Algebra I All-in-One For Dummies. Mary Jane Sterling
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Название: Algebra I All-in-One For Dummies
Автор: Mary Jane Sterling
Издательство: John Wiley & Sons Limited
Жанр: Математика
isbn: 9781119843061
isbn:
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?
FIGURE 2-1: A number line.
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
2 Which number is larger,
3 Which number is larger,
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. |
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.
A.
Q. Write the description using math notation:
A.