Properties of Addition

Did you know that addition has special rules that can make solving math problems much easier? These rules are called properties. Let's look at two of the most helpful addition properties!

The Commutative Property (The Flip-Flop Rule)

The commutative property means that you can add numbers in any order, and you will still get the exact same answer. Think of it like a flip-flop!

For example, if you have $34$ red apples and $28$ green apples, you have the same total amount of fruit as if you had $28$ green apples and $34$ red apples.

$34 + 28 = 28 + 34$

Both sides equal $62$. You can always flip the numbers around if one way is easier for you to add!

The Associative Property (The Grouping Rule)

The associative property means that when you are adding three or more numbers, you can group them together in any way you want, and the total stays the same. We use parentheses $()$ to show which numbers we are grouping together first.

Let's say you want to calculate: $17 + 45 + 3$

Instead of adding $17$ and $45$ first, look for numbers that make a "friendly" ten. $17$ and $3$ are a perfect match because $7 + 3 = 10$!

Let's group them together using the associative property (and move them using the commutative property): $(17 + 3) + 45$

Now the math is super easy: $20 + 45 = 65$

Because of the associative property, $(17 + 45) + 3$ gives you the exact same answer as $17 + (45 + 3)$.

Making Math Easier

By using these properties, you can move numbers around and group them to make mental math a breeze.

Let's try one more example: $(25 + 38) + 12 = 25 + (38 + \_\_)$

What goes in the blank? Because we are just grouping the numbers differently, the missing number is $12$!

If we solve the right side, grouping $38 + 12$ makes a nice, friendly $50$. Then, $25 + 50 = 75$. Grouping numbers to make tens makes addition much faster!