You Can
Pass The
GED!!
GED MATH LESSONS
PRACTICE PROBLEMS
WORKBOOK
By John Zimmerman
Practice Problems
Workbook
This workbook is designed to give students practice
problems and solutions to strengthen their skills. In order
to truly master math concepts you must practice a wide
variety of problems. As such, this workbook is an
extremely valuable supplement to the free online video
lessons provided at GEDMathLessons.com.
Suggestions to using workbook include:
• Do practice problems only after watching lesson online
• Complete all problems in order
• Track your errors for review and practice
Note: Answer keys are on last page of each lesson
worksheet
TABLE OF CONTENTS
CHAPTER 1: FRACTIONS AND DECIMALS
1
LESSON 1 – INTRODUCTION TO FRACTIONS AND DECIMALS
LESSON 2 – LEAST COMMON MULTIPLE/DENOMINATOR
LESSON 3 – MULTIPLYING AND DIVIDING FRACTIONS
LESSON 4 – ADDING AND SUBTRACTING FRACTIONS
2
8
14
20
CHAPTER 2: POSITIVE AND NEGATIVE NUMBERS
26
LESSON 1 – INTRODUCTION TO REAL NUMBERS
LESSON 2 – ADDING REAL NUMBERS
LESSON 3 – SUBTRACTING REAL NUMBERS
LESSON 4 – MULTIPLYING AND DIVIDING REAL NUMBERS
27
33
39
45
CHAPTER 3: ORDER OF OPERATIONS AND VARIABLES
51
LESSON 1 – BASIC NUMBER OPERATIONS
LESSON 2 – UNDERSTANDING VARIABLES
LESSON 3 – ORDER OF OPERATIONS
LESSON 4 – TRANSLATING VERBAL AND ALGEBRAIC EXPRESSIONS
52
60
66
72
CHAPTER 4: SIMPLIFYING ALGEBRAIC EXPRESSIONS
80
LESSON 1 – THE DISTRIBUTIVE PROPERTY
LESSON 2 – SIMPLIFYING BY COMBINING LIKE TERMS
81
87
CHAPTER 5: SOLVING EQUATIONS
98
LESSON 1 – BASIC CONCEPTS OF EQUATIONS/INEQUALITIES/SOLUTIONS
LESSON 2 – SOLVING ONE STEP EQUATIONS
LESSON 3 – SOLVING TWO STEP EQUATIONS
LESSON 4 – SOLVING MULTI-STEP EQUATIONS
LESSON 5 – FORMULAS AND LITERAL EQUATIONS
99
105
113
121
129
CHAPTER 6: SLOPE AND GRAPHING LINES
135
LESSON 1 – GRAPHING LINES WITH ONE VARIABLE
LESSON 2 – GRAPHING LINES WITH TWO VARIABLES
LESSON 3 – THE SLOPE OF A LINE
LESSON 4 – SLOPE-INTERCEPT METHOD
LESSON 5 – XY INTERCEPT METHOD
Lesson 6 – FINDING THE EQUATION OF A LINE USING THE y=mx+b METHOD
LESSON 7 – FIND THE EQUATION OF A LINE- POINT SLOPE FORMULA
LESSON 8 – FIND THE EQUATION OF A LINE- GIVEN SLOPE AND POINT
LESSON 9 – FIND THE EQUATION OF A LINE- GIVEN TWO POINTS
LESSON 10 – FINDING THE BEST FITTING LINE
LESSON 11 – LINEAR MODELS/WORD PROBLEMS
136
138
144
156
162
176
184
188
194
198
206
GED Math Lessons Workbook
i
CHAPTER 7: POSITIVE AND NEGATIVE NUMBERS
211
LESSON 1 – BASIC CONCEPTS OF EQUATIONS/INEQUALITIES/SOLUTIONS
LESSON 2 – LINEAR INEQUALITIES
LESSON 3 – COMPOUND INEQUALITIES
212
218
226
CHAPTER 8: POWERS AND EXPONENTS
234
LESSON 1 – PRODUCT AND POWER RULES OF EXPONENTS
LESSON 2 – NEGATIVE AND ZERO EXPONENTS RULES
LESSON 3 – DIVISION RULES OF EXPONENTS
LESSON 4 – SCIENTIFIC NOTATION
LESSON 5 – COMPOUND INTEREST
LESSON 6 – EXPONENTIAL GROWTH AND DECAY
235
241
245
249
255
259
CHAPTER 9: PERCENT, RATES, RATIOS, AND PROPORTIONS
263
LESSON 1 – RATIOS AND PROPORTIONS
LESSON 2 – UNDERSTANDING PERCENT
LESSON 3 – DIRECT AND INVERSE VARIATION
LESSON 4 – SIMPLIFYING RATIONAL EXPRESSIONS
264
271
277
282
CHAPTER 2: 10: SYSTEMS AND BASIC MATRIX OPERATIONS
288
LESSON 1 – SOLVING SYSTEMS BY GRAPHING
LESSON 2 – SOLVING SYSTEMS BY THE SUBSTITUTION METHOD
LESSON 3 – SOLVING SYSTEMS BY ELIMINATION/LINEAR COMBINATIONS
LESSON 4 – INTRODUCTION TO MATRICES
LESSON 5 – BASIC MATRIX OPERATIONS
289
295
301
309
315
CHAPTER 2: 11: GEOMETRY
321
LESSON 1 – CIRCLES: AREA AND CIRCUMFERENCE
LESSON 2 – AREA OF BASIC FIGURES
LESSON 3 – SURFACE AREA OF BASIC FIGURES
LESSON 4 – VOLUME OF BASIC FIGURES
LESSON 5 – THE DISTANCE AND MID-POINT FORMULA
LESSON 6 – THE PYTHAGOREAN THEOREM
322
326
332
338
344
348
GED Math Lessons Workbook
ii
Chapter1
Fractions and Decimals
This chapter reviews how to work with fractions.
Although it is assumed students possess these skills,
time is taken to ensure the student has mastered the
procedures to perform operations involving fractions.
Sections:
• Introduction to Fractions and Decimals
• Least Common Multiple/Denominator
• Multiplying and Dividing Fractions
• Adding and Subtracting Fractions
1
Fractions and Decimals
Overview of problems
Example Set: A
Write each fraction as a decimal.
Example Set: B
Write each decimal as fraction or mixed number.
Chapter 1 - Fractions and Decimals
2
Example Set: C
Write each fraction is simplest form (reduce).
Chapter 1 - Fractions and Decimals
3
Example Set: D
Answer the following.
Approximately 22 out of 30 teachers have a masters
degree. Express this relationship as a fraction in
simplest form and a decimal.
In a business .68 of the total work force gets paid
overtime. If the total number of workers is 400, express
the relationship of paid workers that earn overtime as a
fraction in simplest form.
Chapter 1 - Fractions and Decimals
4
Fractions and Decimals
Overview of problems- KEY
Example Set: A
Write each fraction as a decimal.
Example Set: B
Write each decimal as fraction or mixed number.
Chapter 1 - Fractions and Decimals
5
Example Set: C
Write each fraction is simplest form (reduce).
Chapter 1 - Fractions and Decimals
6
Example Set: D
Answer the following.
Approximately 22 out of 30 teachers have a masters
degree. Express this relationship as a fraction in
simplest form and a decimal.
In a business .68 of the total work force gets paid
overtime. If the total number of workers is 400, express
the relationship of paid workers that earn overtime as a
fraction in simplest form.
Chapter 1 - Fractions and Decimals
7
Finding the Least Common Multiple (LCM)
Overview of problems
Example Set: A
Find the least common multiple (LCM) of each pair of
numbers.
Example Set: B
Find the least common denominator (LCD) of each pair of
fractions.
Chapter 1 - Fractions and Decimals
8
Example Set: C
When adding fractions one needs to be able to determine
the LCD. Find the least common denominator (LCD) of
each fraction expression.
Chapter 1 - Fractions and Decimals
9
Example Set: D
When subtracting fractions one needs to be able to
determine the LCD. Find the least common denominator
(LCD) of each fraction expression.
Chapter 1 - Fractions and Decimals
10
Finding the Least Common Multiple (LCM)
Overview of problems- KEY
Example Set: A
Find the least common multiple (LCM) of each pair of
numbers.
Example Set: B
Find the least common denominator (LCD) of each pair of
fractions.
Chapter 1 - Fractions and Decimals
11
Example Set: C
When adding fractions one needs to be able to determine
the LCD. Find the least common denominator (LCD) of
each fraction expression.
Chapter 1 - Fractions and Decimals
12
Example Set: D
When subtracting fractions one needs to be able to
determine the LCD. Find the least common denominator
(LCD) of each fraction expression.
Chapter 1 - Fractions and Decimals
13
Multiplying and Dividing Fractions
Overview of problems
Example Set: A
Find each product. Write your answer in simplest form.
Example Set: B
Find each quotient. Write your answer in simplest form.
Chapter 1 - Fractions and Decimals
14
Example Set: C
Find the product or quotient of the following problems.
Write your answer in simplest form.
Chapter 1 - Fractions and Decimals
15
Example Set: D
Evaluate the expression using the following values for a,
b and c. Write your answer in simplest form.
Example Set: E
To find the area of a rectangle multiply the length by the
width. Determine the area of rectangle below. Write your
answer in both fraction and decimal form.
Chapter 1 - Fractions and Decimals
16
Multiplying and Dividing Fractions
Overview of problems- KEY
Example Set: A
Find each product. Write your answer in simplest form.
Example Set: B
Find each quotient. Write your answer in simplest form.
Chapter 1 - Fractions and Decimals
17
Example Set: C
Find the product or quotient of the following problems.
Write your answer in simplest form.
Chapter 1 - Fractions and Decimals
18
Example Set: D
Evaluate the expression using the following values for a,
b and c. Write your answer in simplest form.
Example Set: E
To find the area of a rectangle multiply the length by the
width. Determine the area of rectangle below. Write your
answer in both fraction and decimal form.
Chapter 1 - Fractions and Decimals
19
Adding and Subtracting Fractions
Overview of problems
Example Set: A
Find each sum or difference. Write your answer in simplest
form.
Example Set: B
Find each sum or difference. Write your answer in
simplest form.
Chapter 1 - Fractions and Decimals
20
Example Set: C
Find each sum or difference. Write your answer in
simplest form.
Example Set: D
Evaluate the expression using the following values for a,
b and c. Write your answer in simplest form.
Chapter 1 - Fractions and Decimals
21
Example Set: E
A construction worker wants to install molding around
the door. How many inches of molding will be
needed?
Chapter 1 - Fractions and Decimals
22
Adding and Subtracting Fractions
Overview of problems- KEY
Example Set: A
Find each sum or difference. Write your answer in simplest
form.
Example Set: B
Find each sum or difference. Write your answer in
simplest form.
Chapter 1 - Fractions and Decimals
23
Example Set: C
Find each sum or difference. Write your answer in
simplest form.
Example Set: D
Evaluate the expression using the following values for a,
b and c. Write your answer in simplest form.
Chapter 1 - Fractions and Decimals
24
Example Set: E
A construction worker wants to install molding around
the door. How many inches of molding will be
needed?
Chapter 1 - Fractions and Decimals
25