PORTAGE LEARNING
MATH 110 Module 1 Exam
Official Practice Exam - 2026/2027 Edition
Exam Questions and Answers - Portage Learning 2026/2027
Questions: 75 | Minutes: 90 | Passing Score: 80% | Sections: 5
Table of Contents
Section 1: Real Numbers & Number Systems (15 Questions, starting Q1)
Section 2: Exponents & Scientific Notation (15 Questions, starting Q16)
Section 3: Algebraic Expressions & Polynomials (15 Questions, starting Q31)
Section 4: Linear Equations & Inequalities (15 Questions, starting Q46)
Section 5: Graphing & Linear Functions (15 Questions, starting Q61)
Instructions
This practice exam contains 75 multiple-choice questions divided into 5 sections. You have 90 minutes to
complete the entire exam. Each question has four answer choices (A, B, C, D). Select the best answer for each
question. A passing score of 80% (60 out of 75 correct) is required. The correct answers and detailed rationales
are provided after each question for study purposes. An answer key grid is included at the end of the exam for
quick reference.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 1 of 40
, Section 1: Real Numbers & Number Systems
Q1 Question 1 of 75
A student is classifying numbers for a homework assignment. She encounters the number -7 and must
determine which sets it belongs to. She reasons that since -7 is negative, it cannot be a natural number
or a whole number. She wonders whether -7 belongs to the set of integers and the set of rational
numbers. After checking her textbook, she needs to identify the most complete classification. To which
of the following sets does -7 belong?
A. Integers only
B. Rational numbers only
C. Integers and rational numbers
D. Whole numbers and integers
Correct Answer: C
Rationale:
The number -7 is an integer (all whole numbers and their negatives). Since -7 can be written as -7/1, it is also a rational
number. It is not a whole number (whole numbers are 0, 1, 2, ...) nor a natural number (1, 2, 3, ...). Therefore, -7 belongs
to both the integers and the rational numbers.
Q2 Question 2 of 75
During a study session, a student reviews the properties of real numbers. She evaluates the expression
3 + (4 + 5) and then evaluates (3 + 4) + 5 to check whether she gets the same result. Both expressions
equal 12, which illustrates a specific property of addition. She wants to name the property correctly on
her upcoming quiz. This example demonstrates which property of real numbers?
A. Commutative property of addition
B. Distributive property
C. Associative property of addition
D. Identity property of addition
Correct Answer: C
Rationale:
The associative property of addition states that (a + b) + c = a + (b + c). Here, (3 + 4) + 5 = 3 + (4 + 5) = 12. The
commutative property involves reordering (a + b = b + a), the distributive property connects multiplication and addition,
and the identity property involves adding zero.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 2 of 40
, Q3 Question 3 of 75
A contractor is calculating the total cost of materials for a building project. She needs to evaluate the
expression 4(3 + 7) using the correct order of operations. She remembers that she must perform
operations inside parentheses first, but she wants to confirm the result. After simplifying, she needs to
report the correct total. What is the value of 4(3 + 7)?
A. 19
B. 40
C. 31
D. 70
Correct Answer: B
Rationale:
Using the order of operations (PEMDAS), first evaluate inside the parentheses: 3 + 7 = 10. Then multiply: 4 * 10 = 40. If
you distributed first, you would get 4(3) + 4(7) = 12 + 28 = 40, which gives the same result by the distributive property.
Q4 Question 4 of 75
A meteorologist reports that the temperature dropped to -12 degrees overnight. The next afternoon, it
rose to 5 degrees. A student wants to find the absolute value of the overnight low temperature to
describe how far it was from zero. He also needs to determine the difference between the high and low
temperatures. What is |(-12)|, and what is the difference between the high and the low?
A. 12 and 7 degrees
B. 12 and 17 degrees
C. -12 and 17 degrees
D. 12 and 5 degrees
Correct Answer: B
Rationale:
The absolute value of -12 is |(-12)| = 12, since absolute value gives the distance from zero. The difference between the
high (5) and the low (-12) is 5 - (-12) = 5 + 12 = 17 degrees.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 3 of 40
, Q5 Question 5 of 75
A baker needs to combine 2/3 cup of flour with 1/4 cup of sugar for a recipe. She wants to add these
fractions correctly to know the total dry ingredient volume. She finds a common denominator before
adding, and then simplifies her result. What is 2/3 + 1/4?
A. 3/7
B. 11/12
C. 3/12
D. 5/12
Correct Answer: B
Rationale:
Find a common denominator: the LCD of 3 and 4 is 12. Convert: 2/3 = 8/12 and 1/4 = 3/12. Add: 8/12 + 3/12 = 11/12.
This fraction is already in simplest form.
Q6 Question 6 of 75
A carpenter is cutting a board that is 5/8 of a meter long. She needs to remove 1/3 of a meter from it for
a shelf. She subtracts the fractions by finding a common denominator first, then simplifies the result.
What is 5/8 - 1/3?
A. 4/5
B. 7/24
C. 4/24
D. 7/12
Correct Answer: B
Rationale:
Find the LCD of 8 and 3, which is 24. Convert: 5/8 = 15/24 and 1/3 = 8/24. Subtract: 15/24 - 8/24 = 7/24. This fraction
cannot be simplified further.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 4 of 40
MATH 110 Module 1 Exam
Official Practice Exam - 2026/2027 Edition
Exam Questions and Answers - Portage Learning 2026/2027
Questions: 75 | Minutes: 90 | Passing Score: 80% | Sections: 5
Table of Contents
Section 1: Real Numbers & Number Systems (15 Questions, starting Q1)
Section 2: Exponents & Scientific Notation (15 Questions, starting Q16)
Section 3: Algebraic Expressions & Polynomials (15 Questions, starting Q31)
Section 4: Linear Equations & Inequalities (15 Questions, starting Q46)
Section 5: Graphing & Linear Functions (15 Questions, starting Q61)
Instructions
This practice exam contains 75 multiple-choice questions divided into 5 sections. You have 90 minutes to
complete the entire exam. Each question has four answer choices (A, B, C, D). Select the best answer for each
question. A passing score of 80% (60 out of 75 correct) is required. The correct answers and detailed rationales
are provided after each question for study purposes. An answer key grid is included at the end of the exam for
quick reference.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 1 of 40
, Section 1: Real Numbers & Number Systems
Q1 Question 1 of 75
A student is classifying numbers for a homework assignment. She encounters the number -7 and must
determine which sets it belongs to. She reasons that since -7 is negative, it cannot be a natural number
or a whole number. She wonders whether -7 belongs to the set of integers and the set of rational
numbers. After checking her textbook, she needs to identify the most complete classification. To which
of the following sets does -7 belong?
A. Integers only
B. Rational numbers only
C. Integers and rational numbers
D. Whole numbers and integers
Correct Answer: C
Rationale:
The number -7 is an integer (all whole numbers and their negatives). Since -7 can be written as -7/1, it is also a rational
number. It is not a whole number (whole numbers are 0, 1, 2, ...) nor a natural number (1, 2, 3, ...). Therefore, -7 belongs
to both the integers and the rational numbers.
Q2 Question 2 of 75
During a study session, a student reviews the properties of real numbers. She evaluates the expression
3 + (4 + 5) and then evaluates (3 + 4) + 5 to check whether she gets the same result. Both expressions
equal 12, which illustrates a specific property of addition. She wants to name the property correctly on
her upcoming quiz. This example demonstrates which property of real numbers?
A. Commutative property of addition
B. Distributive property
C. Associative property of addition
D. Identity property of addition
Correct Answer: C
Rationale:
The associative property of addition states that (a + b) + c = a + (b + c). Here, (3 + 4) + 5 = 3 + (4 + 5) = 12. The
commutative property involves reordering (a + b = b + a), the distributive property connects multiplication and addition,
and the identity property involves adding zero.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 2 of 40
, Q3 Question 3 of 75
A contractor is calculating the total cost of materials for a building project. She needs to evaluate the
expression 4(3 + 7) using the correct order of operations. She remembers that she must perform
operations inside parentheses first, but she wants to confirm the result. After simplifying, she needs to
report the correct total. What is the value of 4(3 + 7)?
A. 19
B. 40
C. 31
D. 70
Correct Answer: B
Rationale:
Using the order of operations (PEMDAS), first evaluate inside the parentheses: 3 + 7 = 10. Then multiply: 4 * 10 = 40. If
you distributed first, you would get 4(3) + 4(7) = 12 + 28 = 40, which gives the same result by the distributive property.
Q4 Question 4 of 75
A meteorologist reports that the temperature dropped to -12 degrees overnight. The next afternoon, it
rose to 5 degrees. A student wants to find the absolute value of the overnight low temperature to
describe how far it was from zero. He also needs to determine the difference between the high and low
temperatures. What is |(-12)|, and what is the difference between the high and the low?
A. 12 and 7 degrees
B. 12 and 17 degrees
C. -12 and 17 degrees
D. 12 and 5 degrees
Correct Answer: B
Rationale:
The absolute value of -12 is |(-12)| = 12, since absolute value gives the distance from zero. The difference between the
high (5) and the low (-12) is 5 - (-12) = 5 + 12 = 17 degrees.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 3 of 40
, Q5 Question 5 of 75
A baker needs to combine 2/3 cup of flour with 1/4 cup of sugar for a recipe. She wants to add these
fractions correctly to know the total dry ingredient volume. She finds a common denominator before
adding, and then simplifies her result. What is 2/3 + 1/4?
A. 3/7
B. 11/12
C. 3/12
D. 5/12
Correct Answer: B
Rationale:
Find a common denominator: the LCD of 3 and 4 is 12. Convert: 2/3 = 8/12 and 1/4 = 3/12. Add: 8/12 + 3/12 = 11/12.
This fraction is already in simplest form.
Q6 Question 6 of 75
A carpenter is cutting a board that is 5/8 of a meter long. She needs to remove 1/3 of a meter from it for
a shelf. She subtracts the fractions by finding a common denominator first, then simplifies the result.
What is 5/8 - 1/3?
A. 4/5
B. 7/24
C. 4/24
D. 7/12
Correct Answer: B
Rationale:
Find the LCD of 8 and 3, which is 24. Convert: 5/8 = 15/24 and 1/3 = 8/24. Subtract: 15/24 - 8/24 = 7/24. This fraction
cannot be simplified further.
MATH 110 Module 1 -- 2026/2027 | Passing Score: 80% | Page 4 of 40
