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Adding and Subtracting with Negatives

ADDING WITH NEGATIVE NUMBERS

The first thing to know is that x and its additive inverse,–x, add up to zero. So:

–999 + 999 = 0

(1/3) + (–1/3) = 0

1 + (–1) = 0

Once you know this, it's easy to add any two integers using imaginary tiles.

For example, suppose you want to add 5 + (–2). Let yellow tiles stand for positive ones, and let red tiles stand for negative ones.

Group the two negative tiles with two positive tiles.

Since 2 + (–2) = 0, these tiles disappear. We are left with 3 positive tiles.

So 5 + (–2) = 3.

When both numbers are negative, we have only negative tiles, so the answer is also negative. For example:

–6 + (–11) = –17

–2000 + (–3000) = –5000

When one number is positive and the other number is negative, either use tiles (as above) OR:

Subtract the smaller absolute value from the greater absolute value. Then, give your answer the same sign as the number with greater absolute value.

For example:

–11 + 8

The absolute value of –11 is 11, and the absolute value of 8 is 8.

So, subtract: 11 – 8 = 3

Since –11 had the greater absolute value, the answer is negative.

–11 + 8 = –3

SUBTRACTING WITH NEGATIVE NUMBERS

You can use imaginary tiles to help you here, too.

Start with 7 red (negative) tiles, and remove 3 of them. You are left with 4 negative tiles. So,

–7 – (–3) = –4

For other problems, you may need to add "zero pairs."

Start with 5 positive tiles.

We need to subtract 8 positive tiles, so we add 3 zero pairs.

After removing the 8 positive tiles, we are left with 3 negative tiles. So,

5 – 8 = –3

Start with 3 negative tiles.

We need to subtract 5 negative tiles. So, add 2 zero pairs.

Now, after removing 5 negative tiles, we are left with 2 positive tiles. So,

–3 – (–5) = 2