SKILL
Are You Ready?
55
Order of Operations
Teaching Skill 55
Objective Use the correct order of operations
to evaluate expressions.
Alternative Teaching Strategy
Objective Use the correct order of operations
to evaluate expressions.
Explain to students that order of operations
gives us a set of rules as to which operations
are carried out first when an expression
involves more than one operation.
Some students may benefit from manipulating
numbers and the order of operations.
Write the following numbers on the board:
2, 3, 4, 5, and 6. Tell students that you are
going to use each number exactly once,
along with one set of parentheses and one
each of , , , and to arrive at a final
result of 4.
Review the correct order of operations with
students and the trick for remembering the
order.
Direct students’ attention to the first example.
Demonstrate why having a set of rules is
necessary by working out the problem left
to right instead of using the correct order of
operations. (8 2 3 6 3 18) Ask: Do
you get the same result? (No)
Write: 6 (2 3 4) 5. Work through the
correct order of operations to demonstrate
that the result is 4.
Have students consider the second and
third examples. Before working through
the examples, ask a volunteer to list the
operations they see in each problem, in the
order in which they would be performed.
6 (2 3 4) 5
6 (6 4) 5
6 10 5
62
4
Instruct students to repeat this exercise
using the same numbers and the same rules
to arrive at a result of 3. Point out that they
can have as many, or as few, numbers inside
the parentheses as they need. (Students
may arrive at different results; one possible
result is (2 3) 5 6 4.)
Have students complete the exercises.
PRACTICE ON YOUR OWN
In exercises 1–12, students evaluate
expressions using order of operations.
If students have trouble reaching an answer,
have them work in pairs. As students become
more comfortable, use larger numbers and mix
up the operations. For example, require the
use of one exponent, two additions, and two
subtractions. Be sure to specify whether any
parentheses are allowed.
CHECK
Determine that students know how to use
the correct order of operations to evaluate
expressions.
Students who successfully complete the
Practice on Your Own and Check are
ready to move on to the next skill.
Sample problems:
COMMON ERRORS
Students may always work from left to right
and forget to follow the correct order of
operations.
1) Use the numbers 1, 2, 3, 4, and 5 with
one exponent, and one each of , , and to arrive at a result of 13. No parentheses
3
allowed. Possible answer: 5 4 2 1.
Students who made more than 2 errors in
the Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
2) Use the numbers 2, 3, 4, 6, and 10 with
one exponent, one set of parentheses, and
one each of , , and to arrive at a result
2
of 14. Possible answer: 3 10 (6 4).
Copyright © by Holt, Rinehart and Winston.
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121
Holt Algebra 1
Name
Date
SKILL
Are You Ready?
55
Order of Operations
Class
The Correct Order of Operations
1.
Parentheses
2.
Exponents
3.
Multiply / Divide
4.
Add / Subtract
(left to right)
(left to right)
One way to remember the correct order: Please excuse my dear Aunt Sally.
Example 1
Evaluate 8 2 3.
Example 2
2
Evaluate (6 4) 5.
Example 3
3
Evaluate 2 4 3 6.
8 6
10 2 5
84 36
2
100 5
8 12 6
20
20 6
14
Practice on Your Own
Evaluate each expression.
1. (5 1) 3
2. 8 8 16
3. 6 5 1
4. 24 3 5
5. (8 10) 3
6. 20 1 7
7. 7 2 1
8. 72 2 3
9. 21 15 ÷ 3
10. 8 7 5
11. 3 6 2 9
12. (4 2) 2 9
Check
Find the absolute value of each expression.
13. (6 10) 4
14. 40 4 10
15. 5 10 2
16. 15 3 10
17. 4 8 4 2
18. 8 5 3 6
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122
Holt Algebra 1
SKILL
Are You Ready?
51
Add and Subtract Integers
Teaching Skill 51
Objective Add and subtract integers.
Alternative Teaching Strategy
Objective Add and subtract integers using a
number line.
Explain to students that adding and
subtracting integers is best understood by
thinking about absolute values, that is, the
numbers without the negative signs.
Materials needed: copies of the number lines
shown below.
Some students may benefit from visualizing
addition and subtraction using a number
line. Give each student copies of the number
lines. Tell students they are going to add
integers using the number lines.
Review with students how to add integers
with the same signs. Ask: If both signs
are positive, what will be the sign of the
sum? (positive) If both signs are negative,
what will be the sign of the sum?
(negative) Does it matter which number is
larger? (No) Work through Example 1.
–10
–5
–15
Review with students how to add integers
with opposite signs. Stress that the sign of
the sum is determined by the larger number.
Work through Example 2.
–10
–5
–5
0
–5
0
0
5
0
5
5
10
5
10
10
15
Write “3 (7)” on the board. Direct
students’ attention to the first number line.
Ask: What do each of the tick marks
represent on the number lines? (one unit)
Review with students how to subtract
integers. Ask: What is the opposite of 5?
(5) What is the opposite of 8? (8)
Work through Example 3.
Instruct students to place a dot on the number
3. Ask: If you were going to add 7 to 3,
which direction would you move on the
number line? (right) Since you are adding
7 instead, which way do you move? (left)
Instruct students to move 7 units to the left.
Ask: What is the result? (4)
Remind students that zero is neither positive
nor negative. Ask: When is the sum of
two integers zero? (when the numbers are
opposites, e.g. 4 and 4)
Have students complete the exercises.
–7
PRACTICE ON YOUR OWN
In exercises 1–12, students add and subtract
integers.
–10
0
5
10
Next, have students use the second number
line to add –13 15. Ask: Where do you
place your first dot? (–13) In which
direction should you move? (right) Make
sure students arrive at 2 as an answer.
CHECK
Determine that students know how to add
and subtract integers.
After students have a good understanding
of adding integers, explain how to use the
number line to subtract integers. Have students
use the third and fourth number lines to
practice the following: 8 14 and 2 (9).
Make sure students know to move to the left
when subtracting positive numbers and to the
right when subtracting negative numbers (the
opposite of when adding).
Students who successfully complete the
Practice on Your Own and Check are
ready to move on to the next skill.
COMMON ERRORS
Students may confuse a subtraction sign
with a negative sign.
Students who made more than 2 errors in
the Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
–5
Have the students make up additional
problems and draw their own number lines.
113
Holt Algebra 1
Name
Date
SKILL
Are You Ready?
51
Add and Subtract Integers
Class
Adding Integers
Same Signs
Subtracting Integers
Opposite Signs
Step 1: Ignore the signs.
Step 2: Add the two
numbers.
Step 3: Add the sign of the
larger number to the answer.
Step 1: Ignore the signs.
Instead of subtracting, add
Step 2: Subtract the smaller
the opposite of the second
number from the larger number.
number and then use the rules
Step 3: Add the sign of the
for adding integers.
larger number to the answer.
Example 1: Add 3 (9).
Example 2: Add 7 (12).
3 9 12
12 7 5
Since both numbers are
negative, the answer is also
negative.
Since the larger number
is negative (12 7), the
answer is also negative.
3 (9) 12
7 (12) 5
Example 3: Subtract 6 (3).
The opposite of 3 is 3.
639
Practice on Your Own
Perform each indicated operation.
1. 11 16
2. 22 18
3. 15 (10)
4. 3 14
5. 20 (9)
6. 6 ( 5)
7. 6 (13)
8. 8 14
9. 100 95
10. 7 (10)
11. 10 (–10)
12. 25 (40)
Check
Perform each indicated operation.
13. 2 8
14. 10 18
15. 14 (21)
16. 7 (3)
17. 40 (35)
18. 17 4
19. 12 12
20. 18 (13)
Copyright © by Holt, Rinehart and Winston.
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114
Holt Algebra 1
SKILL
Are You Ready?
48
Add and Subtract Fractions
Teaching Skill 48
Objective Add and subtract fractions.
Alternative Teaching Strategy
Objective Add like fractions.
Review with students the meaning of “like
fractions” and “unlike fractions.”
Some students may benefit from a visual
model of adding like fractions. Encourage
students to use a model until they are
comfortable without it.
Point out that adding and subtracting
like fractions (fractions with the same
denominators) requires simple addition
or subtraction of the numerators; the
denominator in the answer does not change.
To create a model for fifths, have students
draw a rectangle and divide it into 5 columns
of equal length. Explain that each column
represents one-fifth.
Remind students that simplest form means
no common factors in the numerator and
denominator and no improper fractions.
Review with students how to convert an
improper fraction to a mixed number.
Work through the addition example.
Tell students they are going to find the
3
4
sum of __ __. Instruct students to begin
5
5
by shading 3 of the five columns in their
rectangle.
Review with students the steps for adding or
subtracting unlike fractions. Point out that in
some cases, one of the denominators may
be the LCD, in which case only the other
fraction must be rewritten. Work through the
subtraction example.
Since there are not enough fifths
to shade 4 more, draw a second
rectangle with 5 columns.
Instruct students to shade the remaining 2
fifths in the first rectangle and 2 more in the
second rectangle.
Ask: When subtracting a fraction from a
mixed number, what should you do first?
(Convert the mixed number to an improper
fraction.)
Instruct students to count the shaded fifths.
7
(7) Show that the sum is __. Remind students
5
that they can rewrite this as a mixed number.
2
1__
5
Ask: How would you model fourths?
(Draw a rectangle with 4 columns.) Tenths?
(Draw a rectangle with 10 columns.)
Have students complete the exercises.
PRACTICE ON YOUR OWN
In exercises 1–8, students add and subtract
fractions.
CHECK
Determine that students know how to add
and subtract fractions.
Have student practice this technique by
3
6 2
5
7
find the sums __ __ 1__ and ___ ___
7
7 7
12
12
12
___
1.
12
As an extension of this exercise, have
1
7
students consider the example __ __. Ask:
4
8
Could you use this technique to add the
fractions as they are written? (No) What
1
would you need to do first? Rewrite __
4
2
__
as . Have students complete this problem.
8
Students who successfully complete the
Practice on Your Own and Check are
ready to move on to the next skill.
COMMON ERRORS
Students may add or subtract the
denominators.
Students who made more than 2 errors in
the Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
107
Holt Algebra 1
Name
Date
SKILL
Are You Ready?
48
Add and Subtract Fractions
Class
General Operation Reminders
Adding and Subtracting Fractions
Like Fractions (same denominators)
Unlike Fractions (different denominators)
Step 1: Add or subtract the numerators.
Step 2: Write the sum or difference of the
numerators over the denominator.
Step 3: Write the answer in simplest form.
Step 1: Find the least common denominator
(LCD) and then rewrite each fraction
so that its denominator is the LCD.
Step 2: Follow the steps for adding or
subtracting like fractions.
5
1
Example 1: Add __ __.
8
8
5
1
5
6
1
__ __ _____ __ (GCF of 6 and 8 is 2.)
8
8
8
8
6
62
3
3
__
_____ __ The sum is __.
8
82
4
4
3
1
Example 2: Subtract 1__ __.
2
4
3
1
Rewrite 1__ as __. The LCD of 2 and 4 is 4.
2
2
3 __
6
2
__
__
2
2
4
The difference
6 __
3
3
__
__
3
4
4
4
is __.
4
Practice on Your Own
Add or subtract. Give your answer in simplest form.
2
1
1. __ __
5
5
5
2
2. __ __
7
7
2
1
3. __ ___
5
10
4
1
4. __ __
9
3
5
2
5. 1__ __
9
9
3
7
6. __ __
8
4
5
2
7. 1__ __
3
6
5
2
1
8. __ __ ___
3
6
12
Check
Add or subtract. Give your answer in simplest form.
6
3
9. __ __
11
11
3
7
13. 1__ __
8
8
8
2
10. __ __
9
9
3
1
11. ___ __
7
14
7
1
12. ___ __
12
4
3
7
14. ___ __
5
10
3
1
15. 1__ __
8
4
3
1
4
16. __ ___ ___
5
15
10
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
108
Holt Algebra 1
SKILL
Are You Ready?
60
Evaluate Expressions
Teaching Skill 60
Objective Evaluate expressions.
Alternative Teaching Strategy
Objective Evaluate expressions.
Explain to students that evaluating an
expression simply means replacing the
variable with a given value and simplifying.
Explain to students that most expressions
can be evaluated for any given number.
Create the table below on the board and
have students duplicate it. Tell students
they are going to evaluate an expression for
several different values.
Review with students the order of operations
and point out that they will need to follow
them to correctly simplify expressions.
Also review integer operations as some
expressions, and some given values, may
involve negative numbers.
Value
Have students consider Example 1. Ask:
What two operations will be used to
simplify this expression? (multiplication
then addition) What number replaces y ? (6)
Work through the example.
Simplification
2
6(
)3
___ 3 ___
1
6(
)3
___ 3 ___
0
6(
)3
___ 3 ___
1
6(
)3
___ 3 ___
2
6(
)3
___ 3 ___
Ask: Based on the center column, what
expression are you evaluating? (6y 3)
For what values are you evaluating the
expression? (2, 1, 0, 1, and 2)
Next have students consider Example 2.
Ask: What two operations will be used to
simplify this expression? (multiplication
then subtraction) What number replaces p?
(4) Stress that students must be careful
when working with negatives since it is easy
to overlook them when simplifying. Work
through the example.
Have students complete the table and check
their answers. (2, 1, 0, 1, 2; 12, 6, 0,
6, 12; 9, 3, 3, 9, 15)
Have students duplicate the two tables
below, identify the expression, and complete
the last two columns.
Have students complete the practice exercises.
PRACTICE ON YOUR OWN
In exercises 1–9, students evaluate
expressions.
Value
CHECK
Determine that students know how to
evaluate expressions.
Students who successfully complete the
Practice on Your Own and Check are
ready to move on to the next skill.
Substitution
Simplification
3
4(
)5
___ 5 ___
1
4(
)5
___ 5 ___
2
4(
)5
___ 5 ___
4
4(
)5
___ 5 ___
Value
COMMON ERRORS
Students may not follow the correct order
of operations and may arrive at an incorrect
result.
Substitution
Simplification
3
3(
)2
___ 2 ___
2
3(
)2
___ 2 ___
1
3(
)2
___ 2 ___
2
3(
)2
___ 2 ___
When students are comfortable completing
tables, give them several expressions and
have them create their own tables using the
given values 3, 2, 1, 0, 1, 2, and 3.
Students who made more than 2 errors in
the Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Substitution
131
Holt Algebra 1
Name
Date
SKILL
Are You Ready?
60
Evaluate Expressions
Class
To evaluate a variable expression, replace the variable(s) with the given
value(s) and use the order of operations to simplify.
Example 1: Evaluate 10y 3 for y 6.
10y 3 10(6) 3
Replace y with 6 since 6 is the given value.
60 3
Order of operations says to multiply first.
63
Add.
Example 2:
Evaluate 6p 15 for p 4.
6p 15 6(4) 15
Replace p with 4 since 4 is the given value.
24 15
Order of operations says to multiply first.
9
Subtract.
Practice on Your Own
Evaluate each expression for the given value of the variable.
1. 7x 1 for x 5
2. 8m 12 for m 5
3. 2y 9 for y 6
4. 6p 3 for p 4
5. 27 9x for x 2
6. 10 4q for q 3
7. 7c 11 for c 3
1
8. __t 5 for t 9
3
1
9. __m 16 for m 20
2
Check
Evaluate each expression for the given value of the variable.
10. 2n 3 for n 9
11. x 7 for x 5
12. 15 3h for h 5
13. 15 7m for m 3
14. 5a 9 for a 1
1
15. __y (4) for y 12
2
Copyright © by Holt, Rinehart and Winston.
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132
Holt Algebra 1
SKILL
Are You Ready?
58
Connect Words and Algebra
Teaching Skill 58
Objective Connect words and algebra.
Alternative Teaching Strategy
Objective Connect words and algebra.
Point out to students that an algebraic
expression (or equation) is simply a
mathematical way of writing a phrase or
sentence.
Materials needed: multiple copies of the
flashcards shown below (index cards work
nicely), blank index cards
Have students work in pairs. Distribute
copies of the flashcards and have students
shuffle the cards and divide them in half so
that each student has six cards.
Ask: What is the difference between
an expression and an equation? (An
expression does not have an equal sign
while an equation does.)
Tell students that associating key words with
the correct operation is critical to being able
to make the connection between words and
algebra.
3x 1
n5
x7
1n 2
__
C 3(25)
t 6(2)
C 12 2.50
P 2(8) 2w
1 (6)(h)
A __
2
I (500)(2)r
A 50 10w
S 600 50w
2
Review with students the table of key words.
Provide some real life examples. Start with
the following two: (1)If your age is 10 years
more than your sister’s, and your sister is
12, how do you find your age? (Add 12 plus
10.) If you receive $10 per week allowance
for 8 weeks, how do you find the total
amount you received? (Multiply 10 times 8.)
Have students provide additional examples.
Review with students key words and the
operations with which the words are associated.
Tell students they are going to make up
phrases or situations that match the algebraic
expressions and equations on the cards. Give
the following example: 5n 3. Ask: How
would you verbalize 5n? (5 times a number)
And ⴙ 3? (increased by 3) Write the phrase on
the board: “5 times a number increased by 3.”
Point out that variations of this phrase are also
correct, such as 3 more than 5 times a number.
Review the lawn cutting example with students
and then have them complete the exercises.
PRACTICE ON YOUR OWN
In exercises 1–6, students write algebraic
expressions and equations.
CHECK
Determine that students know how to write
algebraic expressions and equations.
COMMON ERRORS
Students may not know the key words
associated with operations, and as a result
may use the wrong operation.
Next, write the equation C 40 5(d ) on
the board. Remind students that variables
typically represent something that makes
sense. For example, C might represent
cost and d number of days. Or, provide the
following scenario: There are 40 cookies in
a bag and Tom eats 5 cookies per day.
C 40 5(d ) could be the number of
cookies remaining at the end of any given day.
Students who made more than 1 error in the
Practice on Your Own, or who were not
successful in the Check section, may benefit
from the Alternative Teaching Strategy.
Instruct students to take turns making up
situations to match the cards they have. As
an extension of the exercise, have students
make flashcards and continue.
Students who successfully complete the
Practice on Your Own and Check are
ready to move on to the next skill.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
127
Holt Algebra 1
Name
Date
SKILL
Are You Ready?
58
Connect Words and Algebra
Class
To connect words and algebra, you must understand the operations involved
and how to represent them. Key words are helpful in determining the operations.
Key Words
Operation or Representation
a number; an unknown quantity
any variable, such as x or n
Twice, three times, etc.
multiplication (2n, 3n, etc.)
sum; more than; increased by
addition ()
difference; less than; decreased by
subtraction ()
each; per
multiplication
is; equals
Example: Jared must cut 6 lawns over the weekend. Each of the lawns takes
2 hours to cut. Write an equation representing the total time t to cut all 6 lawns.
Answer: Since each lawn takes 2 hours, multiply 2 times the number of
lawns to get the total time: t 6(2).
Practice on Your Own
1. Write an expression that represents the quantity 5 more than a number.
2. Write a phrase that could be modeled by the expression x 15.
3. John bought 3 CDs and 2 DVDs. Each CD costs $9.95, and each DVD costs
$14.98. Write an equation representing the total cost C.
4. A triangle has sides of length 7, 10, and s. Write an equation representing the
perimeter P of the triangle.
5. The value of a painting begins at $12,000 and increases by $500 per year.
Write an equation representing the value V of the painting at the end of any
given year y.
6. David has 56 baseball cards of which he sells 3 cards per week. Write an
equation representing the number of cards n he has left at the end of any
given week w.
Check
7. Write an expression that represents a number decreased by 6.
8. Tina bought 6 plates and 2 glasses. Each plate costs $6.99, and each glass
costs $22.98. Write an equation representing the total cost C.
9. Joseph opens a checking account with $400. Each month he adds $150 to the
account. Write an equation representing the total amount A in the account at the
end of any given month m.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
128
Holt Algebra 1
Answer Key
continued
SKILL 53 ANSWERS:
11. 0
Practice on Your Own
12. 12
1. 5
Check
2. 18
9
3. __
11
4. 9
13. 11
5. 20
16. 25
6. 8
17. 13
7. 13
18. 0
1
8. ___
25
19. 1.1
Check
9. 4
10. 72
14. 2.3
15. 10
20. 1
SKILL 55 ANSWERS:
Practice on Your Own
11. 7
2
12. __
5
13. 10
1. 3
2. 4
3. 31
14. 12
4. 3
15. 6
1
16. __
2
5. 6
6. 14
SKILL 54 ANSWERS:
7. 50
Practice on Your Own
8. 9
1. 15
9. 26
2. 8
10. 43
3. 0.4
11. 0
4. 1.19
12. 4
5. 10
Check
6. 4
13. 4
7. 0.75
14. 0
8. 0.7
15. 25
9. 6
16. 22
10. 7
17. 2
18. 58
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
225
Holt Algebra 1
Answer Key
continued
SKILL 50 ANSWERS:
Check
Practice on Your Own
13. 6
1. 75
14. 8
2. 800
15. 7
3. 0.02
16. 10
4. $300
17. 5
5. $144
18. 21
6. $2000
19. 0
7. 3%
20. 31
8. 4%
SKILL 52 ANSWERS:
Check
Practice on Your Own
9. 200
1. 15
10. 500
2. 4
11. 0.015
3. 55
12. $2400
4. 8
13. $12,000
5. 63
14. 5%
6. 6
SKILL 51 ANSWERS:
7. 150
Practice on Your Own
8. 15
1. 5
9. 26
2. 4
10. 7
3. 25
11. 32
4. 17
12. 3
5. 11
Check
6. 11
13. 70
7. 19
14. 6
8. 6
15. 72
9. 5
16. 7
10. 17
17. 64
11. 0
18. 12
12. 15
19. 9
20. 12
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
224
Holt Algebra 1
Answer Key
continued
SKILL 47 ANSWERS:
Practice on Your Own
4
1. ___
15
2. 3
1
3. __
9
1
4. 1__
2
1
__
5.
7
1
6. __
11
1
7. 4__
2
8. 6
Check
1
9. ___
18
2
10. __
3
5
___
11.
14
12. 9
1
13. ___
12
1
14. __
7
1
15. 1__
2
16. 15
Check
9
9. __
11
2
10. __
3
5
___
11.
14
1
12. __
3
1
13. 1__
2
3
___
14. 1
10
3
15. __
8
23
___
16.
30
SKILL 49 ANSWERS:
Practice on Your Own
1. 18
2. 9
3. 280
4. 30
5. 6
6. 21
7. 33
8. 45
SKILL 48 ANSWERS:
9. 84
Practice on Your Own
3
1. __
5
3
__
2.
7
1
__
3.
2
1
__
4.
9
1
5. 1__
3
5
__
6. 1
8
5
__
7.
6
1
8. 1__
4
10. 2600
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Check
11. 20
12. 21
13. 240
14. 360
15. 6
16. 23
17. 81
18. 285
223
Holt Algebra 1
Answer Key
continued
4. 45p 3q
5
5. 25b c
2
6. 6x y
7. 16z
12. 0
4
14. 4
2
5
15. 2
3 2
8. 8d e
9. 18t
10. w
SKILL 61 ANSWERS:
2
Practice on Your Own
8
11. 22r
13. 6
4 2
1. 10m n
7
2
2. 4x y
2 2
12. 50x y
4
3. 20a b
5
4. ___3
2t
Check
13. 30f
2
f 2
5. ___
3
2
14. 27x y
15. 60h
4
6. 3p 3q 2r 3
2 2
16. 49a b
4
7. u v
4 2
17. 4p q
4c 2
8. ___
d5
18. 21u v
3
19. g
9. 144h 2k 2
8
2 2
20. 16y z
10. 1
3 2
11. 10xy z
SKILL 60 ANSWERS:
Practice on Your Own
wz
12. ___
9
1. 36
Check
2. 28
13. 35s t
3. 3
x
14. ___
5y
4. 27
5. 9
6. 2
4
15. 8b 4c 4
16. 5pq
3
7. 10
5mn
17. ____
3
8. 8
18. 36u 3w 4
9. 6
Check
10. 15
8 2
19. 10x y
7
20. __
f
11. 2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
227
Holt Algebra 1
Answer Key
continued
SKILL 56 ANSWERS:
8. 0
Practice on Your Own
9. 11h
1. 5x 30
10. 9y 9
2. 5z 35
11. 10 10x
3. 2n 4
12. 5 5u
4. 12 4k
13. 13y 6x
5. 48 8y
14. 4
6. 6m 18
Check
7. 10p 10
15. 10x
8. 60 3c
16. 3c
9. 7q 7
17. 3a
10. 55 11t
18. 8.4z
11. 14 2b
19. 10m 11
12. 36 9w
20. 8q 5r
Check
SKILL 58 ANSWERS:
13. 12c 24
Practice on Your Own
14. 15 5a
1. 5 n
15. 25 25d
2. a number decreased by 15; 15 less than
a number; the difference between a
number and 15; etc.
16. 50 10j
17. 4x 12
3. C 3(9.95) 2(14.98)
18. 30 15y
4. P 7 10 s
19. 3g 75
5. V 12,000 500y
20. 9m 9
SKILL 57 ANSWERS:
2
6. n 56 3w
Check
7. n 6
Practice on Your Own
1. 12x
8. C 6(6.99) 2(22.98)
2. 4m
9. A 400 150m
3. 7a
2
SKILL 59 ANSWERS:
4. 7t
5. 3b
6. 8d
Practice on Your Own
1. 10x
2
2. 21a
7. x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
2
4
3. 16mn
226
Holt Algebra 1