Algebra · Properties

Properties of Addition

Addition always follows the same three rules, no matter what numbers you use. Once you know them, you can add faster — and later, they're the reason algebra tricks actually work.

Part 01

The Commutative Property — Order Doesn't Matter

You can add two numbers in either order and get the same sum. "Commute" means to travel back and forth — the numbers can swap places and the answer doesn't change.

a + b = b + a
Try It — Cars Commuting

Watch the sum stay the same when the numbers commute

Part 02

The Associative Property — Grouping Doesn't Matter

When you add three or more numbers, it doesn't matter which two you add first — the total comes out the same. "Associate" means to group together, so this is about which numbers team up first.

(a + b) + c = a + (b + c)
Try It — The Grouping Switcher

Pick which pair adds first — the total won't change

Part 03

The Identity Property — Adding Zero Changes Nothing

Any number plus zero stays exactly the same. Zero is called the additive identity because adding it never changes a number's identity.

a + 0 = a
Try It Yourself

Pick any number — adding 0 never changes it

+ 0 = 17

A sneak peek: the inverse property 👀

There's a fourth idea worth knowing: every number has an opposite that adds with it to make zero — like 8 + (−8) = 0. You'll see this a lot more in the Positive & Negative Numbers unit.

Your Turn!

Practice

Eight questions mixing all three properties — identify which one is being used, or fill in the missing number.

Question 1 of 8 Score: 0/8