Key Math Properties

Some of the math properties shown below you will already know.  Some you will know, but always forget the name, and others you will see for the first time.  By the way, make sure know the order of operations before you take a look at these important properties!

On the left side of the table we show the general form – using all letters.  We know that can be confusing, so we also give an example with numbers on the right side of the table.  Use what works best for you.

 Remember, you always do what is inside the parentheses first.   

Notice how the order of the numbers did not change.  In the examples with numbers, the order always goes 3, 5, 1. 

How can we remember the name of this math property?  One possibility is to think of the word associate – which is another word for friends.  You probably have different groups of friends and you hang out with them at different times.  The associative property deals with changing groups (parentheses).  You don’t change the order, you just change the groups.   

 Take a look at this useful math property:

In the commutative property you do change the order of the numbers.  The 4 was first originally, and then it was switched to second.

How can we remember this property?  The word commute means to travel:  “A half hour commute to work.”  When you see the word commutative, think of travel – or of moving the order of the numbers.

Commutative also sounds like com-move-ative if that helps you. 

The distributive property is a math property that combines addition and multiplication.  You use it when you have two numbers being added inside parentheses, and one number multiplied by the entire quantity.

The word distribute means to give out.  In the example at the right, we are giving out the 3 to both the 4 and the 1 – see the arrows shown?

 Another way to think of this math property is like this: 

Because you are multiplying 3 times (4+1), that means you have three (4+1)’s.  Instead of multiplying, you can add all 3 of them up.  Look at the figure with the 3 arrows.

You might be thinking:  I could just add up 4+1 to get 5, and then multiply 3 times 5 to get 15.  That is certainly true. 

The distributive property will be most useful when one of the numbers inside the parentheses is a variable.  Certain math properties are only useful in some situations.

The word identity means “who you are.”  You may have heard of identity theft.  In math, we want a number to keep its same identity – in other words, stay as the same number.  What number would you have to add to a number to keep it the same?  What about multiplication?

The identity operator of addition is 0 because any number plus 0 is always equal to that number – and yes, you can switch the order!

The identity operator of multiplication is 1 because any number times 1 is always equal to that number – again you can use the commutative prop!

This math property states that any number multiplied by zero will always be equal to zero.  You probably already knew this one.

Hopefully the zero property and all the math properties listed here make sense to you.  They will be very helpful in your mathematical adventures.

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