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

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

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

      Comparing positives and negatives with symbols

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 2-1 Comparing 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.

      Two other signs related to the greater-than and less-than signs are the greater-than-or-equal-to sign (≥) and the less-than-or-equal-to sign (≤).

So, putting the numbers 6, –2, –18, 3, 16, and –11 in order from smallest to largest gives you –18, –11, –2, 3, 6, and 16, which are shown as dots on a number line in Figure 2-3.

      FIGURE 2-3: Positive and negative numbers on a number line.

      

Q. Write the description using math notation: is greater than .

      A. . The point of the arrow is always in the direction of the smaller of the two numbers.

      Q. Write the description using math notation: is less than or equal to 0.

      A. . You could also write the inequality as , which is read, “0 is greater than or equal to .”

      6 Write the description using math notation: is less than 1.

      7 Write the description using math notation: is greater than .

      8 Write the description using math notation: is less than or equal to 11.

      9 Write the description using math notation: is greater than or equal to .

10 Write the description using math notation: is greater than or equal to .

      Zeroing in on Zero

      But what about 0? I keep comparing numbers to see how far they are from 0. Is 0 positive or negative? The answer is that it’s neither. Zero has the unique distinction of being neither positive nor negative. Zero separates the positive numbers from the negative ones — what a job! When using the number line to determine the order of numbers — which one is larger — you look at how far the number is from 0. You already know that a positive number is going to be larger than a negative number, but comparing two negative numbers can be a bit more challenging. You put the two negative numbers on the number line. The negative number that’s farthest from 0 is the smaller of the two numbers.

      

Q. Which number is larger, –3 or –13?

      A. –3. Look at the following number line. You see that –3 is to the right of –13. In terms of distance from 0, –13 is much farther away, so it is smaller than –3.

      11 Which is larger, –2 or –8?

      12 Which has the greater value, –13 or –1?

      13 Which is bigger, –0.003 or –0.03?

14 Which is larger, or