Idiot\'s Guides Basic Math and Pre-Algebra

18 Part 1: The World of Numbers

Keep the chain of additions going, column by column, and don’t be alarmed when the thousands

column adds to 25. Just put down the 5 and carry a 2 over to the ten-thousands column.

There are a lot of little steps in an addition like this, and you may wonder why some people

are so quick at it while others take more time. The answer probably has to do with the order in

which those speedy folks do the job.

You can only add two numbers at a time, but you don’t have to add them in the order they’re

given to you. There are two properties of addition that help to simplify and speed up your work.

They’re called the commutative property and the associative property.

The commutative property tells us that order doesn’t matter when adding. It doesn’t take long

to realize that 4 + 7 is the same as 7 + 4, and the same is true for any two numbers you add.

If you add 3,849,375 + 43,991, you’ll probably put the 3,849,375 on top and the 43,991 under that,

because that’s the way it was given to you, but you’d get exactly the same answer if you did it

with the 43,991 on the top.

It’s important to remember that not every operation has this property. If you have $1,000 in the

bank and withdraw $100, no one at the bank will blink, but if you have $100 and try to withdraw

$1,000, there’s likely to be an unpleasant reaction. Withdrawing money from your bank account

is a subtraction, and subtraction isn’t commutative.

DEFINITION

The commutative property is a property of addition or multiplication that says that

reversing the order of the two numbers will not change the result.

The other useful property of addition is the associative property. This property tells us that when

adding three or more numbers, you can group the addends in any combination without changing

the outcome.

For example, when adding 8 + 5 + 5 + 2, you might decide that adding those two 5s first is easier

than going left to right. The associative property says you can do that without changing the

result. You can take 8 + 5 + 5 + 2, add the two 5s first, and make the problem 8 + 10 + 2. That

will give you 20, which is the same answer you would have gotten going left to right.



59,201

18,492

81,002

6,478

165,173

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