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      A. 5. First, do the subtraction, which tells you . To find the negation of −5, attach a negative sign to the answer: . The two adjacent negative signs cancel out, which gives you 5.

      Q. What number does equal?

      A. 9. The number 9 is already positive, so the absolute value of 9 is also 9.

      Q. What number does equal?

      A. 17. Because −17 is negative, the absolute value of .

      Q. Solve this absolute value problem:

      A. −4. Do the subtraction first: , which is negative, so the absolute value of . But the negative sign on the left (outside the absolute value bars in the original expression) negates this result, so the answer is −4.

      3 Negate each of the following numbers and expressions by attaching a negative sign and then canceling out negative signs when possible:

      (a)

      (b)

      (c)

      (d)

      (e)

      (f)

      4 Solve the following absolute value problems:

      (a)

      (b)

      (c)

      (d)

      (e)

(f)

Addition and Subtraction with Negative Numbers

      The great secret to adding and subtracting negative numbers is to turn every problem into a series of ups and downs on the number line. When you know how to do this, you find that all these problems are quite simple.

      So in this section, I explain how to add and subtract negative numbers on the number line. Don’t worry about memorizing every little bit of this procedure. Instead, just follow along so you get a sense of how negative numbers fit onto the number line. (If you need a quick refresher on how the number line works, see Chapter 1.)

      Starting with a negative number

      When you’re adding and subtracting on the number line, starting with a negative number isn’t much different from starting with a positive number. For example, suppose you want to calculate . Using the up and down rule, you start at and go up :

      Similarly, suppose you want to calculate . Again, the up and down rule helps you out. You’re subtracting, so move to the left: start at , down :

      .

      Adding a negative number

      Suppose you want to calculate . You already know to start at , but where do you go from there? Here’s the up and down rule for adding a negative number:

       Adding a negative number is the same as subtracting a positive number — go down on the number line.

By this rule, is the same as , so start at , down :

       If you rewrite a subtraction problem as an addition problem — for instance, rewriting you can use the commutative and associative properties of addition, which I discuss earlier in this chapter. Just remember to keep the negative sign attached to the number when you rearrange the problem: Скачать книгу