Adding and Subtracting Integers

🧱 See It

A positive tile and a negative tile standing next to each other cancel out completely — together they're worth 0. That's called a zero pair.

−1

One positive, one negative — net value 0. They cancel.

Now try (+4) + (−3): lay out 4 positive tiles and 3 negative tiles together.

−1

Match up 3 positive tiles with the 3 negative tiles — those 3 pairs cancel to zero. Only 1 positive tile has no partner left, so it's the answer: (+4) + (−3) = 1.

✏️ Draw It

On a number line, adding and subtracting are just moves:

Add a positive → move right.
Add a negative → move left.
Subtract → turn around and move the opposite way you normally would.

Example: start at 2, then compute 2 + (−5) — add a negative, so move 5 steps left.

−5

−4

−3

−2

−1

Start at 2, move 5 steps left, land on −3. So 2 + (−5) = −3.

🔢 Write It

Two signs sitting next to each other always simplify to one:

Adding a negative is the same as subtracting: a + (−b) = a − b

Subtracting a negative is the same as adding: a − (−b) = a + b

Rewrite first, calculate second — never both at once:

5 − (−3) = 5 + 3 = 8

💡 Worked Examples

Example 1: (+4) + (−3)

Lay out 4 positive tiles and 3 negative tiles.
Pair up positives with negatives — each pair is a zero pair and cancels.
3 pairs cancel, leaving 1 positive tile with no partner.
Answer: (+4) + (−3) = 1

Example 2: −2 − (−6)

Two signs together: subtracting a negative is the same as adding. Rewrite first: −2 − (−6) = −2 + 6
Now it's just addition. Start at −2 on the number line.
Add a positive, so move 6 steps right: −2 → −1 → 0 → 1 → 2 → 3 → 4.
Answer: −2 − (−6) = 4

🧠 Quick Reference

You see	It really means
`+ (−x)`	`−x`
`− (−x)`	`+x`

Two signs together always collapse into one: a plus and a minus together act like a minus. Two minuses together act like a plus.

Once it's a plain addition problem: same signs → add the numbers, keep the sign. Different signs → cover up the signs for a second, subtract the smaller number from the bigger number (e.g. for 4 and 3, that's 4 − 3 = 1), then give the answer the sign of whichever original number was farther from zero.