Algebra Textbook Volume 1 Student Edition wc

Note: In word problems of this type, the first sentence often defines quantities, while the
second sentence defines the relationship of the quantities. It is critical in setting up these
word problems that the explanation includes defining the second quantity (e.g. x + 12) in
terms of the first (e.g. x). This expression (x+2) can then be used to determine the second
number or the first number (x) can be subtracted from the sum. Both methods are
acceptable.
Area and Perimeter The length of a rectangle is x = the width width = 10
seven more than the width. The x + 7 = the length = 17
perimeter is 54. Find the length length
and width of the rectangle.
2x +2( x+7) = 54
Angles
complementary Two angles are complementary. x = one angle 550 , 350
One angle is 20 less than its x − 200 = its
complement. Find the measure complement
of these two angles
x + x−20 = 900
supplementary Two angles are supplementary. x = one angle 600 , 1200
One angle is twice the other. 2x= its
Find the measure of these two supplement
angles.
x + 2x = 1800
Money (Cost) - Peppermint patties cost 25 x = the number 8
Purchasing cents each. Jaw breakers cost of peppermint jawbreakers
Quantity 35 cents each. Starving Adele patties 7
wants to buy 15 pieces of candy 15−x = the peppermint
for $4.55. How many number of jaw patties
peppermint patties and jaw breakers
breakers can she purchase?

.25x +.35 (15−x)
= $4.55

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Name _________________________
3.1A Type 1 - Solving Number Equality Word Problems

The following type of word problems illustrates pre-defined _________________, where

a number is defined by its relationship to another. Setting up the equality statement

involves representing English expressions _________________________. The translation

chart below provides examples:

English Math
Is equal to
Less than, difference =
More than, sum
−
+

Practice writing out the equation and then solving the problems below. The first one has
been done for you.

Note: With expressions like “seven less than twice a number” and “six more than three
times a number,” it is a very good idea to get in the habit of putting the term with x first.

This means that in the expressions just given, the answers would become 2x−7 and 3x+6.
Problems Pattern & Attack Answer
1) Twelve less than five times x = the number
a number is four more
than three times the Equation: 5x − 12 = 3x + 4
solve for x 5x − 3x = 4 + 12
number. Find the number. 2x = 16

x = 16 ÷ 2
x=8
2) Eight times a number is x = the number
nine more than five times Equation:
the number. Find the
number.

3) Five more than three x = the number
times a number is seven Equation:
less than four times the
number. Find the number.

4) Twenty-eight less than x = the number
nine times a number is ten Equation:
less than six times the
number. Find the number.

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Practice 3.1 B Type 1 Name _________________________

Write the equation and solve each problem below:

Problems Pattern & Attack Answer
1) Eleven more than five x = the number
Equation:
times a number is three
less than twelve times the
number. Find the number.

2) Twenty-five more than five x = the number
times a number is eleven Equation:
more than seven times the
number. Find the number.

3) Twenty more than seven x = the number
times a number is eleven Equation:
times that number. Find
the number.

4) Nine less than four times a x = the number
number is thirteen more Equation:
than twice the number.
Find the number.

5) Forty-five less than ten x = the number
times a number is eighteen Equation:
less than seven times the
number. Find the number.

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Practice 3.1 C Type 1 Name _________________________

Write the equation and solve each problem below:

Problems x= Pattern & Attack Answer
1) Eighteen less than eleven Equation:

times a number is six less
than nine times the
number. Find the number.

2) Seventeen less than three x=
times a number is nine Equation:
more than the number.
Find the number.

3) Seventeen more than nine x=
times a number is five Equation:
more than twelve times
the number. Find the
number.

4) Eight times a number is x=
fifty more than three times Equation:
the number. Find the
number.

5) Seven more than five times x=
a number is five less than Equation:
nine times the number.
Find the number.

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Name _________________________

SKILL Development

3.2A Addition of Simple Fractions

The easiest fractions to add and subtract are those with the same
_______________________________. The numbers on top, the ___________________________, are
added or subtracted and the number on the bottom, the ______________________________,
________________ _________________ _________________. Remember to ___________________________
your answer if possible. Answers can be left as improper fractions or changed to
mixed numbers.

Example: 1 + 1 = 1+1 = 2 1
6 6 6 6 3

Problems:

1) 1 + 3 7) 5 + 1
8 8 8 8

2) 4 + 2 8) 11 + 1
15 15 12 12

3) 4 + 3 9) 7 + 2
7 7

4) 7 + 3 10) 15 + 14
8 8

5) 9 + 3
10 10

6) 2 + 4


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Practice 3.2 B Name _________________________

1) 3 + 1 9) 5 + 7
10 10 9 9

2) 8 − 2 10) 17 − 5
9 9 18 18

3) 2 + 1 11) 11 + 5
5 5 12 12

4) 11 − 5 12) 17 − 1
12 12 24 24

5) 11 + 3 13) 17 + 7
20 20 18 18

6) 5 + 4 14) 5 + 2
9 9 7 7

7) 4 + 3 15) 5 + 3
5 5

8) 17 − 9 16) 5 + 3
20 20 2 2

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Practice 3.2 C Name _________________________

1) 4 + 1 10) 8 + 10
15 15 27 27

2) 2 + 4 11) 7 + 5
9 9 8 8

3) 5 + 3 12) 23 − 7
14 14 30 30

4) 2 + 1 13) 7 − 3
7 7 10 10

5) 7 + 9 14) 1 + 5
10 10 12 12

6) 9 − 3 15) 7 − 2
10 10

7) 5 + 1 16) 7 − 2
6 6 2 2

8) 9 + 3 17) 8 − 2
14 14

7 1 18) 2 + 4
8 8
9) −

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Name _________________________
3.3A Type 2 - Solving Consecutive Number Word Problems

Consecutive number word problems require the identification of numbers that follow in
a natural, logical ___________________. 1, 2, and 3 are examples of
___________________ numbers. However, there are two other types of consecutive
numbers – odds and evens. 1, 3, 5 is an example of ______________ consecutive
numbers. 2, 4, and 6 is an example of _________________consecutive numbers.

These consecutive word problems require identifying three or four consecutive numbers

whose sum is given. There are two basic equations that will be used in these problems.

Three Consecutive Equations
Example: 3, 4, 5 x + x+1 + x+2 = sum
Example (evens): 2, 4, 6 x + x+2 + x+4 = sum
Example (odds): 1, 3, 7

The sum of three Define x Equation Answers
consecutive x = the first x + x+1 + x+2 = 12 Consecutive
numbers is 12. Find number numbers
the numbers. x = 1st number 3x + 3 = 12 3, 4, 5
x+1 = 2nd number 3x = 12−3
x+2 = 3rd number 3x = 9
x = 9 ÷3
x= 3

The sum of three x = the first even x + x+2 + x+4 = 12 Consecutive
consecutive even number 3x + 6 = 12 evens numbers
numbers is 12. Find x = 1st number 3x = 12−6 2, 4, 6
the numbers. x+2 = 2nd number 3x = 6 Consecutive odds
The sum of three x+4 = 3rd number x = 6 ÷3 numbers
consecutive odd x = the first odd x= 2 3, 5, 7
numbers is 15. Find number
the numbers. x + x+2 + x+4 x + x+2 + x+4 = 15
3x + 6 = 15
3x = 15−6
3x = 9
x = 9 ÷3
x= 3

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Practice 3.3 B Type 2 Name _________________________

Write the equation and solve: Define x Equation
Problems Answers
1) The sum of three x=
consecutive
numbers is fifty-
four. Find the
numbers.

2) The sum of three x=
consecutive even
numbers is eighty-
four. Find the
numbers.

3) The sum of three x=
consecutive odd
numbers is twenty-
seven. Find the
numbers.

4) The sum of four x=
consecutive
numbers is one
hundred thirty-four.
Find the numbers.

5) The sum of three x=
consecutive even
numbers is one
hundred thirty-two.
Find the numbers.

6) The sum of three x=
consecutive odd
numbers is fifty-
seven. Find the
numbers.

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Practice 3.3 C Type 2 Name _________________________

Write the equation and solve: Define x Equation
Problems Answers
1) The sum of three x=
consecutive
numbers is ninety.
Find the numbers.

2) The sum of three x=
consecutive even
numbers is thirty.
Find the numbers.

3) The sum of three x=
consecutive odd
numbers is fifty-one.
Find the numbers.

4) The sum of four x=
consecutive x=
numbers is two
hundred twenty-
two. Find the
numbers.

5) The sum of three
consecutive even
numbers is one
hundred eighty-six.
Find the numbers.

6) The sum of three x=
consecutive odd
numbers is thirty-
nine. Find the
numbers.

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Practice 3.3 D Type 2 Name _________________________

Write the equation and solve: Define x Equation
Problems Answers
1) The sum of three x=
consecutive odd
numbers is sixty-
nine. Find the
numbers.

2) The sum of three x=
consecutive
numbers is one
hundred thirty-eight.
Find the numbers.

3) The sum of three x=
consecutive even
numbers is ninety-
six. Find the
numbers.

4) The sum of three x=
consecutive odd x=
numbers is thirty- x=
three. Find the
numbers.

5) The sum of four
consecutive even
numbers is one
hundred sixteen.
Find the numbers.

6) The sum of three
consecutive even
numbers is one
hundred seventy-
four. Find the
numbers.

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3.4 A Lowest Common Multiple Name: _________________________________

The _____________________ ________________________ ________________________ (LCM) is the
smallest number that both original numbers will divide into with no remainder. To
find the LCM of two numbers, think of the multiples of the larger number. The LCM is
the smallest one that the other number will divide into with no remainder.

16 and 24 Multiples of larger number reasoning LCM
9 and 12 24: 24, 48, 72, … 48
24 is not divisible by 16,
12: 12, 24, 36, … but 48 is. [16  3 = 48] 36

12 is not divisible by 9,

24 is not divisible by 9
But 36 is. [9  4 = 36]

Problems: Find the LCM of each set of numbers below:

Numbers Multiples of Larger Number LCM
1) 4 and 8
2) 2 and 5
3) 6 and 9
4) 10 and 6
5) 6 and 8
6) 5 and 7
7) 10 and 8
8) 24 and 8
9) 52 and 5
10) A2 and A

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Practice 3.4 B Name ________________________________

Find the LCM of each set of numbers:

Numbers Multiples of Larger Number LCM
1) 7 and 2
2) 9 and 12
3) 21 and 7
4) 5 and 10
5) 15 and 10
6) 6 and 15
7) 10 and 4
8) 7 and 5
9) 8 and 12
10) 8 and 3
11) 4 and 6
12) 27 and 9

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Practice 3.4 C Name ________________________________

Find the LCM of each set of numbers:

Numbers Multiples of Larger Number LCM
1) 3 and 5
2) 7 and 21
3) 9 and 2
4) 10 and 4
5) 2 and 7
6) 8 and 12
7) 10 and 5
8) 15 and 6
9) 8 and 5
10) 12 and 9
11) 4 and 14
12) 18 and 6

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Section Two – Solving NOT pre-defined Word Problems
& Fraction Skill Development

Type 3 - Solving Sums of Numbers Word Problems ............................................ 3.5A
Quiz ......................................................................................................... 3.5D

SKILL DEVELOPMENT
Addition and subtraction of Fractions with different denominators...... 3.6A
Quiz ..............................................................................................3.6E

Type 4 - Solving Perimeter Word Problems ........................................................ 3.7A
Quiz ......................................................................................................... 3.7D
Selecting Flooring for your Home – Area Exploration .............................3.7E

SKILL DEVELOPMENT
Addition and Subtraction of Mixed Numbers ......................................... 3.8A
Quiz .............................................................................................3.8Ia
Quiz .............................................................................................3.8Ib

Type 5 - Solving Angles Word Problems.............................................................. 3.9A
Quiz ......................................................................................................... 3.9D

SKILL DEVELOPMENT
Multiplying Fractions ............................................................................ 3.10A
Quiz ..........................................................................................3.10Ea
Quiz ..........................................................................................3.10Eb

Type 6 - Solving Money (Cost) - Quantity Word Problems................................ 3.11A
Quiz ....................................................................................................... 3.11D

SKILL DEVELOPMENT
Dividing Fractions.................................................................................. 3.12A
Quiz ............................................................................................3.12E

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3.5 A Type 3 Sums of Numbers Name ___________________

In the word problem types reviewed thus far, the relational values have been defined
(such as twelve less than five times a number is four more than three times a number). In
the following word problems, the relational values are not defined. They are found by
finding the relationship between ________ of the numbers.

When reading these types of word problems, the first sentence often defines this

______________________ (how much more or less or how many times one number is in

relation to another number). The second sentence defines the quantities. For example

one number (x) is two more than another number (x+2). Their sum is eight (x + x + 2 = 8).

In setting up these word problems, make certain that the explanation includes defining

the second quantity (e.g. x + 2) in terms of the first (e.g. x).

Example Define and Equation Answer
1) One number is two more than another x = the smaller number x=3
x + 2 = the larger number x+2 = 5
number. Their sum is eight. What are Equation: x + x + 2 = 8 x = 10
the numbers? 2x + 2 = 8 x+12 = 22
2) One number is twelve more than x = 11
another. Their sum is thirty-two. What 2x = 6 8x = 88
are the numbers? x=3
3) One number is eight times another x = the smallest number
number. Their sum is ninety-nine. What x + 12
are the two numbers? Equation: x + x + 12 = 32
2x + 12 = 32
2x = 20

x = 10
x = the smallest number
8x = larger number
Equation: x + 8x = 99

9x = 99
x = 11

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3.5 A (cont.) Name ___________________

Teacher-guided problems

4) One number is twenty-five more than x = the smallest number
another number. Their sum is forty-one.
What are the two numbers? Equation:

Note: The above problem can be solved in two ways. After the first number is found,
there are two ways to find the second number. (1) It is possible to find the second
number by simply substituting 8 into the expression for the second number, x + 25,
to give 33. (2) It is also possible to use the fact that the numbers add up to 41. If one

number is 8, the other must be 33, since 41 − 8 = 3. Either method can be used.
5) One number is six more than twice x = the smallest number
another number. Their sum is thirty.
What are the two numbers? Equation:

6) One number is eleven less than another x = the largest number
number. Their sum is twenty-five. What
are the numbers? Equation:

7) One number is six less than four times x = the smaller number
another number. Their sum is nine. Equation:
What are the two numbers?

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Practice 3.5 A Name __________________
Example
1. One number is five times another Define and Equation Answer
x = the smaller number
number. Their sum is fifty-four. What
are the two numbers? Equation:

2. One number is sixteen more than x = the smaller number
another number. Their sum is forty-two. Equation:
What are the two numbers?

3. One number is nine more than five x = the smaller number
times another number. Their sum is Equation:
twenty-seven. What are the two
numbers?

4. One number is fifteen less than another x = the larger number
number. Their sum is eighty-one. What Equation:
are the two numbers?

5. One number is seven less than three x = the smaller number
times another number. Their sum is Equation:
fifty-three. What are the two numbers?

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Practice 3.5 B Name __________________

Example Define and Equation Answer
1. One number is sixteen less than another x=
Equation:
number. Their sum is ninety-two. What
are the two numbers?

2. One number is three less than seven x=
times another number. Their sum is Equation:
sixty-one. What are the two numbers?

3. One number is thirteen more than x=
another number. Their sum is forty- Equation:
seven. What are the two numbers?

4. One number is nine times another x=
number. Their sum is seventy. What are Equation:
the two numbers?

5. One number is four more than five x=
times another number. Their sum is Equation:
forty-six. What are the two numbers?

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Practice 3.5 C Name __________________

Example Define and Equation Answer
1. One number is six more than three x=
times another number. Their sum is Equation:
thirty-eight. What are the two
numbers?

2. One number is eleven less than five x=
times another number. Their sum is Equation:
forty-three. What are the two
numbers?

3. One number is fifteen times another x=
number. Their sum is forty-eight. Equation:
What are the two numbers?

4. One number is eight less than x=
another number. Their sum is forty- Equation:
two. What are the two numbers?

5. One number is nine more than x=
another number. Their sum is thirty- Equation:
nine. What are the two numbers?

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Name __________________________
3.6 A Addition and Subtraction of Fractions with Different Denominators

When two fractions that have different ____________________________ are added or
subtracted, they have to be rewritten as fractions with the same
__________________________________. The new denominator will be the ____________________
______________________ ______________________ (LCM) of the denominators of the two
original fractions. This new denominator is called the ____________________
______________________ ______________________ (LCD). Each of the original fractions must be
rewritten as an equal fraction with the new denominator. Remember to
__________________ all final answers if possible.

Example: 1 + 4 LCD (similar to LCM) = 15.
5 15

1  3 + 6 = 3 + 6 = 3+6 = 9 reduced to 3
5  3 15 15 15 15 15 5

Problems:

1. 1 3 2. 2 1 3. 14 3
2 10 3 4 15 5
+ + −

4. 3 1 5. 3 2 6. 5 3
4 6 5 3 6 4
+ + −

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