Algebra I All-in-One For Dummies. Mary Jane Sterling

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СКАЧАТЬ wish I had something as alliterative for all the rules, but this is math, not poetry!

      Say you’re adding –3 and –2. The signs are the same; so you find the sum of 3 and 2, which is 5. The sign of this sum is the same as the signs of –3 and –2, so the sum is also a negative.

      Here are some examples of finding the sums of same-signed numbers:

       : The signs are both positive, and so is the sum.

       : The sign of the sum is the same as the signs.

       : Because all the numbers are positive, add them and make the sum positive, too.

       : 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.

      

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.

      

Q.

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

      Q.

      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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      Making a Difference with Signed Numbers

      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 that you find 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 isn’t the same as . 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?)

When subtracting signed numbers, change the minus sign to a plus sign and change the number that the minus sign was in front of (the second number) to its opposite. Then just add the numbers using the rules for adding signed numbers.

       

       

       

       

      

These first examples put the process of subtracting signed numbers into real-life СКАЧАТЬ