MAT 091 Final Exam | Basic Algebra (Algebra I) Exam
Q&A | Portage Learning
1. Which of the following best describes the set of whole numbers?
A) The set of counting numbers including zero
B) The set of all positive and negative numbers
C) The set of all numbers that can be written as fractions
D) The set of numbers that cannot be expressed as decimals
Correct Answer: The set of counting numbers including zero
Rationale: Whole numbers are the set of non-negative integers: 0, 1, 2, 3, and so on.
They do not include fractions, decimals, or negative numbers. Integers include negative
numbers, while rational numbers include fractions.
2. What is the primary function of the order of operations in mathematics?
A) To ensure calculations are performed in a consistent sequence
B) To determine the sign of the final answer
C) To simplify fractions to lowest terms
D) To convert decimals to percentages
Correct Answer: To ensure calculations are performed in a consistent sequence
Rationale: The order of operations (PEMDAS) provides a standardized sequence for
evaluating expressions: parentheses, exponents, multiplication and division (left to
right), and addition and subtraction (left to right). This ensures that everyone obtains the
same result for a given expression.
3. According to the rules of signed numbers, what is the result of subtracting a
negative number?
A) The result is always negative
B) The result is always positive
C) The result is equivalent to adding the positive of that number
D) The result is zero
Correct Answer: The result is equivalent to adding the positive of that number
,Rationale: Subtracting a negative number is the same as adding its positive counterpart.
For example, 5 - (-3) = 5 + 3 = 8. This rule is fundamental when working with integers and
algebraic expressions.
4. A student is simplifying the expression 3 + 4 x 2. What is the correct result?
A) 14
B) 11
C) 10
D) 24
Correct Answer: 11
Rationale: According to the order of operations, multiplication is performed before
addition. First, 4 x 2 = 8, then 3 + 8 = 11. If addition were performed first, the incorrect
result would be 14.
5. What is the value of the digit 7 in the number 5,672,103?
A) 7,000
B) 70,000
C) 700
D) 70
Correct Answer: 70,000
Rationale: In the number 5,672,103, the digit 7 is in the ten-thousands place, so its value
is 7 x 10,000 = 70,000. Place value depends on the position of the digit within the
number.
6. Which principle explains why 0.75 is equivalent to 3/4?
A) The principle of equivalent fractions
B) The principle of cross multiplication
C) The principle of decimal expansion
D) The principle of reciprocals
Correct Answer: The principle of equivalent fractions
Rationale: 0.75 and 3/4 represent the same rational number. Dividing 3 by 4 yields 0.75.
Equivalent fractions represent the same portion of a whole, just written in different
forms. This is a foundational concept in converting between fractions and decimals.
7. In the context of fractions, what does the denominator represent?
, A) The number of equal parts in the whole
B) The number of parts being considered
C) The decimal equivalent of the fraction
D) The percentage of the whole
Correct Answer: The number of equal parts in the whole
Rationale: In a fraction, the denominator (bottom number) indicates the total number of
equal parts into which the whole is divided. The numerator (top number) indicates how
many of those parts are being considered. For example, in 3/5, the whole is divided into
5 equal parts.
8. A researcher is converting the fraction 7/8 to a decimal. What is the correct
decimal equivalent?
A) 0.875
B) 0.78
C) 0.87
D) 0.785
Correct Answer: 0.875
Rationale: To convert 7/8 to a decimal, divide 7 by 8: 7 ÷ 8 = 0.875. This is a terminating
decimal. Converting fractions to decimals is essential for comparing and performing
operations with different numerical forms.
9. What is the sum of 3/5 and 1/3?
A) 4/8
B) 14/15
C) 4/15
D) 2/3
Correct Answer: 14/15
Rationale: To add fractions, find a common denominator. The least common
denominator for 5 and 3 is 15. Convert: 3/5 = 9/15 and 1/3 = 5/15. Then 9/15 + 5/15 =
14/15. The fraction cannot be simplified further.
10. What is the product of 2/3 and 3/4?
A) 1/2
B) 6/7
Q&A | Portage Learning
1. Which of the following best describes the set of whole numbers?
A) The set of counting numbers including zero
B) The set of all positive and negative numbers
C) The set of all numbers that can be written as fractions
D) The set of numbers that cannot be expressed as decimals
Correct Answer: The set of counting numbers including zero
Rationale: Whole numbers are the set of non-negative integers: 0, 1, 2, 3, and so on.
They do not include fractions, decimals, or negative numbers. Integers include negative
numbers, while rational numbers include fractions.
2. What is the primary function of the order of operations in mathematics?
A) To ensure calculations are performed in a consistent sequence
B) To determine the sign of the final answer
C) To simplify fractions to lowest terms
D) To convert decimals to percentages
Correct Answer: To ensure calculations are performed in a consistent sequence
Rationale: The order of operations (PEMDAS) provides a standardized sequence for
evaluating expressions: parentheses, exponents, multiplication and division (left to
right), and addition and subtraction (left to right). This ensures that everyone obtains the
same result for a given expression.
3. According to the rules of signed numbers, what is the result of subtracting a
negative number?
A) The result is always negative
B) The result is always positive
C) The result is equivalent to adding the positive of that number
D) The result is zero
Correct Answer: The result is equivalent to adding the positive of that number
,Rationale: Subtracting a negative number is the same as adding its positive counterpart.
For example, 5 - (-3) = 5 + 3 = 8. This rule is fundamental when working with integers and
algebraic expressions.
4. A student is simplifying the expression 3 + 4 x 2. What is the correct result?
A) 14
B) 11
C) 10
D) 24
Correct Answer: 11
Rationale: According to the order of operations, multiplication is performed before
addition. First, 4 x 2 = 8, then 3 + 8 = 11. If addition were performed first, the incorrect
result would be 14.
5. What is the value of the digit 7 in the number 5,672,103?
A) 7,000
B) 70,000
C) 700
D) 70
Correct Answer: 70,000
Rationale: In the number 5,672,103, the digit 7 is in the ten-thousands place, so its value
is 7 x 10,000 = 70,000. Place value depends on the position of the digit within the
number.
6. Which principle explains why 0.75 is equivalent to 3/4?
A) The principle of equivalent fractions
B) The principle of cross multiplication
C) The principle of decimal expansion
D) The principle of reciprocals
Correct Answer: The principle of equivalent fractions
Rationale: 0.75 and 3/4 represent the same rational number. Dividing 3 by 4 yields 0.75.
Equivalent fractions represent the same portion of a whole, just written in different
forms. This is a foundational concept in converting between fractions and decimals.
7. In the context of fractions, what does the denominator represent?
, A) The number of equal parts in the whole
B) The number of parts being considered
C) The decimal equivalent of the fraction
D) The percentage of the whole
Correct Answer: The number of equal parts in the whole
Rationale: In a fraction, the denominator (bottom number) indicates the total number of
equal parts into which the whole is divided. The numerator (top number) indicates how
many of those parts are being considered. For example, in 3/5, the whole is divided into
5 equal parts.
8. A researcher is converting the fraction 7/8 to a decimal. What is the correct
decimal equivalent?
A) 0.875
B) 0.78
C) 0.87
D) 0.785
Correct Answer: 0.875
Rationale: To convert 7/8 to a decimal, divide 7 by 8: 7 ÷ 8 = 0.875. This is a terminating
decimal. Converting fractions to decimals is essential for comparing and performing
operations with different numerical forms.
9. What is the sum of 3/5 and 1/3?
A) 4/8
B) 14/15
C) 4/15
D) 2/3
Correct Answer: 14/15
Rationale: To add fractions, find a common denominator. The least common
denominator for 5 and 3 is 15. Convert: 3/5 = 9/15 and 1/3 = 5/15. Then 9/15 + 5/15 =
14/15. The fraction cannot be simplified further.
10. What is the product of 2/3 and 3/4?
A) 1/2
B) 6/7
