Math 7 · Unit 3, Lesson 1: Adding Signed Numbers · Tile 2 of 5
Adding Signed Numbers
Pay off what you can. What's left is the answer.
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.
Same signs
| Have (+) | Owe (−) |
|---|---|
| $4 | |
| $6 | |
| Net worth $4 and $6 more. Net worth: $10. | |
| Have (+) | Owe (−) |
|---|---|
| $4 | |
| $6 | |
| Net worth Owe $4 and $6 more. Net worth: −$10. | |
To add two numbers with the same sign, add their absolute values and keep the sign.
Money plus money is more money. Debt plus debt is more debt. If you owe 4 dollars and then owe 6 more, you owe 10 dollars.
Different signs
| Have (+) | Owe (−) |
|---|---|
| $5 | |
| $9 | |
| Net worth Pay off $5. You still owe $4. Net worth: −$4. | |
To add two numbers with different signs, subtract their absolute values. The sum has the sign of the addend with the greater absolute value.
Use the money you have to pay off what you owe. If you owe more than you have, you still owe some, so the answer is negative. If you have more than you owe, you have money left, so the answer is positive.
On the number line
Adding a positive moves right. Adding a negative moves left.
More than two numbers
Use the commutative and associative properties to group the positive addends and the negative addends. Then add.
Put all your money in one pile and all your debts in another pile. Then pay off what you can. What's left is your net worth.
NC standard: NC.7.NS.1.