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Adding different signs

Can a relationship between a Leo and a Gemini ever add up to anything? I don’t know the answer to that question, but I do know that numbers with different signs add up very nicely. You just have to know how to do the computation, and, in this section, I tell you.

When the signs of two numbers are different, forget the signs for a while and find the difference between the numbers. This is the difference between their absolute values (see the “Getting it absolutely right with absolute value” section, earlier in this chapter). The number farther from 0 determines the sign of the answer.

if the positive a is farther from 0.

if the negative b is farther from 0.

Look what happens when you add numbers with different signs:

You had $20 in your wallet and spent $12 for your movie ticket:After settling up, you have $8 left. You knew the answer would be positive, because +20 is farther from 0 than –12, and the difference between 20 and 12 is 8.

I have $20, but it costs $32 to fill my car’s gas tank:I’ll have to borrow $12 to fill the tank. This time the answer will be negative, because –32 is farther from 0 than +20. The difference between the two numbers is 12.

Here’s how to solve these two situations using the rules for adding signed numbers.

: Find the difference between 20 and 12: . Because 20 is farther from 0 than 12, the result is positive, so .

: Find the difference between 20 and 32: . Because 32 is farther from 0 than 20 and is a negative number, the result is negative, so .

Here are some more examples of finding the sums of numbers with different signs:

: The difference between 6 and 7 is 1. Because 7 is farther from 0 than 6 is, and 7 is negative, the answer is –1.

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

: If you take these operations 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 –1 to the +7 to get +6. Then add +6 to –5, the last number, to get +1.

A. The signs are the same, so you find the sum and apply the common sign. The answer is –10.

A. The signs are different, so you find the difference and use the sign of the number with the larger absolute value. The answer is –7.

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