UNIV 104 | Math Assessment Part 1 & Part 2
Liberty University — Developmental Mathematics
Complete Solutions with Step-by-Step Rationales
Total Questions: 110 | Parts 1 & 2 | Multiple Choice (A–D)
Part 1 — Math Assessment
Section 1: Whole Numbers, Integers, and Order of Operations (Q1–Q8)
Q1: Evaluate the expression using the order of operations: 8 + 4 × 3 − 6 ÷ 2
A. 15
B. 17 [CORRECT]
C. 33
D. 14
Correct Answer: B
Rationale: Following PEMDAS, perform multiplication and division first: 4 × 3 = 12 and 6 ÷ 2 = 3. Substitute back: 8
+ 12 − 3. Then add and subtract left to right: 8 + 12 = 20, then 20 − 3 = 17. Choice A (15) results from evaluating
strictly left to right (8+4=12, ×3=36, −6=30, ÷2=15), ignoring precedence. Choice C (33) comes from adding 8+4
before multiplying by 3: (8+4)×3 − 6÷2 = 36 − 3. Choice D (14) skips the division step entirely (8+12−6).
Q2: Evaluate: −5 + (−3) − (−7)
A. −15
B. −1 [CORRECT]
C. 5
D. −9
Correct Answer: B
Rationale: Add the first two integers: −5 + (−3) = −8. Subtracting a negative is the same as adding: −8 − (−7) = −8 +
7 = −1. Choice A (−15) mistakenly treats −(−7) as −7, computing −8 − 7. Choice C (5) reverses every sign
inappropriately (−5 + 3 + 7). Choice D (−9) flips the wrong sign, computing −5 − (−3) − 7 = −5 + 3 − 7.
Q3: Evaluate the product: (−4)(−3)(−2)
A. 24
B. −24 [CORRECT]
C. 9
D. −9
Correct Answer: B
Rationale: Multiply the first two factors: (−4)(−3) = 12 (negative × negative = positive). Then 12 × (−2) = −24
(positive × negative = negative). With an odd count of negative factors (three), the product must be negative. Choice A
, (24) ignores the sign rule and treats all factors as positive. Choice C (9) adds the absolute values (4+3+2). Choice D
(−9) adds the absolute values and applies a negative sign.
Q4: Evaluate: |−9| − |5| + |−2|
A. −12
B. 6 [CORRECT]
C. 16
D. 2
Correct Answer: B
Rationale: Take each absolute value: |−9| = 9, |5| = 5, |−2| = 2. Substitute: 9 − 5 + 2. Compute left to right: 9 − 5 = 4,
then 4 + 2 = 6. Choice A (−12) ignores the absolute-value bars and uses −9 − 5 + (−2). Choice C (16) treats every
operation as addition of the absolute values (9+5+2). Choice D (2) applies the negative sign incorrectly, computing 9 −
5 − 2.
Q5: Simplify by distributing and combining like terms: 3(2x − 5) + 4(x + 1)
A. 10x − 4
B. 10x − 19
C. 10x − 11 [CORRECT]
D. 14x − 11
Correct Answer: C
Rationale: Distribute 3 into (2x − 5): 3·2x − 3·5 = 6x − 15. Distribute 4 into (x + 1): 4x + 4. Combine: (6x − 15) + (4x
+ 4) = (6x + 4x) + (−15 + 4) = 10x − 11. Choice A (10x − 4) only distributes the coefficients to the variable terms, not
the constants (6x − 5 + 4x + 1). Choice B (10x − 19) makes a sign error, treating the +4 as −4 (−15 − 4 = −19).
Choice D (14x − 11) multiplies the coefficient sums incorrectly: (3+4)·2x = 14x.
Q6: What is the value of −24?
A. 16
B. −16 [CORRECT]
C. 8
D. −8
Correct Answer: B
Rationale: Without parentheses, the exponent applies only to the base 2 (not to −2): 24 = 16, then the leading negative
sign is applied, giving −16. By contrast, (−2)4 would equal +16 because the negative base is raised to an even power.
Choice A (16) incorrectly treats −24 as (−2)4. Choice C (8) multiplies −2 by 4 instead of evaluating the exponent.
Choice D (−8) multiplies 2 by 4 and then applies the negative sign.
Q7: A store sells pens for $3 each. If a customer buys 5 pens and pays with a $20 bill, how much change
should they receive?
A. $12
B. $5 [CORRECT]
C. $7
D. $15
, Correct Answer: B
Rationale: Compute the total cost: 5 × $3 = $15. Subtract from the amount paid: $20 − $15 = $5 in change. Choice A
($12) subtracts both 5 and 3 from 20 (20 − 5 − 3). Choice C ($7) computes 20 ÷ 5 + 3. Choice D ($15) returns the cost
of the pens rather than the change.
Q8: Which property is illustrated by: 7 + (3 + 5) = (7 + 3) + 5?
A. Commutative Property of Addition
B. Associative Property of Addition [CORRECT]
C. Distributive Property
D. Identity Property of Addition
Correct Answer: B
Rationale: The Associative Property of Addition states that the grouping of addends may change without affecting the
sum: (a + b) + c = a + (b + c). The numbers themselves are not reordered, only regrouped. Choice A (Commutative)
involves reordering, e.g., a + b = b + a, which is not shown here. Choice C (Distributive) involves multiplication over
addition, e.g., a(b + c) = ab + ac. Choice D (Identity) involves adding zero, e.g., a + 0 = a.
Section 2: Fractions, Decimals, and Percents (Q9–Q18)
Q9: Add. Write the answer in lowest terms: 5/6 + 3/8
A. 4/7
B. 1 5/24 [CORRECT]
C. 29/48
D. 1/6
Correct Answer: B
Rationale: Find the LCD of 6 and 8, which is 24. Convert: 5/6 = 20/24 and 3/8 = 9/24. Add: 20/24 + 9/24 = 29/24. As
a mixed number: 29 ÷ 24 = 1 remainder 5, so 1 5/24. Choice A (4/7) adds numerators and denominators directly:
(5+3)/(6+8) = 8/14 = 4/7. Choice C (29/48) adds the numerators but multiplies the denominators (6·8 = 48). Choice D
(1/6) writes (5+3)/(6·8) = 8/48 = 1/6, mixing the two prior errors.
Q10: Multiply. Write the answer in lowest terms: (3/4) × (2/9)
A. 5/13
B. 1/6 [CORRECT]
C. 27/8
D. 6/9
Correct Answer: B
Rationale: Multiply numerators: 3 × 2 = 6. Multiply denominators: 4 × 9 = 36. So the product is 6/36. Reduce by
dividing numerator and denominator by the GCF 6: 6/36 = 1/6. Choice A (5/13) adds numerators and denominators
(3+2)/(4+9). Choice C (27/8) inverts the second fraction (multiplies by 9/2 instead of 2/9). Choice D (6/9) multiplies
numerators correctly but fails to multiply the denominators.
Q11: Divide. Write the answer in lowest terms: (5/8) ÷ (2/3)
A. 5/12
Liberty University — Developmental Mathematics
Complete Solutions with Step-by-Step Rationales
Total Questions: 110 | Parts 1 & 2 | Multiple Choice (A–D)
Part 1 — Math Assessment
Section 1: Whole Numbers, Integers, and Order of Operations (Q1–Q8)
Q1: Evaluate the expression using the order of operations: 8 + 4 × 3 − 6 ÷ 2
A. 15
B. 17 [CORRECT]
C. 33
D. 14
Correct Answer: B
Rationale: Following PEMDAS, perform multiplication and division first: 4 × 3 = 12 and 6 ÷ 2 = 3. Substitute back: 8
+ 12 − 3. Then add and subtract left to right: 8 + 12 = 20, then 20 − 3 = 17. Choice A (15) results from evaluating
strictly left to right (8+4=12, ×3=36, −6=30, ÷2=15), ignoring precedence. Choice C (33) comes from adding 8+4
before multiplying by 3: (8+4)×3 − 6÷2 = 36 − 3. Choice D (14) skips the division step entirely (8+12−6).
Q2: Evaluate: −5 + (−3) − (−7)
A. −15
B. −1 [CORRECT]
C. 5
D. −9
Correct Answer: B
Rationale: Add the first two integers: −5 + (−3) = −8. Subtracting a negative is the same as adding: −8 − (−7) = −8 +
7 = −1. Choice A (−15) mistakenly treats −(−7) as −7, computing −8 − 7. Choice C (5) reverses every sign
inappropriately (−5 + 3 + 7). Choice D (−9) flips the wrong sign, computing −5 − (−3) − 7 = −5 + 3 − 7.
Q3: Evaluate the product: (−4)(−3)(−2)
A. 24
B. −24 [CORRECT]
C. 9
D. −9
Correct Answer: B
Rationale: Multiply the first two factors: (−4)(−3) = 12 (negative × negative = positive). Then 12 × (−2) = −24
(positive × negative = negative). With an odd count of negative factors (three), the product must be negative. Choice A
, (24) ignores the sign rule and treats all factors as positive. Choice C (9) adds the absolute values (4+3+2). Choice D
(−9) adds the absolute values and applies a negative sign.
Q4: Evaluate: |−9| − |5| + |−2|
A. −12
B. 6 [CORRECT]
C. 16
D. 2
Correct Answer: B
Rationale: Take each absolute value: |−9| = 9, |5| = 5, |−2| = 2. Substitute: 9 − 5 + 2. Compute left to right: 9 − 5 = 4,
then 4 + 2 = 6. Choice A (−12) ignores the absolute-value bars and uses −9 − 5 + (−2). Choice C (16) treats every
operation as addition of the absolute values (9+5+2). Choice D (2) applies the negative sign incorrectly, computing 9 −
5 − 2.
Q5: Simplify by distributing and combining like terms: 3(2x − 5) + 4(x + 1)
A. 10x − 4
B. 10x − 19
C. 10x − 11 [CORRECT]
D. 14x − 11
Correct Answer: C
Rationale: Distribute 3 into (2x − 5): 3·2x − 3·5 = 6x − 15. Distribute 4 into (x + 1): 4x + 4. Combine: (6x − 15) + (4x
+ 4) = (6x + 4x) + (−15 + 4) = 10x − 11. Choice A (10x − 4) only distributes the coefficients to the variable terms, not
the constants (6x − 5 + 4x + 1). Choice B (10x − 19) makes a sign error, treating the +4 as −4 (−15 − 4 = −19).
Choice D (14x − 11) multiplies the coefficient sums incorrectly: (3+4)·2x = 14x.
Q6: What is the value of −24?
A. 16
B. −16 [CORRECT]
C. 8
D. −8
Correct Answer: B
Rationale: Without parentheses, the exponent applies only to the base 2 (not to −2): 24 = 16, then the leading negative
sign is applied, giving −16. By contrast, (−2)4 would equal +16 because the negative base is raised to an even power.
Choice A (16) incorrectly treats −24 as (−2)4. Choice C (8) multiplies −2 by 4 instead of evaluating the exponent.
Choice D (−8) multiplies 2 by 4 and then applies the negative sign.
Q7: A store sells pens for $3 each. If a customer buys 5 pens and pays with a $20 bill, how much change
should they receive?
A. $12
B. $5 [CORRECT]
C. $7
D. $15
, Correct Answer: B
Rationale: Compute the total cost: 5 × $3 = $15. Subtract from the amount paid: $20 − $15 = $5 in change. Choice A
($12) subtracts both 5 and 3 from 20 (20 − 5 − 3). Choice C ($7) computes 20 ÷ 5 + 3. Choice D ($15) returns the cost
of the pens rather than the change.
Q8: Which property is illustrated by: 7 + (3 + 5) = (7 + 3) + 5?
A. Commutative Property of Addition
B. Associative Property of Addition [CORRECT]
C. Distributive Property
D. Identity Property of Addition
Correct Answer: B
Rationale: The Associative Property of Addition states that the grouping of addends may change without affecting the
sum: (a + b) + c = a + (b + c). The numbers themselves are not reordered, only regrouped. Choice A (Commutative)
involves reordering, e.g., a + b = b + a, which is not shown here. Choice C (Distributive) involves multiplication over
addition, e.g., a(b + c) = ab + ac. Choice D (Identity) involves adding zero, e.g., a + 0 = a.
Section 2: Fractions, Decimals, and Percents (Q9–Q18)
Q9: Add. Write the answer in lowest terms: 5/6 + 3/8
A. 4/7
B. 1 5/24 [CORRECT]
C. 29/48
D. 1/6
Correct Answer: B
Rationale: Find the LCD of 6 and 8, which is 24. Convert: 5/6 = 20/24 and 3/8 = 9/24. Add: 20/24 + 9/24 = 29/24. As
a mixed number: 29 ÷ 24 = 1 remainder 5, so 1 5/24. Choice A (4/7) adds numerators and denominators directly:
(5+3)/(6+8) = 8/14 = 4/7. Choice C (29/48) adds the numerators but multiplies the denominators (6·8 = 48). Choice D
(1/6) writes (5+3)/(6·8) = 8/48 = 1/6, mixing the two prior errors.
Q10: Multiply. Write the answer in lowest terms: (3/4) × (2/9)
A. 5/13
B. 1/6 [CORRECT]
C. 27/8
D. 6/9
Correct Answer: B
Rationale: Multiply numerators: 3 × 2 = 6. Multiply denominators: 4 × 9 = 36. So the product is 6/36. Reduce by
dividing numerator and denominator by the GCF 6: 6/36 = 1/6. Choice A (5/13) adds numerators and denominators
(3+2)/(4+9). Choice C (27/8) inverts the second fraction (multiplies by 9/2 instead of 2/9). Choice D (6/9) multiplies
numerators correctly but fails to multiply the denominators.
Q11: Divide. Write the answer in lowest terms: (5/8) ÷ (2/3)
A. 5/12
