−−→−
Two negatives added together stay negative.
-4 + (-6) = -10Rules & properties reference
Integer Rules
Integers are positive whole numbers, negative whole numbers, and zero. We use them to show gains and losses, money earned and spent, and temperatures above or below zero.
In simple words:A positive number shows more, up, or a gain. A negative number shows less, down, or a loss.
Gain $8+8
Spend $8-8
See the signs
Integer Sign Rules
Look at the signs first.
++→+
Two positives added together stay positive.
4 + 6 = 10−−× or ÷+
Same signs when multiplying or dividing give positive.
(-4) · (-6) = 24+−× or ÷−
Different signs when multiplying or dividing give negative.
4 · (-6) = -24Why should I care?
You use integers when you spend money, check the temperature, move up or down a building, or gain and lose points in a game. These same rules will help you solve algebra problems.
Quick-reference chart
The Rules
Read the rule, then study the example.
Add Two Negative Numbers
Add the numbers like you normally would. Then put a negative sign in front.
-5 + (-7)5 + 7 = 12Answer: -12Real life: You spent $5 on candy and $7 on ice cream. You spent $12 total, so your money changed by -$12.Add a Positive and a Negative
Think: Which side wins? Find the difference. Use the sign of the number that is larger without its sign.
-9 + 49 - 4 = 5Answer: -5Real life: You owe $9 and pay back $4. You still owe $5, so your balance is -$5.Subtract a Positive Number
Start at the first number and move left on a number line.
3 - 8Move 8 left from 3Answer: -5Real life: You have $3 but spend $8. You are short $5.Subtract a Negative Number
Two signs together turn into a plus sign.
6 - (-3)Change - (-3) to + 36 + 3 = 9Real life: A game removes a 3-point penalty. Removing the loss gives you 3 points back.Multiply or Divide: Same Signs
Same signs give a positive answer.
− and − → +(-5) × (-2) = 10Real life: Removing two $5 charges gives back $10. Removing a loss creates a gain.Multiply or Divide: Different Signs
Different signs give a negative answer.
+ and − → −18 ÷ (-3) = -6Real life: Losing 18 points equally over 3 rounds means a change of -6 points each round.Follow the thinking
Worked Examples
You owe $13 and pay $5
- Owing $13 is -13.
- Paying $5 moves your balance 5 spaces toward zero.
- 13 - 5 = 8. You still owe money, so the answer stays negative.
-13 + 5 = -8
A 6-point penalty is removed
- The score change starts at -4.
- Removing a -6 penalty changes - (-6) into +6.
- Move 6 spaces right from -4.
-4 - (-6) = 2
Watch out
Common Mistakes
- A negative sign does not always make the final answer negative. Look at both signs.
- When you see two signs together, slow down: subtracting a negative becomes addition.
- For multiplication and division, same signs give positive and different signs give negative.
Check yourself
Quick Practice
1. -4 + (-3)
-7. Add 4 + 3 and keep the negative sign.
2. 5 - (-2)
7. Two signs together change to addition: 5 + 2.
3. (-3)(4)
-12. Different signs give a negative answer.
Your turn
10-Question Integer Practice
Type each answer. Press Enter or select Check to see whether you are correct.
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