Never Subtract Signed Numbers

The rule

Here is the whole lesson: don't ever subtract signed numbers. Every time you see a minus sign, change it to adding the opposite. Then add, the same way you did in Lesson 1.

a − b = a + ⁻b

ElleMath-speak

To subtract a signed number, add its opposite. The opposite of a number is the same distance from zero on the other side.

FinnPlain English

Minus turns into plus, and the next number flips its sign. Then you're just adding.

Two ways to change it

You can change the problem on paper, or you can change it in your head. Both use the same rule. The only difference is whether you want to miss half the problems or get them all right.

On paper

⁻3 − ⁻9⁻3 + 96

Correct.

In your head

⁻3 − ⁻9⁻12

Wrong: two minus signs, one of them got lost.

The paper way takes one extra line. That line is where the right answer comes from.

Elle and Finn talk it over

Finn

But we might waste paper if we write it all down.

Elle

True. One sheet of paper costs about two cents. Missing half your problems could cost you your future as a rocket scientist. Tough call.

Finn

I'll go get a pencil.

Watch it work

5 − 85 + ⁻8 Change⁻3 Add

7 − (⁻2)7 + 2 Change9 Add

6 − (2 − 9)6 − (2 + ⁻9) Inside first: change6 − (⁻7) Inside first: add6 + 7 Change13 Add

8x − 5 − (⁻3x) − 48x + ⁻5 + 3x + ⁻4 Change8x + 3x + ⁻5 + ⁻4 Group: x terms together, numbers together11x + ⁻9 Add each group11x − 9 Write it the short way

x terms work like money in one pocket and plain numbers like money in another. Change every minus first, then add the x terms together and the plain numbers together. The last step may write 11x + ⁻9 as 11x − 9. Both mean the same thing.

In money. You have $5 and spend $12. 5 − 12 → 5 + ⁻12 → ⁻7. You owe $7.

Want to know why it works? Look back at Lesson 1, Tile 3.

ElleMath-speak

Rewrite the whole problem as addition before you compute anything.

FinnPlain English

Change first, on paper, every time. Then add.

Let me try a few

NC standard: NC.7.NS.1.

Where to go next

Let me try a few12 problems on never subtract signed numbers. All tilesAll 1 parts of this lesson. Tell us what you thought about this tileA few quick questions about just this tile. It takes a few minutes, and opens in a new tab so you keep your place.