Comparing%20and%20Ordering%20Rational%20Numbers

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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Write the prime factorization of 364.
22 x 7 x 13
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
(For help, go to Lesson 4-3.)
Write the prime factorization of each
number. 1. 20 2. 125 3. 45 4. 186
5. 621 6. 1,575
Check Skills Youll Need
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3
Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Solutions 1. 20 2. 125 3. 45 2 10 5
25 3 15 2 2 5 5 5 5 3 3 5
20 22 5 125 53 45 32
5 4. 186 5. 621 6. 1,575 2 93 3 207 3
525 2 3 31 3 3 69 3 3 175 186
2 3 31 3 3 3 23 3 3 5
35 621 33 23 3 3 5 5
7 1,575 32 52 7
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Today, the schools baseball and soccer teams
had games. The baseball team plays every 7 days.
The soccer team plays every 3 days. When will the
teams have games on the same day again?
Quick Check
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Find the LCM of 16 and 36.
The LCM of 16 and 36 is 144.
Quick Check
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Find the LCM of 5a4 and 15a.
The LCM of 5a4 and 15a is 15a4.
Quick Check
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Graph and compare the fractions in each pair.
Quick Check
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
The softball team won of its games and the
hockey team won of its games. Which team won
the greater fraction of its games?
Quick Check
The softball team won the greater fraction of its
games.
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Order , , and from least to greatest.
Quick Check
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Comparing and Ordering Rational Numbers
PRE-ALGEBRA LESSON 5-1
Find the LCM of each pair of numbers. 1. 8,
6 2. 12, 16 3. Compare and order ,
, and from least to greatest.
24
48
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
Without actually dividing, which expression is
the largest? 6.1 ?2.8 12.6
1.1 9.305 2.99
12.6 1.1
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
(For help, go to Skills Handbook page 728.)
Write the decimals in order from least to
greatest. 1. 2.41, 0.241, 24.1,
12.4 2. 1.030, 13.03, 1.300, 1.003 3. 0.1,
0.01, 0.1, 0.01
Check Skills Youll Need
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
Solutions 1. 0.241, 2.41, 12.4,
24.1 2. 1.003, 1.030, 1.300, 13.03 3. 0.1,
0.01, 0.01, 0.1
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
The fuel tank of Scotts new lawn mower holds
gal of gasoline. Scott poured 0.4 gal into the
tank. Did Scott fill the tank?
Quick Check
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
Write each fraction as a decimal. State the
block of digits that repeats.
a.
b.
Quick Check
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
Write the numbers in order, from least to
greatest.
Quick Check
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
Write 1.72 as a mixed number in simplest form.
Quick Check
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
Write 0.18 as a fraction in simplest form.
Quick Check
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Fractions and Decimals
PRE-ALGEBRA LESSON 5-2
1. Order , , 0.625, 0.35 from least to
greatest. 2. Write as a
decimal. Write each decimal as a fraction or
mixed number in simplest form. 3. 6.04 4. 0.21
0.85
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Adding and Subtracting Fractions
PRE-ALGEBRA LESSON 5-3
Five consecutive multiples of 6 have a sum of
270. What are they?
42, 48, 54, 60, 66
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Adding and Subtracting Fractions
PRE-ALGEBRA LESSON 5-3
(For help, go to Lesson 5-1.)
Find the LCM of each group of numbers or
expressions. 1. 4, 8 2. 9, 18 3. 2n, 10
4. 3, 6, 9 5. 8, 5, 4 6. 10, n
Check Skills Youll Need
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Adding and Subtracting Fractions
PRE-ALGEBRA LESSON 5-3
Solutions 1. 4 22 2. 9 32 3.
2n 2 n 8 23 18 2 32 5
5 LCM 23 LCM 2 32 LCM 2 5 n
8 18 10n
4. 3 3 5. 8 23 6. 10 2 5
6 2 3 5 5 n n 9 32 4
22 LCM 2 5 n LCM 2 32 LCM 23
5 10n 18 40
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Adding and Subtracting Fractions
PRE-ALGEBRA LESSON 5-3
Find each sum or difference. Simplify if
possible.
a.


b.
Quick Check
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Adding and Subtracting Fractions
PRE-ALGEBRA LESSON 5-3
Simplify each difference.

a.

b.
Quick Check
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Adding and Subtracting Fractions
PRE-ALGEBRA LESSON 5-3
Suppose one day you rode a bicycle for 3
hours, and jogged for 1 hours. How many hours
did you exercise?
Quick Check
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Adding and Subtracting Fractions
PRE-ALGEBRA LESSON 5-3
Find each sum or difference. 1. 2. 5
2 3. 4.


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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4
Write each number as an improper fraction. a. 4
b. 3
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4
(For help, go to Skills Handbook page 738.)
Write each mixed number as an improper
fraction. 1. 2 2. 3 3. 1 4. 4 5. 7 6. 5
Check Skills Youll Need
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4
Solutions (continued) 4. 5. 6.







4
7
5
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4
Find .
Quick Check
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4

a.
Find .
b.
Find .
Quick Check
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4

Keeshas desktop is a rectangle 3 ft long and
1 ft wide. What is the area of her desktop?
Quick Check
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4

a.
Find .
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4
(continued)
b.
Find .
Quick Check
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4

Find 4 (3 ).
Quick Check
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Multiplying and Dividing Fractions
PRE-ALGEBRA LESSON 5-4
Simplify each expression. 1. 2. 3.
4.

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Using Customary Units of Measurement
PRE-ALGEBRA LESSON 5-5
In 2002, a disc jockey broadcast her show for 27
h each week. How many hours did she broadcast
that year?
1,430 h
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Using Customary Units of Measurement
PRE-ALGEBRA LESSON 5-5
(For help, go to Lesson 5-4.)
Find each product. 1. 4 2. 3 3. 1
4. 4
Check Skills Youll Need
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Using Customary Units of Measurement
PRE-ALGEBRA LESSON 5-5
Solutions 1. 2.
52
3. 4.
10
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Using Customary Units of Measurement
PRE-ALGEBRA LESSON 5-5
Choose an appropriate unit of measure. Explain
your choice.
a. weight of a hummingbird
Measure its weight in ounces because a
hummingbird is very light.
b. length of a soccer field
Measure its length in yards because it is too
long to measure in feet or inches and too short
to measure in miles.
Quick Check
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Using Customary Units of Measurement
PRE-ALGEBRA LESSON 5-5

Use dimensional analysis to convert 68 fluid
ounces to cups.
Quick Check
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Using Customary Units of Measurement
PRE-ALGEBRA LESSON 5-5
1 2

Freds fruit stand sells homemade lemonade in 6
-pint bottles for 1.99. Jills fruit stand
stand sells homemade lemonade in 3 -qt
containers for the same price. At which stand do
you get more lemonade for your money?
1 2
Quick Check
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Using Customary Units of Measurement
PRE-ALGEBRA LESSON 5-5
Choose an appropriate unit of measure. Explain
your choice. 1. weight of a dog
2. length of a football field 3. Use
dimensional analysis to convert 1 mi to ft.
Pounds dogs are too heavy to measure in ounces
and too light to measure in tons.
Yards it is too long to measure in feet or
inches and too short to measure in miles.
7,920 ft
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Problem Solving Strategy Work Backward
PRE-ALGEBRA LESSON 5-6
Use mental math to decide whether or not each
pair of fractions is
yes, yes, no
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Problem Solving Strategy Work Backward
PRE-ALGEBRA LESSON 5-6
(For help, go to Lesson 5-2.)
Order from least to greatest. 1. 2. 3.
4.
,
,
,
,
,
,
,




,
,
,
,
,
,
Check Skills Youll Need
5-6
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Problem Solving Strategy Work Backward
PRE-ALGEBRA LESSON 5-6
Solutions 1. 2.
,
,
,
0.50, 0.3, 0.25, 0.20, 0.10
2.3, 1.6, 4.3, 1
,
,
,
,
,
,
,
3. 4.




,
,
,
,
,
,
0.43, 0.6, 0.23, 1
0.43, 0.6, 0.23, 1




,
,
,
,
,
,
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Problem Solving Strategy Work Backward
PRE-ALGEBRA LESSON 5-6
Your flight leaves the airport at 1000 A.M. You
must arrive 2 hours early to check your luggage.
The drive to the airport takes about 90 minutes.
A stop for breakfast takes about 30 minutes. It
will take about 15 minutes to park and get to the
terminal. At what time should you leave home?
Move the hands of the clock to find the time you
should leave home.
Write the starting time for each event.
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Problem Solving Strategy Work Backward
PRE-ALGEBRA LESSON 5-6
(continued)
You should leave home at 545 A.M.
Quick Check
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Problem Solving Strategy Work Backward
PRE-ALGEBRA LESSON 5-6
Solve by working backward. 1. Jason has a
total of 212 sheep. Last spring, 52 lambs were
born, but 9 died. How many sheep did he have
before the lambs were born? 2. The bus
picks up Tom every morning at 720 A.M. Tom walks
his dog every morning before school for 36
minutes. It takes him 25 minutes to get ready for
school and 7 minutes to walk to the bus stop. At
what time does Tom need to wake up in order to
get to the bus stop on time?
169 sheep
612 A.M.
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
Find the sum or difference. If possible, write
each answer in lowest terms. a. ?
b. 7 5
?
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
(For help, go to Lesson 5-3.)
Find each sum or difference. 1. 1 2 2. 3
2 3. 5 3 4. 4 3
Check Skills Youll Need
5-7
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
(continued)
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
(continued)
Quick Check
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7

Solve x .
Quick Check
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7

Quick Check
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Solving Equations by Adding or Subtracting
Fractions
PRE-ALGEBRA LESSON 5-7
Solve the following equations. 1. s
2. k 3. u 4.
g 5. x 2 4
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8
Because of a mishap, of the oranges in a
crate were ruined. If the oranges originally
weighed 50 lb, how many pounds of oranges were
ruined?
35 lb
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8
(For help, go to Lesson 5-4.)
Check Skills Youll Need
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8
Solutions 1. 2.
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8
Solutions (continued) 3. 4.





3
6
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8
Solve 7y .
Quick Check
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8

Quick Check
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8

Solve c .
Quick Check
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8

(continued)
6 Simplify.
Quick Check
You can place 6 trucks on the rail car.
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Solving Equations by Multiplying Fractions
PRE-ALGEBRA LESSON 5-8
Solve each equation. 1. 2. 3. 15 3 m
g
b
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Powers of Products and Quotients
PRE-ALGEBRA LESSON 5-9
112 x 32 x 22 is the prime factorization for ?.
4,356
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Powers of Products and Quotients
PRE-ALGEBRA LESSON 5-9
(For help, go to Lesson 4-7.)
Simplify each expression. 1. (22)3 2. (32)2 3.
(15)4 4. (x3)6 5. (b2)5 6. (a7)4
Check Skills Youll Need
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Powers of Products and Quotients
PRE-ALGEBRA LESSON 5-9
Solutions 1. (22)3 2. (32)2 3. (15)4 22
3 32 2 15 4 26 34 120
64 81 1 4. (x3)6 5. (b2)5 6. (a7)4
x3 6 b2 5 a7 4 x18 b10 a28
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Powers of Products and Quotients
PRE-ALGEBRA LESSON 5-9
Simplify (3z5)4.
(3z5)4 34 (z5)4 Raise each factor to the
fourth power.
34 z5 4 Use the Rule for
Raising a Power to a Power.
34 z20 Multiply exponents.
81z20 Simplify.
Quick Check
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Powers of Products and Quotients
PRE-ALGEBRA LESSON 5-9


a. Simplify (3a)4.
(3a)4 (3)4(a)4
81a4
b. Simplify (3a)4.
(3a)4 (1)(3a)4
(1)(3)4(a)4
81a4
Quick Check
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Powers of Products and Quotients
PRE-ALGEBRA LESSON 5-9

A s2 s length of a side
Quick Check
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Powers of Products and Quotients
PRE-ALGEBRA LESSON 5-9
Simplify each expression. 1. (12x2yz)2 2. (4ab
3)3 3. (2g2h)8 4. 5.
144x4y2z2
64a3b9
256g16h8
6
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