Properties of Addition

This is an addition equation:

Addition equations have **addends **and a **sum.**

**Addends **are the numbers that are being added. There can be more than 2 addends in an addition equation.

The **sum **is the answer we get when we put addends together.

There are 3 **properties of addition**.

The **identity property of addition **says that when 0 is added to a number the answer is the same number. Nothing changes.

For example,

4 + 0=4

68 + 0=68

71 + 0=71

0 + 93=93

0 + 117=117

So, adding 0 to a number is adding nothing to it.

The **commutative property of addition **says that when the order of the addends is changed, the answer still stays the same.

**Tip: **The word **commutative **is kind of like the word commute, which means to move around.

So, think of the commutative property as the rule of moving around the addends.

Look at these two equations.

56 + 17=73

17 + 56=73

What did you notice?

Yes, their sums are the same even if the order of their addends are different.

😀 Tip: Just remember that **commute means to move around.**

So, even if we move the addends around, the sum will not change.

Here's another equation...

674 + 82=756

What do you think is the sum of this equation?

82 + 674=?

That's right!

It's **756!**

Just like the sum of the other equation.

That's because of the commutative property of addition.

The **associative property of addition **says that when three or more numbers are added, the sum is the same no matter which two addends you add first.

In math, parentheses **( )** are used show which operations to do first.

The associative property shows that the sum for this equation...

(3 + 9)+ 5=17

is the same as the sum for this equation:

3 +(9 + 5)=17

Let's try to check how these equations were solved.

(3 + 9)+ 5=?

_=12+5

=17

The other way is this...

3 +(9 + 5)_=?

=3+14

=17

😀 Tip: When you see a **parenthesis,** it means that you have to add the numbers in it first.

Here's another example.

(12 + 48)+ 76=136

Now, figure out the sum for this:

12 +(48 + 76)=?

Is it also 136? Yes!

Remember: when adding a bunch of numbers together, the order of which numbers you add doesn't matter.

This is called the **associative property.**

You can now try practice! 😎

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