**GETTING RID OF
CARRYING:*****The first rule
in making math quick and easy is to change something difficult into something easy,
whenever that is possible.**
Now when adding two numbers, the larger a digit, the
more likely it is to involve carrying. The digit 9, when added to any digit but 0,
will make carrying necessary. On the other hand, a small digit is easy to handle,
and 0 is the easiest of all. No matter what digit you add to a 0, even a 9, no
carrying is needed.
So **LET'S GO AND CREATE SOME ZEROES!**
Example:
Add 48 + 76.
Let's change the 48 to 50 by adding 2 to it.
If it is 50, it will be super easy to add to anything! I know, you are
saying..."You can't do that!"
Well technically you are correct, but if I can do
something to balance out this extra 2 the final answer will be the same.
To balance it out I will **subtract** 2
from the the answer. The net result is 0 change because you added a number and then
you subtracted the same number.
The mental benefits of this 0 change are terrific
however. (*this is one of those....."why didn't anyone ever show me this
before" type of things*) Here let's take a look:
Instead of 48 + 76, we now have 50 + 76 which equals
126 which is 2 units too large. So we simply subtract 2 from the 126. This balances out the
problem and we are left with the correct answer. Absolutely no carrying needed!
The algebra that verifies this is quite simple:
The sum of **a **and **b** is **a + b**.
Suppose you add any number (**n**) to **a** and subtract that
same number from **the final answer**. The number **a**
becomes** a+n** while the **sum** becomes **a+n +b**.
Now subtract the **n** we added and we get, **a+n+b-n **which
gives us just **a+b. **The n's just undo themselves.
**Now try the following: **write the problems and then
transform them to create zeroes for easy adding.
27
__+34__ |
89
__+13__ |
$1.98
__+$.34__ |
$14.95
__+$11.60__ |
This is a very powerful trick when adding prices at the
grocery store.
**YOUR TURN:**
To "own" this trick you need
to **practice it a lot**. Soon you will find yourself adding like this
naturally in mental situations. But it DOES take practice.
You need to fill o**ne side of a piece of notebook paper **with examples
of this kind of addition. The more you do,
the faster you will get!
Be sure to make up different kinds and lengths of
addition problems. Ex. whole numbers, decimals, money, etc. |