Math 7 · Unit 3, Lesson 1: Adding Signed Numbers · Tile 3 of 5
Subtraction? Add the Opposite
Change it, then add
You already know how to add signed numbers. So here is the plan: change every subtraction to adding the opposite, then add the way you did in Tile 2.
Write it down. Do every change on paper, one line per step. Changing signs in your head is the number one reason for missed problems. If you changed something, it should be on the paper.
Change, then add
Rewrite each subtraction as addition of the opposite. Then add.
Every time you see a minus sign, change it to a plus, and change the next number to its opposite. Then just count up your money and your debts.
One symbol, two jobs
In 6 − −4, the first − means subtract. The second sign is part of the number: it says the 4 is negative.
Only the subtract sign changes. It becomes +, and the number after it becomes its opposite.
In 6 minus negative 4, the first sign means subtract. The second sign means the 4 is negative.
Only the subtract sign changes. 6 minus negative 4 becomes 6 plus 4, which is 10.
Why does subtracting a negative add?
Money. You owe your brother $4. He says, "Forget it." He just subtracted your $4 debt. Your net worth went up $4. So taking away −4 is the same as adding 4.
The pattern.
Each time you subtract one less, the answer goes up by 1. Keep going past 0, and subtracting a negative makes the answer bigger.
Keep, change, change. Some classes call this "keep, change, change": keep the first number, change minus to plus, change the next number to its opposite. Now you know why it works.
Subtracting a negative number is the same as adding a positive number.
If someone takes away a debt you owe, you're richer. Taking away a 4 dollar debt is the same as getting 4 dollars.
Worked example
NC standard: NC.7.NS.1.