Unit 7, Lesson 2
Comparing Positive and Negative Numbers
Accelerated 6
2.1
Warm-up
Which of the following numbers could be represented by point ?
2.45
2.11
-2.5
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Which of the following numbers could be represented by point ?
2.45
2.11
-2.5
Plot the numbers -2, 4, -7, and 10 on the number line. Label each point with its numeric value.
Decide whether each inequality statement is true or false. Be prepared to explain your reasoning.
The symbol “>” means “is greater than.” The symbol “<” means “is less than.”
A statement that uses these symbols to compare two values or expressions is called an inequality.
The phrases “greater than” and “less than” can be used to compare numbers on the number line. For example, the numbers -2.7, 0.8, and -1.3, are shown on the number line.
Because -2.7 is to the left of -1.3, we say that -2.7 is less than -1.3. We write:
In general, any number that is to the left of a number is less than .
We can see that -1.3 is greater than -2.7 because -1.3 is to the right of -2.7. We write:
In general, any number that is to the right of a number is greater than .
Here is another labeled number line with some rational numbers. A rational number is a number that can be written as a positive or negative fraction or zero.
The number 4 is positive, and its location is 4 units to the right of 0 on the number line. The number 4 can be written as or or any other equivalent fraction.
The number is negative, and its location is units to the left of 0 on the number line.
An inequality is a statement that compares two values or expressions using symbols such as “” or “”.
For example, the inequality tells us that -3 is greater than -7.
A rational number is a number that can be written as a positive fraction, a negative fraction, or zero.
The sign of any number other than 0 is either positive or negative.
For example, the sign of 6 is positive. The sign of -6 is negative. Zero does not have a sign, because it is not positive or negative.