Move It Around

The secret reason

Here is a secret reason to change subtraction to adding. Subtraction is picky about order: 7 − 3 is not the same as 3 − 7. Adding doesn't care. Once every minus is changed, you can move numbers around and group them however makes the math easiest.

The two properties, in plain English

1. Commutative property (commute means to travel, so the numbers can travel to new spots): You can add in any order. 2 + 5 is the same as 5 + 2.
2. Associative property (associate means to hang out with, so numbers can pick who they hang out with): You can group the adding any way you like. (2 + 5) + 1 is the same as 2 + (5 + 1).

ElleMath-speak

After rewriting subtraction as addition, use the commutative and associative properties to reorder and regroup the terms.

FinnPlain English

Once it's all adding, you can move the numbers anywhere. Find the friends first.

Look for friends

1. Opposites that make zero, like 3.75 and ⁻3.75.
2. Pieces that make a whole number, like 2 13 and ⁻13, or 0.25 and 2.75.
3. Split a mixed number into its whole part and its fraction part, and keep the sign on both: ⁻4 14 = ⁻4 + ⁻14. Then add whole parts together and fraction parts together. That is the negative mixed number trap from Lesson 1, Tile 4: the sign belongs to the whole thing.

Watch it work

That last one is from the North Carolina unpacking document for this standard.

Let me try a few

NC standard: NC.7.NS.1.

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