Practice Maths

L32 — Adding & Subtracting Integers I

Key Terms

integer
Any whole number — positive, negative, or zero. E.g. …−3, −2, −1, 0, 1, 2, 3…
negative number
A number less than zero, written with a minus sign and located to the left of zero on the number line. E.g. −4.
number line
A horizontal scale with numbers increasing from left to right; negative numbers sit to the left of zero, positives to the right.

The Walking Rule

To add or subtract integers, imagine standing on a number line:

  1. Start at the first number.
  2. Face right if the second number is positive; face left if it is negative.
  3. Walk forwards for addition (+); walk backwards for subtraction (−).
  4. Where you land is the answer.

Worked Example

Calculate −3 + 5

Step 1 — Start: Stand at −3 on the number line.

Step 2 — Face: The second number (5) is positive → face right.

Step 3 — Walk: Operation is + (addition) → walk forwards 5 steps.

Answer: −3 + 5 = 2

Integers: Numbers That Go Below Zero

Integers include all whole numbers: …−3, −2, −1, 0, 1, 2, 3… Negative integers are just as real as positive ones.

  • Temperature: −5°C means 5 degrees below freezing.
  • Elevators: floor −2 is 2 levels underground.
  • Bank accounts: −$50 means you owe $50.

The Walking Rule in Full

Imagine yourself standing on a giant number line:

  • Starting position = the first number in the calculation.
  • Which way to face: second number positive → face RIGHT; second number negative → face LEFT.
  • Walk: addition (+) → walk FORWARDS; subtraction (−) → walk BACKWARDS.

Example: 4 − 6. Start at +4. Second number (6) is positive → face RIGHT. Operation is − (subtraction) → walk BACKWARDS 6 steps. Land on −2.

Temperature and Everyday Analogies

  • It’s −4°C and the temperature rises 10°C: −4 + 10 = 6°C.
  • It’s 2°C and the temperature drops 7°C: 2 − 7 = −5°C.
  • A freezer is at −15°C and warms 5°C: −15 + 5 = −10°C.
The most common mistake is confusing the negative sign of a number (where it sits on the number line) with the minus operation (the action of subtracting). In −4 − 3: the first −4 says “start at negative four”; the middle − says “walk backwards three steps.”

Subtracting from a Negative

−5 − 3 = −8, not −2. You start at −5 and walk 3 more steps in the negative direction — you go further into the negatives, not back toward zero. Two negatives only combine to give a positive in multiplication and division.

Common mistake: −5 − 3 ≠ −2. Subtracting a positive from a negative makes it more negative. Walk backwards from −5: that takes you to −6, −7, −8. The answer is −8.

  1. Number Line Orientation

    Use this number line to help you. Numbers increase to the right and decrease to the left.

    −10 −8 −6 −4 −2 0 2 4 6 8 10 ← Smaller Larger →
    1. Which is larger: −3 or −7?
    2. Which is smaller: 0 or −4?
    3. Identify the integer 4 units to the left of 1.
    4. Identify the integer 6 units to the right of −3.
    5. What is the difference between −2 and +5?
    6. What is the difference between −8 and −2?

  2. Vocabulary & Logic

    1. In the problem “−4 − 6”, which number is the starting position?
    2. In the problem “−4 − 6”, which symbol is the operation?
    3. True or False: A negative integer is always smaller than a positive integer.
    4. True or False: Walking backwards while facing Right moves you toward the negative numbers.

  3. Adding Positives (Starting Negative)

    1. −5 + 2
    2. −8 + 8
    3. −1 + 4
    4. −10 + 6
    5. −3 + 7
    6. −7 + 3
    7. −2 + 10
    8. −6 + 1

  4. Subtracting Positives (Starting Positive)

    1. 4 − 6
    2. 2 − 7
    3. 10 − 15
    4. 5 − 5
    5. 3 − 10
    6. 8 − 12
    7. 1 − 4
    8. 9 − 20

  5. Subtracting Positives (Starting Negative)

    1. −1 − 4
    2. −5 − 3
    3. −2 − 6
    4. −8 − 2
    5. −4 − 5
    6. −10 − 5
    7. −3 − 7
    8. −7 − 4

  6. The Lift (Elevator) Challenge

    1. Start at floor −2 (Basement). Go up 5 floors. What floor are you on?
    2. Start at floor 6. Go down 10 floors. What floor are you on?
    3. Start at floor −1. Go down 3 more floors. What floor are you on?
    4. How many floors must you travel to get from floor −5 to floor 2?

  7. Temperature Shifts

    1. The temperature is −4°C. It rises 10°C. What is the new temperature?
    2. The temperature is 2°C. It drops 7°C. What is the new temperature?
    3. A freezer is at −15°C. It warms up 5°C. What is the temperature now?
    4. It is −1°C. It drops 8°C. What is the temperature now?

  8. Directional Expressions

    Write the expression and solve. Use the number line to trace each movement:

    −10 −8 −6 −4 −2 0 2 4 6 8 10
    1. Start at −9, move right 4.
    2. Start at 2, move left 6.
    3. Start at −3, move right 3.
    4. Start at −5, move left 5.

  9. Crossing Zero Check

    Which operations cross zero? (e.g. −2 + 5 crosses zero)

    1. −3 + 2
    2. −3 + 5
    3. 4 − 6
    4. −1 − 4
    5. −10 + 15
    6. 5 − 3

  10. Exam Challenge

    1. Find x if: x − 5 = −2
    2. Find n if: −4 + n = 3
    3. A bank account has −$20. A deposit of $50 is made. What is the balance?
    4. Explain why −4 − 2 = −6 and not −2.
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