Download Comparing and Ordering Rational Numbers

Lesson 1
TAKS Grade 8 Objective 1
(8.1)(A)
Comparing and Ordering
Rational Numbers
The set of whole numbers and their opposites is called the set of integers.
Examples: 5, 3, 0, 6, 11
New Vocabulary
Comparing and Ordering Integers
• integers
• rational numbers
Use a number line to compare integers.
As you move to the right on a horizontal number line, numbers increase
in value.
4
2
0
2
4
2 is to the right of 4, so 2 is greater than 4.
EXAMPLE 1
Use a number line to compare and order these integers: 4, 1, 5, 1.
Step 1 Use a number line to represent the integers.
5
1
1
4
a < b < c < d means:
“a is less than b, b
is less than c, and c is
less than d.”
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Step 2 Compare the integers two at a time using the number line.
5 is to the left of 1, so 5 1.
1 is to the left of 1, so 1 1.
1 is to the left of 4, so 1 4.
Step 3 Order the integers using inequality signs.
5 1 and 1 1 and 1 4, so 5 1 1 4.
Quick Check 1
1a. Use a number line to order these integers:
3, –1, –2.
TAKS Review and Preparation Workbook
1b. Order these integers from least to greatest:
2, 0, 6, 1, 3.
LESSON 1
■
Comparing and Ordering Rational Numbers
1
TAKS Objective 1 (8.1)(A)
LESSON 1
The set of rational numbers consists of all numbers that can be expressed in
the form ba , where a and b are integers and b 0.
Examples: 35, 0.54, 25%
Comparing and Ordering Rational Numbers
To order a set of rational numbers in which some are fractions or percents
and some are decimals, convert them all to decimals. Then line up the
numbers on the decimal point, use trailing zeros to fill out each number to
the same number of decimal digits, and then compare.
EXAMPLE 2
Order 31, 0.41, 0.35, 45, 30%, and 1.2 from least to greatest.
To order a set of rational numbers in which some are fractions and some are decimals,
write each fraction as a decimal: 13 0.333. . . and 45 0.8.
Add trailing zeros and order the decimals from least to greatest. 1.20, 0.80, 0.41,
0.30, 0.333. . ., 0.35.
1.2 45
30%
0.41
1
1
12 1 2
0
1
3
0.35
1
2
1
1
12
2a. Order 23, 1.5, 0.2, 35, 9%, and 0.95 from least to greatest.
2b. Jason worked 23 of an hour and Tara worked from 6:05 P.M. to 6:50 P.M.
Who worked longer?
2
LESSON 1
■
Comparing and Ordering Rational Numbers
TAKS Review and Preparation Workbook
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
Quick Check 2
Name__________________________Class____________Date________
1 A random group of students from four
different classes was asked how many
preferred dogs. Which class had the
greatest fraction that preferred dogs?
A Science class: 94
4 Which fraction below is between 53 and 45?
F 23
G 56
H 87
5
B Math class: 12
J 43
C English class: 87
D History class: 56
5 Which of the following lists of rational
numbers is ordered from greatest to least?
2 Which point on the number line best
represents 256?
0
1
W
XY
2
3
Z
4
F W
A 7, 6.5, 781, 7.05
B 815, 8.95, 8.02, 8
C 6, 5.95, 5.9, 554
D 5.001, 5.01, 5, 478
G X
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
H Y
J Z
6 Which list correctly places these rational
numbers in order from least to greatest?
8, 8.01, 813, 8.1, 883
3 A librarian arranged some books on the
shelf using the Dewey decimal system.
Choose the group of book numbers that
is listed in order from least to greatest.
A 96.1, 96.11, 96.01, 96.001
B 240.12, 204.12, 420.12, 240.21
F 813, 8.01, 8, 8.1, 883
G 838, 8.1, 8, 8.01, 831
H 831, 8.01, 883, 8.1, 8
J 8, 8.1, 883, 8.01, 813
C 855, 855.6, 855.61, 855.601
D 531, 531.9, 531.902, 531.92
TAKS Review and Preparation Workbook
LESSON 1
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Comparing and Ordering Rational Numbers
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