Adding and Subtracting Integers
Learn how to add and subtract positive and negative numbers using number line strategies and rules.
Definition
Key Rules
Adding Integers
- Same signs: Add the absolute values, keep the sign
- - (both positive)
- - (both negative)
- Different signs: Subtract the smaller absolute value from the larger, keep the sign of the larger
- - (positive wins)
- - (negative wins)
Subtracting Integers
- Subtracting is adding the opposite:
- -
- -
- -
Try it now
Worked Examples
Calculate
Identify the signs
Both numbers are negative → Same signs
Add the absolute values
→ Sum is 11
Apply the common sign
Both negative, so result is negative →
Answer:
Common Mistakes
Thinking instead of
Why it's wrong: Forgetting that subtracting a negative means adding: two negatives make a positive.
Correct: . Subtracting is the same as adding .
Writing instead of
Why it's wrong: Mistakenly subtracting instead of adding when both numbers are negative.
Correct: Same signs means ADD absolute values: , then keep the negative: .
Getting the wrong sign when subtracting like
Why it's wrong: Forgetting to check which number has the larger absolute value.
Correct: because and we keep the negative sign.
Confusing with
Why it's wrong: Not carefully reading the operation sign.
Correct: (moving right on number line), but (moving left).
Interactive Visual
Click the buttons to jump left (subtract) or right (add) on the number line.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
16 problemsWhat is ?
Why It Matters
- Temperature changes: If it's and drops 5 more degrees:
- Money and debt: You owe 50 dollars and borrow 30 more: dollars in debt
- Elevators: From floor 2, going down 5 floors: (basement level 3)
- Football: A team gains 8 yards then loses 12: yards total
Real World Applications
Banking Transactions
Banks use integer operations to track deposits (positive) and withdrawals (negative).
Example:
If your account has 120 euros and you withdraw 85 euros, then deposit 40 euros: euros.
Your bank account shows euros (overdraft). You deposit 80 euros.
What is your new balance?
Step 1: Write the mathematical expression
Calculate:
Altitude and Depth
Pilots and divers use integers to track altitude above sea level (positive) or depth below (negative).
Example:
A submarine at meters dives 25 meters deeper: meters.
A submarine is at meters. It rises 75 meters toward the surface.
What is the new depth?
Step 1: Write the mathematical expression
Calculate:
Game Scores
Many games track gains and losses as positive and negative points.
Example:
In a trivia game, you earn 50 points, lose 30, then earn 45: points.
Your game score is points (in the negative). You answer correctly for 40 points, then incorrectly and lose 10.
What is your final score?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1Same signs: Add absolute values and keep the common sign ()
- 2Different signs: Subtract absolute values and keep the sign of the larger ()
- 3Subtracting = adding the opposite:
- 4Double negative:
- 5Use a number line: right is positive, left is negative
Frequently Asked Questions
Glossary
- Integer
- A whole number that can be positive, negative, or zero (e.g., , , )
- Absolute value
- The distance of a number from zero, always positive (e.g., )
- Opposite
- A number that is the same distance from zero but on the other side (e.g., opposite of is )
- Additive inverse
- Another name for the opposite; a number plus its additive inverse equals zero ()