Adding Integers

Q: Does $-6 + (-9)$ mean the same thing as $-6 - 9$?

Yes — both equal $-15$. Adding a negative number is the same as subtracting the positive version of it. That connection becomes the main rule when you learn to subtract integers.

Adding integers comes down to two rules, and which one you use depends on the signs. Same signs — like $-6 + (-9)$ — you add the absolute values and keep that shared sign. Different signs — like $-8 + 3$ — you subtract the absolute values and take the sign of the number that is farther from zero.

If the rules ever feel arbitrary, think money. A debt of $6$ plus a debt of $9$ is a debt of $15$ : same signs, amounts pile up. A debt of $8$ plus an income of $3$ leaves a debt of $5$ : different signs, the amounts fight and the bigger one wins.

Same signs: add and keep the sign

When both integers are positive, you already know what to do: $6 + 4 = 10$ . When both are negative, it works the same way in the other direction: $-6 + (-4) = -10$ . Add the absolute values ( $6 + 4 = 10$ ), then keep the sign both numbers share.

Two negatives never cancel each other when adding — they stack. Each one pushes the total farther left on the number line.

Different signs: subtract, and the bigger absolute value wins

When the signs differ, the numbers pull in opposite directions, so part of each cancels. Subtract the smaller absolute value from the larger one, then give the answer the sign of the number with the larger absolute value.

For $-8 + 3$ : the absolute values are $8$ and $3$ , and $8 - 3 = 5$ . The $8$ belonged to the negative number, so the answer is $-5$ .

Zero pairs

A number plus its opposite is always zero: $7 + (-7) = 0$ . Each $+1$ cancels a $-1$ , so we call them zero pairs. This is exactly what integer tiles show — pair up the positive and negative tiles, cross out the pairs, and whatever is left over is the sum.

In the tiles below, each of the seven positive tiles pairs off with a negative tile, so every tile cancels and $7 + (-7) = 0$ .

Zero pairs also explain the different-signs rule: in $6 + (-4)$ , four of the positives pair off with the four negatives and vanish, leaving $2$ .

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Worked examples

Example 1: same signs

Add $-6 + (-9)$ .

The signs match — both negative

Add the absolute values

6 + 9 = 15

Keep the shared sign

-6 + (-9) = -15

Answer: $-15$

Example 2: different signs, negative wins

Add $-8 + 3$ .

The signs differ — one negative, one positive

Subtract the absolute values

8 - 3 = 5

The larger absolute value (

8

) is negative

-8 + 3 = -5

Answer: $-5$

Example 3: different signs, positive wins

Add $-7 + 12$ .

The signs differ

Subtract the absolute values

12 - 7 = 5

The larger absolute value (

12

) is positive

-7 + 12 = 5

Answer: $5$

Try one yourself

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Common questions

How do I know whether to add or subtract the numbers?

Check the signs. Same signs: add the absolute values and keep that sign. Different signs: subtract the absolute values and take the sign of the number farther from zero.

Why does the answer take the sign of the bigger number?

Because the two numbers pull in opposite directions and only partly cancel. Whatever is left over belongs to the side that had more. In $-8 + 3$ , the negative side had more, so the leftover $5$ is negative.

What is a zero pair?

A positive and a negative that cancel exactly, like $+1$ and $-1$ , or $7$ and $-7$ . Any number plus its opposite equals $0$ . Crossing out zero pairs is how tile diagrams show integer addition.

Does

-6 + (-9)

mean the same thing as

-6 - 9

Yes — both equal $-15$ . Adding a negative number is the same as subtracting the positive version of it. That connection becomes the main rule when you learn to subtract integers.

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