Swapping (Commutativity Property)
When you add two or more numbers, you can change their order, and the sum will stay the same.
Example:
\(8 + (-3) = 5\)
\((-3) + 8 = 5\)
So, changing the order of terms does not change the value.
Grouping (Associative Property)
When you add three or more numbers, you can group them in any way, and the sum will still be the same.
Example:
\((-7) + 10 + (-4)\)
\(=\) \([(-7) + 10] + (-4) = 3 + (-4) = -1\)
\(=\) \((-7) + [10 + (-4)] = (-7) + 6 = -1\)
So, changing the grouping of numbers does not change the value.
In addition you can swap or group numbers any way you like - the final sum remains the same.
Tinker the terms
When you increase one term, the total increases by that much.
When you decrease one term, the decreases by that much.
We don't always need to calculate the whole thing- just look at what changed and how much.
Let us take the expression: \(50 + 20 = 70\) 50+20=70
What happens if you change one term?
Change \(50\) to \(60\) (increase by \(10\))
Now, \(60+20=80\)
The answer increased by \(10\).
We are Tinkering (Changing) the Number!
\((a+b)×c=a×c+b×c\)
\((a−b)×c=a×c−b×c\)