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How to Add Positive Numbers with Negative Numbers

When the signs of two numbers that you're adding are different, forget the signs and find the difference between the numbers — which is the difference between their absolute values. The number farther from zero determines the sign of the answer.

For example:

(+a) + (–b) = + (|a| – |b|) if the positive a is farther from zero.

(+a) + (–b) = – (|a| – |b|) if the negative b is farther from zero.

Look what happens when you add numbers that have different signs:

  • You have $20 in your wallet and spend $12 for your theatre ticket.

    (+20) + (–12) = +8

    After settling up, you have $8 left.

    Because the signs are different, subtract 12 from 20 to get 8, and because +20 if farther from zero than –12, you give a positive sign to the answer, +8.

  • I have $20, but it costs $32 to fill my car’s gas tank.

    (+20) + (–32) = –12

    I’ll have to borrow $12 to fill the tank.

    Because the signs are different, subtract 20 from 32, and because –32 is farther from zero than +20, you make the answer negative, –12.

The following examples give you some more combinations:

(+6) + (–7) = –1

The difference between 6 and 7 is 1. Seven is farther from 0 than 6 is, so the answer is –1.

(–6) + (+7) = +1

This time the 7 is positive. It’s still farther from 0 than the 6, and so the answer is +1.

(–4) + (+3) + (+7) + (–5) = +1

If you take these numbers in order from left to right (although you can add in any order you like), you add the first two together to get –1. Add that amount to the next number to get +6. Then add this amount to the last number to get +1.

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