Integers addition subtraction — rules with number line visualization

Question

Solve: (a) $(-5) + 3$ , (b) $(-7) + (-4)$ , (c) $6 - (-3)$ . Show each on a number line and state the rule used.

(CBSE Class 6 pattern)

Solution — Step by Step

Start at $-5$ on the number line. Adding a positive number means moving right by 3 steps.

-5 \to -4 \to -3 \to -2

(-5) + 3 = \mathbf{-2}

Rule used: When signs are different, subtract the smaller absolute value from the larger and keep the sign of the larger. $|{-5}| - |3| = 5 - 3 = 2$ , and since 5 is bigger and negative, answer is $-2$ .

Start at $-7$ . Adding a negative number means moving left (more negative) by 4 steps.

-7 \to -8 \to -9 \to -10 \to -11

(-7) + (-4) = \mathbf{-11}

Rule used: When both signs are the same, add the absolute values and keep the common sign. $7 + 4 = 11$ , both negative, so $-11$ .

Subtracting a negative is the same as adding a positive. Think of it as removing a debt — that makes you richer!

6 - (-3) = 6 + 3 = \mathbf{9}

Rule used: “Minus of minus is plus.” Two negatives together become a positive.

flowchart TD
    A["Integer addition/subtraction"] --> B{"Same signs?"}
    B -->|"Yes: both + or both -"| C["ADD the numbers"]
    C --> D["Keep the common sign"]
    B -->|"No: one + and one -"| E["SUBTRACT smaller from larger"]
    E --> F["Keep sign of the larger number"]
    A --> G{"Subtracting a negative?"}
    G -->|"Yes: a - (-b)"| H["Change to a + b"]

Why This Works

Integers extend the number line to the left of zero. Positive numbers go right, negative numbers go left. Addition means “move in the direction of the number being added” — add a positive, go right; add a negative, go left.

Subtraction is the reverse of addition. Subtracting $(-3)$ means “undo adding $(-3)$ ” which means “move right by 3” — exactly the same as adding $+3$ . That is why $a - (-b) = a + b$ .

Alternative Method — The Money Analogy

Think of positive numbers as money you HAVE and negative numbers as money you OWE.

$(-5) + 3$ : You owe Rs 5, then earn Rs 3. You still owe Rs 2. Answer: $-2$ .
$(-7) + (-4)$ : You owe Rs 7, then borrow Rs 4 more. Now you owe Rs 11. Answer: $-11$ .
$6 - (-3)$ : You have Rs 6, and someone cancels your Rs 3 debt. You now have Rs 9.

When confused about signs, always fall back to the number line. Draw it out physically. Start at the first number, then move right for addition of positive, left for addition of negative. This visual method never fails, even for complicated problems with multiple operations.

Common Mistake

The most common error: $(-5) + 3 = -8$ . Students add the numbers together instead of subtracting. When the signs are different, you SUBTRACT (take the difference), not add. Think of it as a tug-of-war — the stronger side wins by the difference. Here, $-5$ is stronger than $+3$ by 2 units, so the answer is $-2$ , not $-8$ .

Question

Solution — Step by Step

Why This Works

Alternative Method — The Money Analogy

Common Mistake

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