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Properties of Addition

The Hook

The secret rules of the game.

What is it?

Commutative and Associative laws.

Time Travel (History)

Euclid proved these properties in ancient Greece.

Cheat Code

a + b = b + a. Always.

Practice This Now!

The Field Guide

In Plain English: Addition is friendly. It doesn't care what order you do it in. 5+2 is the same as 2+5. You can swap them around to make math easier.

In The Real World: Loading a truck. It doesn't matter if you load the big box then the small box, or vice versa. The total weight is the same.

Booby Trap!

Thinking this works for Subtraction. It does NOT! 5-2 is not 2-5.

Real World Challenge
"You need to add 90 + 17 + 10. That looks hard."
The Logic: Swap them! 90 + 10 is 100. Then 100 + 17 is 117. Way easier.

Training Drills

Commutative
2 + 5 = 7 5 + 2 = 7
Order swaps, answer stays.
Associative
(1+2)+3 = 6 1+(2+3) = 6
Grouping doesn't matter.