3+1=1+3 is an example of wich property?

Answer 1

commutative

Answer 2

Other posters are almost right...

Specifically, it's the commutative property of addition.
a+b=b+a

There's also one for multiplication.
ab=ba

There's also an associative property for each.
(a+b)+c=a+(b+c) -- for addition
(ab)c=a(bc)-- for mujlbiplication

There's also a distributive property of multiplication over addition... but not one the other way.
a(b+c)=ab+ac

You will note there is no mention of subtraction or division. Here's why...

There is a number 0. It has the following properties
a+0=a for all a... for this reason, 0 is called an additive identity.
0a=0 for all a
In fact, if ab=0, then either a or b... or both... has to be 0.

There's another number 1 that has the following property...
1a=a for all a ... for this reason, 1 is called a multiplicative identity.

Now, for any number you give me, I can give you another number that when you add your number to mine, you get 0. If you give me 7, I'll give you -7. If you give me-3/5, I'll give you 3/5. If you give me -a(b+c), I'll give you a(b+c)... see how it works? These pairs of numbers are called "additive inverses." Some people call them "negative" numbers, but, as you can see, at least one of each pair is positive. What people who don't much about math call "subtraction" is really addition of the additive inverse of a number.

For almost any number you give me, I can give you another number so that when you multiply the two numbers you get 1. If you give me 7, I'll give you 1/7. If you give me -3/5, I'll give you -5/3. If you give me a, I'll give you 1/a (with the stipulation that a≠0 for a reason I'll get to in a minute).. These pairs of numbers are called "multiplicative inverses," or "reciprocals", but some call them "one over" the number... like 7 and 1/7. The same people who call adding additive inverses "subtraction, call multiplying by the multiplicative inverse "division."

NOW... remember I said I can give you a multiplicative for ALMOST any number? Remember the definition of multiplicative inverse? The product of a number and it's multiplicative inverse is 1. Ok look back at the second property of zero. The product of zero and anything is zero. There is, therefore, no multiplicative inverse by which I can multiply zero by to get one. If such a number existed, it would look like 1/0, right? And the uninformed call multiplying by the multiplicative inverse "division." Since there is no multiplicative inverse for zero, these same people say, "You can't divide by zero." Now you know why.

The equal sign has properties too.
If a=b, then b=a... that's the reflexive property.
If a=b and b=c, then a=c... that's called the transitive property.
There are a few other things you need to know abotu "=".
IFF a=b then a+c=b+c (IFF means that if a+c-b+c, then a=b)
If a=b, then ac=bc, but if ac=bc, then a=b ONLY IF c≠0.

Learn these rules. Obey them religiously. They'll save your mathematical life. If you break them, your answer will be wrong. For example, by breaking one of them, I can prove that 1=0... so watch it.

Answer 3

Commutative :)

It doesn't matter what order you mulitply or add numbers, only the order that you divide or subtract them.

Think of it this way - when your parents go to work, they "commute" both ways...they're going the same distance and it equals the same thing, but their positions are switching! At least that's the trick I learned back when we did properties a while ago...the numbers are commutating from one side to the other :)

Hope I've helped :)

Answer 4

The commutative property. Don't get it confused with the associative prop though which deals with multiplication and parenthesis.

Answer 5

it's the commutative property

Answer 6

The "liberal=retarded" property

Answer 7

identity

Answer 8

addition property- duh