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2.1 Use Integers and Rational Numbers
Warm Up
Lesson Presentation
Lesson Quiz
2.1
Warm-Up
Complete the statement using <, >, or =.
1. 1.3
?
1.03
ANSWER
>
5
8
?
6
9
ANSWER
<
2.
2.1
Warm-Up
Complete the statement using <, >, or =.
3. Order from least to greatest: 1 , 0.04, 3 , 0.45
7
2
ANSWER
0.04, 3 , 0.45, 1
7
2
4. A hobby store has balsa wood strips in three
3
thicknesses (in inches):
, 5 , and 1 .
16 32
8
Which strip is the thickest?
ANSWER
3
-inch strip
16
2.1
Example 1
Graph – 3 and – 4 on a number line. Then tell which
number is greater.
ANSWER
On the number line, –3 is to the right of – 4. So, –3 > – 4.
2.1
Guided Practice
Graph the numbers on a number line. Then tell which
number is greater.
1.
4 and 0
0
–6
–5
–4
–3
–2
–1
0
4
1
2
3
4
5
ANSWER
On the number line, 4 is to the right of 0. So, 4 > 0.
6
2.1
2.
Guided Practice
2 and –5
–5
–6
–5
2
–4
–3
–2
–1
0
1
2
3
4
5
ANSWER
On the number line, 2 is to the right of –5. So, 2 > –5.
6
2.1
3.
Guided Practice
–1 and –6
–1
–6
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
ANSWER
On the number line, –1 is to the right of –6. So, –1 > –6.
2.1
Example 2
Tell whether each of the following numbers is a whole
number, an integer, or a rational number: 5, 0.6,
–2 2 , and –24.
3
2.1
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.
2.1
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.
2.1
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.
4. 3, –1.2, –2,0
ANSWER
Number
Whole
number?
Integer?
Rational
number?
3
Yes
Yes
Yes
–1.2
No
No
Yes
–2
No
Yes
Yes
0
Yes
Yes
Yes
–2, –1.2, 0, 3
(Ordered the numbers from least to greatest).
2.1
5.
Guided Practice
4.5, – 3 , – 2.1, 0.5
4
Number Whole
number?
Integer?
Rational
number?
4.5
No
No
Yes
3
4
No
No
Yes
–2 .1
No
No
Yes
0.5
No
No
Yes
–
ANSWER
– 2.1, – 3 , 0.5 , – 2.1.(Ordered the numbers from least to
4
greatest).
2.1
6.
Guided Practice
3.6, –1.5, –0.31, – 2.8
Number
Whole
number?
Integer?
Rational
number?
3.6
No
No
Yes
–1.5
No
No
Yes
–0.31
No
No
Yes
–2.8
No
No
Yes
ANSWER
–2.8, –1.5, – 0.31, 3.6 (Ordered the numbers from least to
greatest).
2.1
7.
Guided Practice
1 , 1.75, – 2 , 0
3
6
Number
Whole
number?
Integer?
Rational
number?
1
6
No
No
Yes
1.75
No
No
Yes
– 2
3
0
No
No
Yes
Yes
Yes
Yes
ANSWER
– 2 , 0 , 1 , 1.75. (Ordered the numbers from least to
3
6
greatest).
2.1
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 , then – a = – 3 .
4
4
2.1
Example 5
For the given value of a, find | a | .
a.
If a = – 2 , then | a | = |– 2 | = – (– 2 ) = 2 .
3
3
3
3
b. If a = 3.2, then |a| = |3.2| = 3.2.
2.1
Guided Practice
For the given value of a, find –a and |a|.
8.
a = 5.3
9.
a=–7
ANSWER
ANSWER
– 5.3, 5.3
7, 7
10. a = – 4
9
ANSWER
4 ,4
9 9
2.1
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.
2.1
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.
11. If a number is a rational number, then the
number is positive
ANSWER
Hypothesis: a number is a rational number
Conclusion: the number is positive – false
The number –1 is a counterexample, because –1 is a
rational number but not positive.
2.1
Guided Practice
12. If the absolute value of a number is a
positive, then the number is positive.
ANSWER
Hypothesis: the absolute value of a number is positive
Conclusion: the number is positive – false
The number –2 is a counterexample, because the
absolute value of –2 is 2, but –2 is negative.
2.1
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, 3 1 , –16.
4
ANSWER
–2.24 :rational number; 6: whole number, integer, rational
number ; 3 1 :rational number; –16 : integer, rational
4
number
2.1
Lesson Quiz
3. The table shows the boiling-point temperature of
some elements. Order the elements from lowest boilingpoint temperature to highest.
Element
Hydrogen
Mercury
Temperature
Nitrogen
Oxygen
– 196°C
– 183°C
– 2593°C
357°C
ANSWER
Hydrogen, Nitrogen, Oxygen, Mercury