Mentally Add 2 Digit Numbers

Adding two one digit numbers together is something, I assume, most of us can do easily in our head.  But how many of us can do two digit addition problems in our head?  For some it’s difficult, for some they may struggle, and for some it may be a breeze.

 

Hopefully this blog will help you to learn how to add two digits numbers together easily and mentally, possibly even faster than you could type the problem into a calculator!

 

To start learning how to do this, we have to remember two things:

1.. Simplify the problem

2.  Add left to right

 

WAIT! add left to right?! We were always taught to add right to left! <<<— Did you just think this?  That’s okay.  Adding right to left is okay for adding on paper but we read left to right and as you will soon see, that by simplifying the problem and reading left to right, the answer comes to you practically instantly!

 

The easiest two digit addition problems are those that do not require you to carry any numbers, when the first digits sum to 9 or below and the last digits sum to 9 or below.  Like the following:

adding-2-digits

To solve 47 + 32, first add 30 then add 2.  After adding 30, you have the simpler problem of 77 + 2, which equals, 79.  We can illustrate this as follows:

adding-2-digits-2

The above diagram is simply a way of representing the mental processes involved in arriving at an answer using this method.

 

Now let’s try a problem that requires you to carry a number…

adding-2-digits-3

Adding from left to right, you can simplify the problem by adding 67 + 20, then 87 + 8 = 95.

adding-2-digits-4

Now try one on your own, mentally calculating from left to right, and then check below to see how it was done.

adding-2-digits-5

How was that?! You added 84 + 50 = 134 and added 134 + 7 = 141, right?!

 

If carrying numbers trips you up a bit, don’t worry about it.  This is probably the first time you have ever made a systematic attempt at mental calculation like this, and if you’re like most people, it will take you time to get used to it.  With practice, however, you will begin to see and hear these numbers in your mind, and carrying numbers when you add will come automatically.

 

Try these sets of exercises for added practice.

adding-2-digits-6

 

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-Trevor.

 

Math Simplified, Multiply Any 2 Digits By 11

Multiplying any two digit number by eleven is easier than most people think!  Would you like to be able to calculate a math problem like this quickly in your head?  Here is how to do it easily, mentally, and faster than you can enter it into a calculator!

 

Consider this Problem:

 

32 X 11

 

To solve this problem, simply add the digits 3 + 2 = 5, then put the 5 between the 3 and the 2, and there is your answer, 352.

 

Try another one:

 

53 x 11

 

Since 5 + 3 = 8, your answer is simply

 

583

 

NOW DON’T GET TOO EXCITED!  Suppose the problem is 85 X 11?  Even though 8 + 5 = 13, the answer is NOT 8135!  As before, the 3 goes in between the numbers, but the 1 needs to be added to the 8 to get the correct answer of 935:

 

Think of it this way:

 

1

835

935

 

Here is another example:  Try 57 x 11.

Since 5 + 7 = 12, the answer would be:

 

1

527

627

 

Now try this one as fast as you can: 77 x 11.

 

If you got the answer 847, then give yourself a high five!  Now if you tell a friend or teacher that you can multiply, in your head, any two digit number by 11 it won’t be long before they ask you to do 99 x 11.  Can you answer them?

 

1

989

1089

 

Now if you are wondering if this method can be used for 3 or 4 digit (or larger) numbers by eleven, then wonder no more because it is!

 

If you have a problem like 314 x 11, the answer still begins with 3 and ends with 4.  Since 3 + 1 = 4, and 1 + 4 = 5, the answer will be 3454.

 

I’ll blog more on the larger numbers at a different time, but for now, enjoy the new way of dazzling your friends and teachers with your new found, simple way to Math!

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Trevor.

 

 

 

Source:

Secrets of Mental Math