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

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

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 1describes 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.

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.

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, or ?

4 Put the numbers in order from smallest to largest: 4, 0, , .

5 Put the numbers in order from smallest to largest: .

Although my mom always told me not to compare myself to other people, comparing numbers to other numbers is often useful. And, when you compare numbers, the greater-than sign (>) and less-than sign (<) come in handy, which is why I use them in Table 2-1, where I put some positive- and negative-signed numbers in perspective.

TABLE 2-1Comparing Positive and Negative Numbers

Comparison	What It Means
	6 is greater than 2; 6 is farther from 0 than 2 is.
	10 is greater than 0; 10 is positive and is bigger than 0.
	–5 is greater than –8; –5 is closer to 0 than –8 is.
	–300 is greater than –400; –300 is closer to 0 than –400 is.
	0 is greater than –6; –6 is negative and is smaller than 0.
	7 is greater than –80; –80 is negative and is smaller than 0.

Positive numbers are always bigger than negative numbers.