✓ (–5) + (–2) + (–3) + (–1) = –11: This time all the numbers are negative, so add them and give the sum a minus sign.
Adding same-signed numbers is a snap! (A little more alliteration for you.)
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.
Tip: 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.
Look what happens when you add numbers with different signs:
✓ You had $20 in your wallet and spent $12 for your movie ticket:
(+20) + (–12) = +8
✓ After settling up, you have $8 left.
✓ 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.
Here’s how to solve the two situations above using the rules for adding signed numbers.
✓ (+20) + (–12) = +8: The difference between 20 and 12 is 8. Because 20 is farther from 0 than 12, and 20 is positive, the answer is +8.
✓ (+20) + (–32) = –12: The difference between 20 and 32 is 12. Because 32 is farther from 0 than 20 and is a negative number, the answer is –12.
Here are some more examples of finding the sums of numbers with different signs:
✓ (+6) + (–7) = –1: The difference between 6 and 7 is 1. Seven is farther from 0 than 6 is, and 7 is negative, so the answer is –1.
✓ (–6) + (+7) = +1: This time the 7 is positive. It’s still farther from 0 than 6 is. The answer this time is +1.
✓ (–4) + (+3) + (+7) + (–5) = +1: If you take these 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 next number to get +6. Then add +6 to the last number to get +1.
Examples
Q. (–6) + (–4) = –(6 + 4) =
A. The signs are the same, so you find the sum and apply the common sign. The answer is –10.
Q. (+8) + (–15) = –(15 – 8) =
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.
Practice Questions
1. 4 + (–3) =
2. 5 + (–11) =
3. (–18) + (–5) =
4. 47 + (–33) =
5. (–3) + 5 + (–2) =
6. (–4) + (–6) + (–10) =
7. 5 + (–18) + (10) =
8. (–4) + 4 + (–5) + 5 + (–6) =
Practice Answers
1. 1. 4 is the greater absolute value.
2. – 6. –11 has the greater absolute value.
3. – 23. Both of the numbers have negative signs; when the signs are the same, find the sum of their absolute values.
4. 14. 47 has the greater absolute value.
5. 0.
6. – 20.
7. – 3.
Or you may prefer to add the two numbers with the same sign first, like this:
You can do this because order and grouping (association) don’t matter in addition.
8. – 6.
Subtracting signed numbers is really easy to do: You don’t! Instead of inventing a new set of rules for subtracting signed numbers, mathematicians determined that it’s easier to change the subtraction problems to addition problems and use the rules I explain in the previous section. Think of it as an original form of recycling.
Consider the method for subtracting signed numbers for a moment. Just change the subtraction problem into an addition problem? It doesn’t make much sense, does it? Everybody knows that you can’t just change an arithmetic operation and expect to get the same or right answer. You found out a long time ago that 10 – 4 isn’t the same as 10 + 4. You can’t just change the operation and expect it to come out correctly.
So, to make this work, you really change two things. (It almost seems to fly in the face of two wrongs don’t make a right, doesn’t it?)
Tip: When subtracting signed numbers, change the minus sign to a plus sign and change the number that the minus sign was in front of to its opposite. Then just add the numbers using the rules for adding signed numbers.
✓ (+a) – (+b) = (+a) + (–b)
