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

faces the smaller side.

      7 . The difference refers to subtraction, and the product refers to multiplication. The point of the symbol faces the smaller result.

      8 3. The three terms are separated by the two subtraction symbols.

      9 3. The number 3 divides each of the terms evenly (leaving no remainder).

      10 All of the terms are real except for . The number is a repeating decimal and is a rational number; it can be written as or . See Chapter 4 for more on repeating decimals. The number is a rational number and so is real. The number is equal to 2,809 and is a whole number. And is a rational number, already written as a fraction. The number has the imaginary factor of i, so it is imaginary and not real.

      11 1. The number 1 is a term that stands alone and isn’t multiplying or dividing any other number. The 4 and 9 are both part of the coefficients of their respective terms.

      12 5. The 5 multiplies the variable x.

      13

      The number line is broken up into units of 0.2 in length. The number has to be estimated, as it’s halfway between and . The other two numbers have tick marks to rest on.

      14 . The “wavy equal sign” symbol means the answer is approximate and has been rounded.

      15 . The two terms are combined by subtracting 1 from 4. The two constants are added together.

Chapter 2

      Deciphering Signs in Expressions

      IN THIS CHAPTER

       Using the number line

       Recognizing operations

       Operating on signed numbers: adding, subtracting, multiplying, and dividing

      Numbers have many characteristics: They can be big, little, even, odd, whole, fractions, positive, negative, and sometimes cold and indifferent. (I’m kidding about that last one.) Chapter 1 describes numbers’ different names and categories. But this chapter concentrates mainly on how numbers compare to one another, what their comparison looks like on the number line, the positive and negative characteristics of numbers, and how a number’s sign reacts to different manipulations. This chapter tells you how to add, subtract, multiply, and divide signed numbers, no matter whether all the numbers are all the same sign or a combination of positive and negative.

Assigning Numbers Their Place

      Positive numbers are greater than 0. They’re on the opposite side of 0 from the negative numbers. If you were to arrange a tug-of-war between positive and negative numbers, the positive numbers would line up on the right side of 0. Negative numbers get smaller and smaller, the farther they are from 0. This situation can get confusing because you may think that –400 is bigger than –12. But just think of –400°F and –12°F. Neither is anything pleasant to think about, but –400°F is definitely less pleasant — colder, lower, smaller.

      Using the number line

      When comparing negative numbers, the number closer to 0 is the bigger or greater number. You may think that recognizing that 16 is bigger than 10 is an easy concept. But what about –1.6 and –1.04? Which of these numbers is bigger?

The easiest way to compare numbers and to tell which is bigger or has a greater value is to find each number’s position on the number line. The number line goes from negatives on the left to positives on the right (see Figure 2-1). Whichever number is farther to the right has the greater value, meaning it’s bigger.

      FIGURE 2-1: A number line.

      

Q. Using the number line in Figure 2-1, determine which is larger, –16 or –10.

      A. The number –10 is to the right of –16, so it’s the bigger of the two numbers.

      Q. Which is larger, –1.6 or –1.04?

      A. The number –1.04 is to the right of –1.6, so it’s larger. A nice way to compare decimals is to write them with the same number of decimal places. So rewrite –1.6 as –1.60; it’s easier to compare to –1.04 in this format.

Now that you’ve seen some examples of using a number line to compare numbers, try the following problems for practice. Use the number line found in Figure 2-2.

      FIGURE 2-2: Another number line.

      1 Which number is larger, 4.6 or ?

      2 Which number is larger, or 0?

3 Which number is larger,