Download Compare and Order Rational Numbers

Multi-Part Lesson
12-1
Rational Numbers
PART
Main Idea
Compare and order
fractions, decimals,
and percents.
NGSSS
MA.7.A.5.1 Express
rational numbers as
terminating or repeating
decimals.
glencoe.com
A
B
C
Compare and Order
Rational Numbers
INSECTS The most common types of
insects are shown in the table.
Insect
1. Which of the insects is the longest?
2. Is the fire ant or housefly longer?
Explain.
3. Are more than or less than half of the
insects shown longer than 0.6 inch?
4. Order the lengths from shortest to
longest.
Length
(in.)
Bumble bee
_3
Cricket
_1
Fire ant
_1
Firefly
_3
Housefly
_1
Japanese beetle
_1
Mosquito
_5
4
1
3
4
4
2
8
Just as positive and negative integers can be represented on a
number line, so can positive and negative rational numbers. You
can use a number line to help you compare and order negative
rational numbers.
Compare Decimals
Replace the with <, >, or = to make a true statement.
-1.2 0.8
Graph the decimals on a number line.
-1.4-1.2 -1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Since -1.2 is to the left of 0.8, -1.2 < 0.8.
-2.40 -2.45
Graph the decimals on a number line.
-2.50
-2.48
-2.46
-2.44
-2.42
-2.40
Since -2.40 is to the right of -2.45, -2.40 > -2.45.
a. 3.1 -3.7
b. -4.5 -4.49
Compare Fractions
Replace the with <, >, or = to make a true statement.
_ _
-7 6
8
8
Since the denominators are the same, compare the numerators
by graphing on a number line.
-8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
7 _
Since -7 < 6, -_
< 6.
8
Least Common Multiple
(LCM)
Find the LCM of 8 and 16.
8: 8, 16, 24
16: 16, 32, 48
The LCM is 16.
_
8
_
-3 - 5
8
16
Rename the fractions using the least common denominator.
5
5
5×1
-_
= -_
= -_
16
16
16
16 × 1
6
5
3
5
< -_
and -_
< -_
.
Since -6 < -5, -_
8
16
16
16
3
3×2
6
-_
= -_
= -_
8×2
8
Check
-6
-5
16
c.
16
-4
16
-3
16
-2
9
12
_
-_
16
16
-1
0
16
7
4
d. -_
-_
16
10
5
Compare Decimals and Fractions
Replace the with <, >, or = to make a true statement.
_
-0.51 - 8
15
8
as a decimal. Then graph both decimals on a
Rename -_
15
number line.
-0.53 -0.51
-0.6
-0.55
-5
−
8
-_
= -0.53
-0.5
-0.45
-0.4
15
−
Since -0.51 is to the right of -0.53 on the number line,
8
.
-0.51 > -_
15
Replace the with <, >, or = to make a true statement.
e. -3_ -3.625
5
8
f.
_3 0.413
7
To order rational numbers, first write them in the same form and
then order the numbers.
Order Rational Numbers
SCIENCE Mr. Plum’s science class is
growing plants under different
conditions. The average plant growth
during a week was 5.5 inches. The table
shows the difference from the average
for some students’ plants. Order the
differences from least to greatest.
Real-World Link
The longest species of
seaweed measures
197 feet. This kelp is
the fastest growing
species, growing
more than 13 inches
per day.
Difference from
Average Plant Growth
Difference
(in.)
Student
1
3_
Ricky
4
Debbie
-2.2
Suni
1.7
7
-1_
Leonora
10
Express each number as a decimal.
1
Ricky’s plant: 3_
= 3.25
Debbie’s plant: -2.2
Suni’s plant: 1.7
7
Leonora’s plant: -1_
= -1.7
4
10
Graph each number on a number line.
1.7
-2.2 -1.7
3.25
-3.5-3 -2.5 -2 -1.5-1-0.5 0 0.5 1 1.5 2 2.5 3 3.5
7
1
From least to greatest, the differences are -2.2, -1_
, 1.7, and 3_
.
10
4
g. OCEANS The average depths of the three deepest oceans are
-2.46 miles, -2.88 miles, and -2.44 miles. Order the depths
from least deep to deepest.
Examples 1–5
Replace the with <, >, or = to make a true statement.
(pp. 677–678)
2. 9.7 -10.3
3.
7
4. -_
_
7
5. -6.7 -6_
5
6. -_
-0.94
12
Example 6
(p. 679)
_5 -_3
1. -7.8 -7.82
5
12
10
8
8
6
7. MONEY Stephen recorded the following amounts in his checkbook:
-$6.50, $7.00, -$6.75, and $7.25. Order these amounts from least
to greatest.
Order the following numbers from least to greatest.
1
8. -3_
, 3.3, -3_, 3.5
3
3
4
9
−
3 _
2.8, -2_
, 3 1 , -2.2
4
8
= Step-by-Step Solutions begin on page R31.
Extra Practice is on page EP32.
Examples 1–5
(pp. 677–678)
Replace the with <, >, or = to make a true statement.
10. -2.5 -2.9
11. -18.6 -18.06
12. -4.08 -4.7
5
4
13. -_
-_
9
9
5
1
14. _ -_
4
4
3
2
15. -_
-_
1
16. -6_
-6.375
3
17. -_
-0.6
2
18. -9_
-9.3
3
Example 6
(p. 679)
7
5
7
5
19. STOCK MARKET The change in four stocks during
a day are shown. Order the changes from least
to greatest.
Company
Change
A
-4_
B
5.6
C
-2_
1
2
3
8
20. IN-LINE SKATING The average amount of time
D
Brent spent in-line skating for one week was
34 minutes. During the next week, the difference
between the average time and actual time spent skating was
1.35
1
1
4.2 minutes, -5_
minutes, -2_
minutes, and 3.75 minutes.
3
2
Order these differences from least to greatest.
Replace the with <, >, or = to make a true statement.
−
−−
−−
−−−
−
4
21. -0.4 -0.45
22. -2.21 -2.212
23. -6.4 -6_
9
Order the following numbers from least to greatest.
−
−
1
1
1
24. 2.1, -2.1, 2_
, -2
25. _
, -0.025, 0.2, -_
8
2
4
26. _
, 60%, 0.65, _
3
5
7
− 1
3
27. 125%, 1_, 1.25, 1_
5
4
28. SNACKS The bar graph shows the
profit or loss of the after-school
snack stand.
a. Write each profit as a positive
number and each loss as a
negative number.
Profit
11
Loss
B
$8.00
$6.00
$4.00
$2.00
$0.00
-$2.00
-$4.00
-$6.00
-$8.00
Profit or Loss
2
3
4
Day
b. Order the numbers from least
to greatest.
29 MODEL ROCKETS For a technology
competition, Julienne constructed a model
rocket. The average height the rocket can
reach is 545 feet. The table shows the
differences between the average height
and the actual height reached. Order the
differences from least to greatest.
1
Trials
Difference Between
Average Height and
Actual Height (ft)
1
-10.8
2
11.4
3
9.0
4
-9.7
30. REASONING Determine whether the following statement is always,
sometimes, or never true. Give examples to justify your answer.
C
If x and y are both greater than zero and x > y, then -x < -y.
4
4
4
4
31. NUMBER SENSE Determine whether the fractions -_
, -_
, -_
, and -_
5
are arranged in order from least to greatest. Explain.
35.
3
"#
-0.4 -0.3 -0.2 -0.1
$%
0
0.1
0.2
0.3
0.4
A. point A
SHORT RESPONSE Student Council’s
goal was to raise $50 each week for
4 weeks to have enough money for
the school dance. The table shows the
difference between the goal and the
actual amount raised. Order these
amounts from least to greatest.
B. point B
Week
C. point C
Difference ($)
D. point D
1
2
3
4
5.50
-6.25
7.80
-2.45
36. Which of the following numbers is less
GRIDDED RESPONSE Which of the
following numbers is the greatest?
-0.73, 0.32, -0.21, 0.19
2
than -_
?
3
F. 0.6
−
H. 0.6
1
G. _
5
I. -_
3
Write each fraction as a decimal.
37.
_5
9
6
(Lesson 12-1B)
2
39. _
1
38. -_
3
8
40. Find the value of x ÷ y if x = -15 and y = -3.
(Lesson 11-3E)
41. BUSINESS The table shows the results of a company’s
operations over a period of three months. Find the
company’s overall profit or loss over this time period.
(Lesson 11-2B)
8
MA.6.A.5.2, MA.7.A.5.1
33. Which point shows the approximate
1
?
location of -_
34.
7
−−
Explain why -0.33 is greater than -0.33.
32.
NGSSS Practice
6
Month
Profit
April
May
June
Loss
$15,000
$19,000
$12,000