Hold your hands in front of you palm facing away from your face.  Starting with your left pinky finger going toward your right pinky finger drop the number finger that you are multiplying 9 by.  For example:

8x9= ?

For this problem we hold our hands up and count 8 fingers from the left.  It should be your middle finger in the right hand.  Put it down and how many fingers are still standing to the left of your right middle finger? 7. And how many to the right?  2.  Therefore your answer is 72! 

2: Multiplying any number by 11 quick and easy.
How many of you can do 21432 x 11 in your head under 5 seconds?   The answer is probably not many but I’ll teach you how!

We all know the slow way of writing it out:

            21432
            x 11
            21432
          21432
          235752

But how can we speed this up?

 First step simply copy the first digit
            2
Then add the first digit to the second digit
            23
Then add the second digit (1) with the third digit (4)
            235
Then add the third digit to the fourth
            2357
Then add the fourth digit to the fifth digit
            23575
Then copy the last digit to the end
            23575.

3: Squaring any number from 30-70.
How fast can you do 53^2?  This one is a little more tricky but I have a trick that solves any number squared between 30 and 70.

All you have to do it simply count the amount your number is from 50.  Lets use 53.
In 53’s case it is 3 away from 50.
Therefore all we have to do is:
            1- Square the first digit ( 5^2 = 25)
            2- add the distance from 50 (25 + 3= 28)
            3- Square the last digit and add it to the end of step 2’s digit (3^2 = 9  therefore 2809)

4: Faster way to multiply any two number near number 10
12 x 13 is normally another problem you would have to write out fully.  Don’t worry about it, math help is on the way!  This is the long way, and here is the faster way:

13 x 12 =
For this we just use 10 as a base number.
How much away from 10 is 12? 2!
Simple add that value to the first number giving us 15
Now multiply our first number minus 10 by the second number –10= so 3 x 2= 6.  Now add it to our above value.  That gives us 156! Perfect!
 
But what about numbers that aren’t close to 10?  Do you not get any math help?
YOU DO!

5: Faster way to multiply any number quickly by another!
Lets try 106 x 101!
For this problem all we have to do is add the last digit of our second number to the first=  106 + 1= 107
Now multiply the last digit of the first number by the last digit of the second. 6 x 1= 06
combine the two sets into one number! 10706
That’s it!

6: Always be aware of your order of operations!
The order of operations MUST done in the correct order to solve a problem.
Here is an example problem:
 6(2+7)^2 = ?
Its possible for someone to come up with several solutions to this problem such as:
 (12+42)^2                                          6(9)^2                          6(9)^2
 54^2 = 2916                                       6*81=  486                  72^2=  5184
But which one is right?!

The best trick is to remember PEMDAS.  It is a mnemonic for our order of operations.
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction!
You should solve your problems by using the order from P to S.
So for our example which one is it?
If you guessed the middle one you guessed right! The answer is 486.

7: Quick Squaring any two digit number ending in five.
 Multiply the first digit by itself + 1, and put 25 on the end.  Really.  That is it!  Math help isn’t that hard to find!

Lets use 25^2 for example
25^ 2 = 2 x (2+1) and add 25 to the end.
Therefore 2 x 3= 6 and add 25! Answer is 625.

8: Multiplying any number by 5, regardless of the size of the number.
Take any number and half it.  If it is a whole number simply add a 0. If the number when halved ignore the decimals and simply place a 5 at the end.

Lets try 2680 x 5 = (2680 / 2) = 1340
The number is whole so we add a 0!
13,400
That’s it!


9: Multiplying any number by 4
It’s a relatively simple trick to some people, but hey I’ll throw it out there just in case one of you hasn’t heard.
When multiplying any number by 4 simply multiply the number by 2 and then by 2 again.

20 x 4 =
20 x 2 = 40
40 x 2 = 80     

10: Percent tricks to solve quickly without a calculator
Let’s try 15% of 300.
For most you would have to put into the calculator 300 x .15 to get 45.
But, all you have to do is find the percent of a single 100 and then multiply it times the number of hundreds.
So for 15% of 300.
Solve for 15% of 100 = 15
There are 3 100’s in 300 so multiply times 3= 15 x 3 = 45
Perfect!

Hopefully you learned a trick or two, if you need any more math help contact us immediately!