Download Chapter 5 DECIMAL NOTATION

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Section:
Chapter 5 DECIMAL NOTATION
5.1 Decimal Notation, Order, and Rounding
Learning Objectives
A Given decimal notation, write a word name.
B Convert between decimal notation and fraction notation.
C Given a pair of numbers in decimal notation, tell which is larger.
D Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or
thousand.
Key Terms
Use the terms listed below to complete each statement in Exercises 1–4. Some of the terms
will be used more than once.
left
larger
right
smaller
zeros
decimal places
1.
To convert from fraction notation to decimal notation when the denominator is 10, 100,
1000, and so on,
a) count the number of ___________________ and
b) move the decimal point that number of places to the ___________________ . Leave
off the denominator.
2.
To convert from decimal notation to fraction notation,
a) count the number of ___________________ ,
b) move the decimal point that many places to the ___________________ , and
c) write the answer over a denominator of 1 followed by that number of
___________________.
3.
To compare two positive numbers in decimal notation, start at the _________________
and compare corresponding digits. When two digits differ, the number with the
___________________ digit is the larger of the two numbers.
4.
To compare two negative numbers in decimal notation, start at the _________________
and compare corresponding digits. When two digits differ, the number with the
___________________ digit is the larger of the two numbers.
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GUIDED EXAMPLES AND PRACTICE
Objective A
Given decimal notation, write a word name.
Review these examples for Objective A:
1. Write a word name for 306.845.
Practice these exercises:
1. Write a word name for 59.07.
a) Write a word name for the whole number.
Three hundred six
b) Write “and” for the decimal point.
Three hundred six
and
c) Write a word name for the number named to
the right of the decimal point, followed by the
place value of the last digit.
Three hundred six
and
eight hundred forty-five thousandths
A word name for 306.845 is three hundred six and
eight hundred forty-five thousandths.
2.
Write a word name for $146.98, as on a check.
2.
One hundred forty-six and 98
100
Objective B
Convert between decimal notation and fraction notation.
Review these examples for Objective B:
3. Write fraction notation for –3.471.
−3.471
N
↑
3 places
Write a word name for $23.79,
as on a check.
− 3.471.
N
→
move 3 places
− 3471
1000
↑
3 zeros
Practice these exercises:
3. Write fraction notation for
16.09.
−3.471 = − 3471
1000
4.
5.
92
Write decimal notation for 61 .
1000
61 = 0.061
61
0.061.
N
1000
1000
←
↑
Move 3 places
3 zeros
Write decimal notation for 5 7 .
10
7
7
7
5 = 5 + = 5 and
= 5.7
10
10
10
4.
Write decimal notation for
− 259 .
100
5.
Write decimal notation for
91 23 .
100
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Objective C
Date:
Section:
Given a pair of numbers in decimal notation, tell which is larger.
Review these examples for Objective C:
6. Which is larger: 0.01 or 0.009?
Practice these exercises:
6. Which is larger: 2.08 or 2.11?
Starting at the left, these digits
0.01
7 are the first to differ; 1 is larger
0.009 than 0.
Thus, 0.01 is larger. In symbols, 0.01 > 0.009.
7.
Which is larger: –2.03 or –2.028?
7.
Starting at the left, these digits
−2.03
7 are the first to differ; 2 is smaller
−2.028 than 3.
Thus, –2.028 is larger. In symbols,
–2.028 > –2.03
Which is larger: –15.2
or –15.23?
Objective D Round decimal notation to the nearest thousandth, hundredth, tenth,
one, ten, hundred, or thousand.
Review this example for Objective D:
8. Round 46.1938 to the nearest hundredth.
46.19 3 8
↓
46.19
Thousandths digit is 4 or lower.
Round down.
Practice this exercise:
8. Round 327.249 to the nearest
tenth.
ADDITIONAL EXERCISES
Objective A Given decimal notation, write a word name.
For extra help, see Examples 1–5 on pages 301–302 of your text and the Section 5.1 lecture
video.
Write a word name for the number in each sentence.
1.
The Suez Canal is 119.9 miles long.
2.
One meter is equivalent to about
1.094 yards.
4.
$215.38
Write in words, as on a check.
3.
$7.49
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Objective B Convert between decimal notation and fraction notation.
For extra help, see Examples 6–12 on pages 303–304 of your text and the Section 5.1
lecture video.
Write each number as a fraction and, if possible, as a mixed numeral. Do not simplify.
5.
4.1376
6.
–5.039
8.
417 496
10, 000
Write decimal notation for each number.
7.
− 213
100
Objective C Given a pair of numbers in decimal notation, tell which is larger.
For extra help, see Examples 13–15 on page 305 of your text and the Section 5.1 lecture
video.
Which number is larger?
9.
0.9, 0.85
10. 0.143, 0.134
11. –146.19, –147.19
12. 0.008,
8
100
Objective D Round decimal notation to the nearest thousandth, hundredth, tenth,
one, ten, hundred, or thousand.
For extra help, see Examples 16–18 on page 306 of your text and the Section 5.1 lecture
video.
Round 234.0645 to the nearest:
13. Tenth
14. Hundredth
15. Thousandth
16. Round –36.4519 to the nearest one.
94
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Section:
Chapter 5 DECIMAL NOTATION
5.2 Addition and Subtraction of Decimals
Learning Objectives
A Add using decimal notation.
B Subtract using decimal notation.
C Add and subtract negative decimals.
D Combine like terms with decimal coefficients.
GUIDED EXAMPLES AND PRACTICE
Objective A Add using decimal notation.
Review this example for Objective A:
1. Add: 14.26 + 63.589.
Practice this exercise:
1. Add: 3.08 + 25.962.
1
14.2 60
+ 63.589
77.849
Objective B
Lining up the decimals and
writing and extra zero
Adding
Subtract using decimal notation.
Review this example for Objective B:
2. Subtract: 67.345 – 24.28.
Practice this exercise:
2. Subtract: 221.04 – 13.192.
2 14
6 7. 3 4 5
− 2 4. 2 8 0
4 3. 0 6 5
Writing an extra zero
Subtracting
Objective C Add and subtract negative decimals.
Review this example for Objective C:
3. Subtract: –6.4 – (–7.9).
Practice this exercise:
3. Add: –11.23 + 5.49.
−6.4 − (−7.9)
= −6.4 + 7.9 Adding the opposite of − 7.9
Subtracting absolute values. The
= 1.5
answer is positive since 7.9 has
the larger absolute value.
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Objective D Combine like terms with decimal coefficients.
Review this example for Objective D:
4. Combine like terms: 4.3 x − 2.1 y − 6.2 x + 4.8 y.
Practice this exercise:
4. Combine like terms:
5.7a + 3.9b − 4.2a − 5.6b.
4.3x − 2.1 y − 6.2 x + 4.8 y
= 4.3x + (−2.1 y ) + (−6.2 x ) + 4.8 y Rewriting
as addition
= 4.3x + (−6.2 x ) + (−2.1 y ) + 4.8 y Using the
commutative law to rearrange
= −1.9 x + 2.7 y
Combining like terms
ADDITIONAL EXERCISES
Objective A Add using decimal notation.
For extra help, see Examples 1–3 on pages 310–311 of your text and the Section 5.2 lecture
video.
Add.
1.
19.74
+ 21.43
2.
2.306 + 5.829
3.
0.347 + 0.16
4.
157 + 0.45 + 2.9
Objective B Subtract using decimal notation.
For extra help, see Examples 4–6 on pages 311–312 of your text and the Section 5.2 lecture
video.
Subtract.
5.
34.192
− 8.341
6.
60.55 – 0.493
7.
5 – 3.1405
8.
125.3 – 16.71
Objective C Add and subtract negative decimals.
For extra help, see Examples 7–10 on pages 312–313 of your text and the Section 5.2
lecture video.
Add or subtract, as indicated.
9.
–25.16 + 19.04
11. –15.8 – 27.3
10. 23.7 – 31.4
12. –42.6 – (–18.7)
Objective D Combine like terms with decimal coefficients.
For extra help, see Examples 11–13 on page 313 of your text and the Section 5.2 lecture
video.
Combine like terms.
13. 3.6 x + 5.8 x
14. 32.38 y − 19.21 y
15. 16.9a + 49.3 + 17.6a
16. 5.9 y − 5.7 x − 4.3 y + 2.8 x
96
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Section:
Chapter 5 DECIMAL NOTATION
5.3 Multiplication of Decimals
Learning Objectives
A Multiply using decimal notation.
B Convert from notation like 45.7 million to standard notation and convert between dollars
and cents.
C Evaluate algebraic expressions using decimal notation.
Key Terms
Use the terms listed below to complete each statement in Exercises 1–4. The terms will be
used more than once.
right
left
1.
To multiply any number by 10, 100, 1000, and so on,
a) count the number of zeros, and
b) move the decimal point that many places to the _________________ .
2.
To multiply any number by a tenth, hundredth, or thousandth, and so on,
a) count the number of decimal places, and
b) move the decimal point that many places to the _________________ .
3.
To convert from cents to dollars, move the decimal points two places to the
_________________ and change the ¢ sign at the end to a $ sign in front.
4.
To convert from dollars to cents, move the decimal point two places to the
_________________ and change the $ in front to a ¢ at the end.
GUIDED EXAMPLES AND PRACTICE
Objective A
Multiply using decimal notation.
Review these examples for Objective A:
1. Multiply: 2.8× 0.03.
2.8
× 0. 0 3
0. 0 8 4
Practice these exercises:
1. Multiply: 4.63× 2.5.
(1 decimal place)
(2 decimal places)
(3 decimal places)
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2.
Multiply: 0.001× 72.4.
2.
Multiply: 14.3× 0.01.
3.
Multiply: 1000 ×85.043.
0.001× 72.4 = 0.072.4
Moving the decimal
N
←
point 3 places to the left. This
requires adding one extra zero.
= 0.0724
3.
Multiply: 34.6 ×100.
34.6×100 = 3460 Moving the decimal point
2 places to the right and
using one zero as a placeholder.
Objective B Convert from notation like 45.7 million to standard notation and convert
between dollars and cents.
Review these examples for Objective B:
4. Convert 45.7 million to standard notation.
45.7 million = 45.7 ×1 million
= 45.7 ×1,000,000
6 zeros
= 45,700,000 Moving the decimal
6 places to the right
5.
Convert $63.42 to cents.
Practice these exercises:
4. Convert 6.2 billion to standard
notation.
5.
Convert $125.49 to cents.
6.
Convert 245¢ to dollars.
$63.42 = 63.42 × $1
We think of $63.42 as
63.42 ×1 dollar or 63.42 × $1
= 63.42 ×100¢ Substituting 100¢ for $1:
$1 = 100¢
Multiplying
= 6342¢
6.
Convert 9168¢ to dollars.
9168¢ = 9168×1¢
We think of 9168¢ as
9168×1 cent or 9168×1¢
= 9168× $0.01 Substituting $0.01 for 1¢:
1¢ =$0.01
= $91.68
Multiplying
Objective C Evaluate algebraic expressions using decimal notation.
Review this example for Objective C:
7. Evaluate Prt for P = 100, r = 0.08, and t = 1.5.
Prt = 100(0.08)(1.5)
= 8(1.5)
= 12
98
Practice this exercise:
7. Evaluate lwh for l = 2.7,
w = 3.4, and h = 0.9.
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ADDITIONAL EXERCISES
Objective A Multiply using decimal notation.
For extra help, see Examples 1–12 on pages 318–321 of your text and the Section 5.3
lecture video.
Multiply.
1.
4.6
× 8
2.
−0.56 ×1000
3.
0.0675×(−0.01)
4.
−15.3×(−45.1)
Objective B Convert from notation like 45.7 million to standard notation and convert
between dollars and cents.
For extra help, see Examples 13–17 on page 322 of your text and the Section 5.3 lecture
video.
Convert from dollars to cents.
5.
$47.13
6.
$0.79
8.
26¢
Convert from cents to dollars.
7.
4351¢
9.
Convert the number in this sentence to standard notation:
The number of real Christmas tress purchased in a recent year was 32.8 million.
Objective C Evaluate algebraic expressions using decimal notation.
For extra help, see Examples 18–20 on page 323 of your text and the Section 5.3 lecture
video.
Evaluate.
10. 2.42 q ( p + q) , for p = 7 and q = 15.4
11. AB + 3B 2 , for A = 4.5 and B = 1.3
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Find (a) the perimeter and (b) the area of a rectangle with the given dimensions.
12. Length: 12.6 ft, width: 5.4 ft
13. Length: 3.3 m, width: 2.9 m
14. The amount it now takes to equal the value of $1 in 1913 can be estimated by the
expression 0.4123x + 13.2617 , where x is the number of years after 1990. Estimate how
much it took to equal the value of $1 in 1913 in 2006. Round to the nearest cent
(hundredth).
100
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Chapter 5 DECIMAL NOTATION
5.4 Division of Decimals
Learning Objectives
A Divide using decimal notation.
B Simplify expressions using the rules for order of operations.
Key Terms
Write the letters A, B, C, and D in the blanks to indicate the order in which operations should
be performed when simplifying expressions.
1.
_________________
2.
_________________
3.
_________________
4.
_________________
A. Evaluate all exponential expressions.
B. Do all additions and subtractions in order from
left to right.
C. Do all calculations within grouping symbols.
D. Do all multiplications and divisions in order from
left to right.
GUIDED EXAMPLES AND PRACTICE
Objective A Divide using decimal notation.
Review these examples for Objective A:
1. Divide: 36.8 ÷ 8.
Practice these exercises:
1. Divide: 615.6 ÷ 12.
4.6
8 3 6.8
32
48
48
0
2.
Divide: −21.35 ÷ 6.1.
2.
Divide: 24.07 ÷ 2.9.
First we find 21.35 ÷ 6.1.
3.5
6.1∧ 2 1.3∧5
183
305
305
0
Since 21.35 ÷ 6.1 = 3.5, we have
−21.35 ÷ 6.1 = −3.5.
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3.
Divide: 16.7 .
1000
HJJJ
16.7 = 0.016.7 = 0.0167 = 0.0167
1000
1000
1.000
HJJJ
3 zeros 3 places to the left
to change 1000 to 1
The answer is 0.0167.
3.
Divide: −3.9 .
100
4.
Divide: 42.93 .
0.001
JJJG
42.93 = 42.930 = 42,930 = 42,930
0.001
0.001
1.
JJJG
3 zeros 3 places to the right to change 0.001 to 1
The answer is 42,930.
4.
Divide: 123.4 .
0.01
Objective B
Simplify expressions using the rules for order of operations.
Review these examples for Objective B:
5. Simplify: (8 − 2.4) ÷ 22 + 4.9 ×10.
(8 − 2.4) ÷ 2 2 + 4.9 ×10
Practice these exercises:
5. Simplify:
3
5 ÷ 0.5 + 2.1×8 − (1− 0.9) .
Working inside
the parentheses
Evaluating the
= 5.6 ÷ 4 + 4.9 ×10
exponential term
Multiplying and dividing
= 1.4 + 49
in order from left to right
= 50.4
= 5.6 ÷ 22 + 4.9 ×10
6.
While on a weekend trip, the Hernandez
family drove 250.6 mi on the first day,
164.5 mi on the second day, and 203.8 mi
the third day. Find the average distance
driven per day.
To find the average distance, find the sum
of the distances and divide by the number
of addends, 3.
(250.6 + 164.5 + 203.8) ÷ 3 = 618.9 ÷ 3 = 206.3
The average distance is 206.3 mi.
102
6.
Keisha walked 3.5 mi on
Tuesday, 1.2 mi on
Wednesday, 2.9 mi on
Thursday, and 4 mi on Friday.
Find the average distance
walked per day.
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ADDITIONAL EXERCISES
Objective A Divide using decimal notation.
For extra help, see Examples 1–9 on pages 327–331 of your text and the Section 5.4 lecture
video.
Divide.
1.
21 70.35
2.
0.48 0.1728
3.
345
−1000
4.
35.17
−0.01
Objective B Simplify expressions using the rules for order of operations.
For extra help, see Examples 10–13 on pages 331–332 of your text and the Section 5.4
lecture video.
Simplify.
5.
15×(3.8 − 6.4)
7.
132 ÷ (11 + 5.9) − [(3 − 3.6) ÷ 0.3]
8.
Marco earned $25.50 in tips on Monday, $21.40 on Tuesday, $24.75 on Wednesday,
$35 on Thursday, and $42.90 on Friday. Find the average amount earned in tips per day
during this period.
6.
10 ÷ 0.01− 0.3× 7 + 0.2 2
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Chapter 5 DECIMAL NOTATION
5.5 Using Fraction Notation with Decimal Notation
Learning Objectives
A Use division to convert fraction notation to decimal notation.
B Round numbers named by repeating decimals.
C Convert certain fractions to decimal notation by using equivalent fractions.
D Simplify expressions that contain both fraction and decimal notation.
GUIDED EXAMPLES AND PRACTICE
Objective A Use division to convert fraction notation to decimal notation.
Review this example for Objective A:
1. Find decimal notation for 1 .
6
Practice this exercise:
1.
Find decimal notation for 5 .
9
0. 1 6 6
6 1. 0 0 0
6
40
36
40
36
4
Since 4 keeps reappearing as a remainder, the
digit repeats and will continue to do so. Thus,
1 = 0.16 .
6
Objective B
Round numbers named by repeating decimals.
Review this example for Objective B:
2. Round 0.37 to the nearest thousandth.
0.37 = 0.3737...
The digit in the ten-thousandths place, 7, is 5 or
higher, so we round up and get 0.374.
Practice this exercise:
2. Round 0.15 to the nearest
hundredth.
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Objective C Convert certain fractions to decimal notation by using equivalent
fractions.
Review this example for Objective C:
3. Find decimal notation for 13 .
20
Practice this exercise:
3.
Find decimal notation for 17 .
25
13 = 13 ⋅ 5
20 20 5
= 65
100
= 0.65
Objective D Simplify expressions that contain both fraction and decimal notation.
Review this example for Objective D:
4. Calculate: 1.512 × 4 .
3
Practice this exercise:
4. Calculate: 5.32 ÷ 4 .
5
We will use the first method.
1.512 × 4 = 1.512 × 4
3
1
3
×
1.512
4
=
3
6.048
=
3
= 2.016
ADDITIONAL EXERCISES
Objective A Use division to convert fraction notation to decimal notation.
For extra help, see Examples 1–5 on pages 339–341 of your text and the Section 5.5 lecture
video.
Find decimal notation for each number.
1.
1
8
2.
− 21
16
3.
−3
11
4.
5
7
106
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Objective B Round numbers named by repeating decimals.
For extra help, see Examples 6–9 page 341 of your text and the Section 5.5 lecture video.
Round the decimal notation for each number to the nearest tenth, hundredth, and
thousandth.
5.
7
11
6.
−7
3
7.
4
7
8.
−1
12
Objective C Convert certain fractions to decimal notation by using equivalent
fractions.
For extra help, see Examples 10–12 page 342 of your text and the Section 5.5 lecture video.
Find decimal notation for each number.
−3
4
10. −19
20
11. 21
25
12. 137
200
9.
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Objective D Simplify expressions that contain both fraction and decimal notation.
For extra help, see Examples 13–14 pages 342–343 of your text and the Section 5.5 lecture
video.
Calculate and write the result as a decimal.
13. 3 (439.6)
5
14. 8 (−24.12)
3
15. 7 × 0.1088 + 5 × 0.4332
8
6
16.
( 43 )123.62 −(107 )435.7
17. Find the area of a triangular flower bed
that is 10.3 m long and 8.4 m wide.
108
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Chapter 5 DECIMAL NOTATION
5.6 Estimating
Learning Objectives
A Estimate sums, differences, products, and quotients.
GUIDED EXAMPLES AND PRACTICE
Objective A Estimate sums, differences, products, and quotients.
Review this example for Objective A:
1. Estimate 4.25 + 6.91 + 1.046 by rounding to the
nearest tenth.
4.25 + 6.91 + 1.046 ≈ 4.3 + 6.9 + 1.0 = 12.2
Practice this exercise:
1. Estimate 68× 4.2. Which of
the following is an appropriate
estimate?
a) 17
b) 280
c) 650
d) 700
ADDITIONAL EXERCISES
Objective A Estimate sums, differences, products, and quotients.
For extra help, see Examples 1–9 on pages 348–350 of your text and the Section 5.6 lecture
video.
Estimate by rounding, as directed.
1.
16.24 + 84.53 + 7.67; nearest one
2.
21.319 − 17.481; nearest tenth
Estimate. Choose a rounding digit that gives one or two nonzero digits. Indicate which
choice is an appropriate estimate.
3.
563.40 – 256.49
a) 820
b) 310
4.
c) 300
d) 270
74.71 ÷ 24.6
a) 0.3
b) 0.4
c) 3
d) 4
An iPod sells for $199.99 and a GPS navigation system sells for $349.99.
5.
About how much more does the GPS
system cost than the iPod?
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Chapter 5 DECIMAL NOTATION
5.7 Solving Equations
Learning Objectives
A Solve equations containing decimals and one variable term.
B Solve equations containing decimals and two or more variable terms.
GUIDED EXAMPLES AND PRACTICE
Objective A Solve equations containing decimals and one variable term.
Review this example for Objective A:
1. Solve: 3.1x − 4.3 = −8.02.
Practice this exercise:
1. Solve: 2.5 y + 16.7 = 8.2.
3.1x − 4.3 = −8.02
Adding 4.3
to both sides
Simplifying
Dividing both
sides by 3.1
3.1x − 4.3 + 4.3 = −8.02 + 4.3
3.1x = −3.72
3.1x = −3.72
3.1
3.1
x = −1.2
The solution is −1.2.
Objective B
Solve equations containing decimals and two or more variable terms.
Review this example for Objective B:
2. Solve: 8 x + 2 = 3 x + 13.
Practice this exercise:
2. Solve: 7 x + 1 = 9 x + 8.
8 x + 2 = 3x + 13
Subtracting 2
from both sides
8 x = 3x + 11
Simplifying
Subtracting 3 x
8 x − 3x = 3x + 11− 3x
from both sides
5 x = 11
Dividing both
5 x = 11
sides by 5
5
5
x = 2.2
The solution is 2.2.
8 x + 2 − 2 = 3x + 13 − 2
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ADDITIONAL EXERCISES
Objective A Solve equations containing decimals and one variable term.
For extra help, see Examples 1–2 on page 354 of your text and the Section 5.7 lecture video.
Solve. Remember to check.
1.
x + 16.5 = 4.2
2.
3.2 x − 5 = 6.2
3.
31.6 + 4.2 y = −6.62
4.
−4.5 = 10.45 + 6.5t
Objective B Solve equations containing decimals and two or more variable terms.
For extra help, see Examples 3–6 on pages 355–356 of your text and the Section 5.7 lecture
video.
Solve. Remember to check.
5.
2 y +1 = 6 y − 6
6.
4.3x + 16 = 2.9 x + 2
7.
3t − 7 = 8(t − 3)
8.
3.2 ( x + 7.1) = 7.6 x − 4.56
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Date:
Section:
Chapter 5 DECIMAL NOTATION
5.8 Applications and Problem Solving
Learning Objectives
A Translate key phrases to algebraic expressions.
B Solve applied problems involving decimals.
Key Terms
Use the vocabulary terms listed below to complete each statement in Exercises 1–2.
radius
diameter
1.
In any circle, a _________________ is a segment that passes through the center of the
circle with endpoints on the circle.
2.
In any circle, a _________________ is a segment with one endpoint on the center and
the other endpoint on the circle.
GUIDED EXAMPLES AND PRACTICE
Objective A Translate key phrases to algebraic expressions.
Review this example for Objective A:
1. Translate to an algebraic expression: 5 more than
7 times a number.
Let n = the number.
7n + 5
Objective B
Practice this exercise:
1. Translate to an algebraic
expression: 9 less the product
of 6 and a number.
Solve applied problems involving decimals.
Review this example for Objective B:
2. Erik’s odometer read 45,918.7 mi at the
beginning of a trip. It read 47,304.2 mi at
the end of the trip. How far did Erik drive?
1. Familiarize. We make a drawing. Let m = the
number of miles Erik drove.
45,918.7 mi
m
47,304.2 mi
Practice this exercise:
2. A car loan of $7791.60 is to be
paid off in 24 equal monthly
payments. How much is each
payment?
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2. Translate. This is a “how much more”
situation.
Additional
First
Final
+ number =
reading
reading
of miles
↓
↓
↓
↓
↓
45,918.7 +
m
= 47,304.2
3. Solve. We subtract 45,918.7 on both sides of
the equation.
45,918.7 + m = 47,304.2
45,918.7 + m − 45,918.7 = 47,304.2 − 45,918.7
m = 1385.5
4. Check. We can check by adding: 45,918.7 +
1385.5 = 47,304.2. The result checks.
5. State. Erik drove 1385.5 mi.
ADDITIONAL EXERCISES
Objective A Translate key phrases to algebraic expressions.
For extra help, see Examples 1–2 on pages 361–362 of your text and the Section 5.8 lecture
video.
Translate to an algebraic expression. Choice of variables used may vary.
1.
18 less than w
2.
The ratio of a number and 50
3.
40 increased by twice a number
4.
One fifth of the sum of 3 and a number
Objective B Solve applied problems involving decimals.
For extra help, see Examples 3–9 on pages 362–367 of your text and the Section 5.8 lecture
video.
Solve using the five-step problem-solving procedure.
5.
Normal body temperature is 98.6°F.
At one point during an illness,
Jessica’s temperature was 101.4°F.
How much did her temperature rise?
6.
The 4 Maloney children buy their
parents an anniversary gift that costs
$139.80 and split the cost equally.
How much does each child pay?
7.
Find the perimeter and the area of a
rectangle with length 15.3 cm and
width 7.6 cm.
8.
Computer Wizard charger $40 for a
house call plus $45.50 for each hour a
job takes. How long did an employee of
Computer Wizard work on a house call
if the bill totals $108.25?
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