1. Use Integers and Rational Numbers
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
Complete the statement using <, >, or =. ?
ANSWER
> ? 5 8 6 9
ANSWER
<

3. Warm-Up
Complete the statement using <, >, or =.
3. Order from least to greatest: , 0.04, , 0.45 1 2 3 7
ANSWER
0.04, , 0.45, 3 7 1 2
A hobby store has balsa wood strips in three thicknesses (in inches): , , and Which strip is the thickest? 3 16 5 32 1 8 4.
ANSWER 3 16
-inch strip

4. Example 1
Graph – 3 and – 4 on a number line. Then tell which number is greater.
On the number line, –3 is to the right of – 4. So, –3 > – 4.
ANSWER

5. Graph the numbers on a number line. Then tell which number is greater.
Guided Practice
Graph the numbers on a number line. Then tell which number is greater.
and 0
– – – – – – 4
On the number line, 4 is to the right of 0. So, 4 > 0.
ANSWER

6. On the number line, 2 is to the right of –5. So, 2 > –5. ANSWER
Guided Practice
and –5
– – – – – – 2 –5
On the number line, 2 is to the right of –5. So, 2 > –5.
ANSWER

7. On the number line, –1 is to the right of –6. So, –1 > –6. ANSWER
Guided Practice
3. –1 and –6
– – – – – – –1 –6
On the number line, –1 is to the right of –6. So, –1 > –6.
ANSWER

8. Example 2
Tell whether each of the following numbers is a whole
number, an integer, or a rational number: 5, 0.6,
–2 , and –24. 2 3

9. Example 3
ASTRONOMY
A star’s color index is a measure of the temperature of the star. The greater the color index, the cooler the star. Order the stars in the table from hottest to coolest.
SOLUTION
Begin by graphing the numbers on a number line.

10. Example 3
Read the numbers from left to right: – 0.22, – 0.03, 0.09, 0.21.
ANSWER
From hottest to coolest, the stars are Shaula, Rigel,
Denebola, and Arneb.

11. Guided Practice
Tell whether each number in the list is a whole number, an integer, or a rational number. Then order the numbers from least to greatest.
, –1.2, –2,0
Yes No –2
–1.2 3
Rational number?
Integer?
Whole number?
Number
ANSWER
–2, –1.2, 0, 3
(Ordered the numbers from least to greatest).

12. – 2.1, – , 0.5 , – 2.1.(Ordered the numbers from least to greatest). 3
Guided Practice
, – , – 2.1, 0.5 3 4
Yes No
0.5
–2 .1
4.5
Rational number?
Integer?
Whole number?
Number 3 4 –
ANSWER
– 2.1, – , 0.5 , – 2.1.(Ordered the numbers from least to
greatest). 3 4

13. Guided Practice
, –1.5, –0.31, – 2.8
Yes No
–2.8
–0.31
3.6
Rational number?
Integer?
Whole number?
Number
–1.5
ANSWER
–2.8, –1.5, – 0.31, 3.6 (Ordered the numbers from least to greatest).

14. – , 0 , , 1.75. (Ordered the numbers from least to greatest). 2 3 1 6
Guided Practice 1 6
, 1.75, – , 0 2 3 1 6
Yes No
Rational number?
Integer?
Whole number?
Number
1.75 2 3 –
ANSWER
– , 0 , , (Ordered the numbers from least to greatest). 2 3 1 6

15. Example 4
For the given value of a, find –a.
a. If a = – 2.5,
then – a = –(– 2.5) = 2.5.
b. If a = , 3 4 3 4
then – a = – .

16. Example 5
For the given value of a, find | a | . 2 3
a. If a = – , 2 3
then | a | = |– | = – (– ) = .
b. If a = 3.2,
then |a| = |3.2| = 3.2.

17. Guided Practice
For the given value of a, find –a and |a|.
8. a = 5.3
9. a = – 7
– 5.3, 5.3
ANSWER
7, 7
ANSWER
a = 4 9 –
ANSWER 4 9 ,

18. Example 6
Identify the hypothesis and the conclusion of the statement “If a number is a rational number, then the number is an integer.” Tell whether the statement is true or false. If it is false, give a counterexample.
SOLUTION
Hypothesis: a number is a rational number
Conclusion: the number is an integer
The statement is false. The number 0.5 is a counterexample, because 0.5 is a rational number but not an integer.

19. Guided Practice
Identify the hypothesis and the conclusion of the statement. Tell whether the statement is true or false. If it is the false, give a counterexample.
If a number is a rational number, then the number is positive
Hypothesis: a number is a rational number
ANSWER
Conclusion: the number is positive – false
The number –1 is a counterexample, because –1 is a rational number but not positive.

20. Guided Practice
If the absolute value of a number is a positive, then the number is positive.
12.
Hypothesis: the absolute value of a number is positive
ANSWER
Conclusion: the number is positive – false
The number –2 is a counterexample, because the absolute value of –2 is 2, but –2 is negative.

21. Lesson Quiz
1. Graph – 3 and –5 on a number line.Then tell which number is greater.
ANSWER
–3 > –5
2. Tell whether each number is a whole number, an integer, or a rational number: –2.24, 6, , –16. 3 1 4
ANSWER
–2.24 :rational number; 6: whole number, integer, rational number ; :rational number; –16 : integer, rational number 3 1 4

22. Lesson Quiz
3. The table shows the boiling-point temperature of some elements. Order the elements from lowest boiling-point temperature to highest.
Element
Temperature
Hydrogen
– 2593°C
Mercury
357°C
Nitrogen
– 196°C
Oxygen
– 183°C
ANSWER
Hydrogen, Nitrogen, Oxygen, Mercury