Adding and Subtracting Integers Made Easy: Tips & TricksAdding and subtracting integers is a foundational skill in math that shows up in everything from temperature changes and bank balances to algebra and coordinate geometry. This article breaks the topic down into clear rules, helpful visuals, common pitfalls, and plenty of practice strategies so you can build confidence and speed.
What are integers?
Integers are whole numbers and their negatives: … −3, −2, −1, 0, 1, 2, 3, … They do not include fractions or decimals. Integers are used to represent quantities that can go up or down, such as elevation, temperature, or money.
Core rules — quick reference
- Adding two positive integers: add their absolute values; the result is positive.
Example: 5 + 3 = 8 - Adding two negative integers: add their absolute values; the result is negative.
Example: (−5) + (−3) = −8 - Adding integers with opposite signs: subtract the smaller absolute value from the larger absolute value; the result has the sign of the number with the larger absolute value.
Example: 7 + (−3) = 4 ; (−7) + 3 = −4 - Subtracting an integer: rewrite subtraction as addition of the opposite. That is, a − b = a + (−b).
Example: 5 − (−2) = 5 + 2 = 7 ; (−3) − 4 = (−3) + (−4) = −7
Tip: If you keep the rule “change the sign of the second number and add,” subtraction becomes just another addition problem.
Visual tools that help
Number line
- Plot numbers on a number line. Moving right means adding; moving left means subtracting.
- Example: For 2 + (−5), start at 2 and move 5 left to land at −3.
Counters (chips)
- Use two colors: one color for positives, one for negatives. Pair off one positive and one negative to cancel to zero.
- Example: For 4 + (−6), start with four positive chips and six negative chips. Pair four pairs to cancel, leaving two negative chips → result = −2.
Temperature/Bank analogies
- Temperature: gaining degrees is positive, losing degrees is negative.
- Bank: deposits are positive, withdrawals/overdrafts are negative.
Step-by-step strategies
- Identify signs of both numbers.
- If signs are the same: add absolute values, keep the common sign.
- If signs differ: subtract the smaller absolute value from the larger; keep the sign of the larger absolute value.
- For subtraction problems, convert to addition by changing the sign of the second number, then follow the above rules.
Example workflow:
- Problem: (−8) − (−3)
- Step 1: Rewrite: (−8) + 3
- Step 2: Signs differ → subtract: 8 − 3 = 5
- Step 3: Keep sign of larger absolute value (8 is larger and negative) → −5
Common mistakes and how to avoid them
- Mixing up signs when subtracting: Always change subtraction to addition of the opposite before solving.
- Forgetting to keep the sign of the number with the larger absolute value when signs differ.
- Cancelling incorrectly with counters—ensure you only cancel one positive with one negative.
- Rushing mental arithmetic—use the number line for tricky or close absolute values.
Practice types and sample problems
Beginner (focus on rules)
- 7 + 4
- (−6) + (−2)
- 9 + (−5)
- (−3) − 7
Intermediate (mix of signs, subtraction)
- (−4) + 9
- 10 − (−3)
- (−12) + 5
- 8 + (−13)
Advanced (multi-step and parentheses)
- (−3) + 5 − (−2)
- −(−7) + (−4) − 2
- 15 + (−20) + 9 − (−6)
Answers:
- Beginner: 11; −8; 4; −10
- Intermediate: 5; 13; −7; −5
- Advanced: (−3) + 5 − (−2) = 4; −(−7) + (−4) − 2 = 1; 15 + (−20) + 9 − (−6) = 10
Mental math shortcuts
- Pair positives and negatives to cancel early.
- Group terms with the same sign to reduce steps (e.g., add all positives first, add all negatives, then combine).
- Use complements: when adding numbers like 9 + (−6), think 9 − 6 = 3.
- For sequences, cumulative running total on a number line keeps track visually.
Teaching tips (for tutors/parents)
- Start with concrete manipulatives (chips, counters) before abstract rules.
- Use real-world contexts (temperature, money) to make signs meaningful.
- Encourage students to verbalize steps: “change subtraction to addition of opposite,” “subtract smaller from larger,” “keep sign of larger.”
- Quick daily drills with mixed-sign problems build fluency.
Final checklist for solving any problem
- Convert subtraction to addition of the opposite when needed.
- Determine whether signs are the same or different.
- Compute absolute-value addition or subtraction accordingly.
- Assign the correct sign (same sign if added; sign of larger absolute value if subtracted).
- Double-check with a number line or counters if unsure.
Adding and subtracting integers becomes intuitive with a few clear rules and regular practice. Use a number line or counters when learning, convert subtraction into addition, and remember: same signs — add; different signs — subtract and take the sign of the larger absolute value.
Leave a Reply