MATH 110 MODULE 1 EXAM QUESTIONS AND
ANSWERS
PORTAGE LEARNING · 2026/2027 ACADEMIC YEAR
Total Questions: 50 | Suggested Time: 90 minutes | Cognitive Distribution: 30% Recall · 50% Application
· 20% Analysis
Instructions: This comprehensive Module 1 examination assesses your mastery of introductory college
mathematics as outlined in the Portage Learning MATH 110 curriculum. The exam contains 50 multiple-choice
questions distributed across five content areas: basic arithmetic, fractions/decimals/percentages, ratios and
proportions, basic algebra, and applied word problems. Each question has exactly one correct answer (marked
with *[CORRECT]*). Select the single best answer for each question. Show your work on scratch paper when
solving multi-step problems. Calculators are permitted for routine arithmetic, but you must demonstrate
conceptual understanding of order of operations (PEMDAS), properties of real numbers, equation-solving
techniques, and proportional reasoning.
Section 1: Basic Arithmetic & Number Operations 10 Questions
Q1: Evaluate: 847 + 236 + 195
A. 1,288
B. 1,278 *[CORRECT]*
C. 1,168
D. 1,277
Correct Answer: B
Rationale: Adding column by column from right to left: 847 + 236 = 1,083, then 1,083 + 195 = 1,278. Choice A adds
an extra carry in the hundreds column; C omits a carry in the tens; D is off by one in the units, a common copying slip.
Q2: Subtract: 5,004 − 1,876
A. 3,128 *[CORRECT]*
B. 3,228
C. 4,128
D. 3,118
Correct Answer: A
Rationale: Borrowing across the zeros gives 5,004 − 1,876 = 3,128 (verify: 3,128 + 1,876 = 5,004). Choice B fails to
borrow from the thousands column; C adds rather than subtracts; D mis-subtracts in the hundreds column.
Q3: Multiply: 47 × 36
A. 1,482
B. 1,792
C. 1,692 *[CORRECT]*
D. 1,582
Correct Answer: C
Rationale: Using the distributive property, 47 × 36 = 47 × 30 + 47 × 6 = 1,410 + 282 = 1,692. Distractor A omits the
cross-term partial product; B carries incorrectly in the tens column; D drops one partial product.
, Q4: Divide: 4,356 ÷ 12
A. 353
B. 363 *[CORRECT]*
C. 373
D. 366
Correct Answer: B
Rationale: Long division yields 4,356 ÷ 12 = 363 because 12 × 363 = 4,356. The distractors reflect common
subtraction errors inside the long-division algorithm: A drops a digit in the quotient; C over-carries; D miscalculates
the partial quotient.
Q5: Evaluate using the order of operations (PEMDAS): 8 + 4 × 32 − 6
A. 38 *[CORRECT]*
B. 174
C. 102
D. 30
Correct Answer: A
Rationale: Following PEMDAS: first evaluate the exponent (32 = 9), then multiply (4 × 9 = 36), then add and subtract
left to right (8 + 36 − 6 = 38). Choice B incorrectly groups (8+4)×32−6; C groups 4×(32−6) incorrectly; D works
strictly left-to-right ignoring PEMDAS.
Q6: Compute: (−15) + 8 − (−3)
A. −4 *[CORRECT]*
B. −20
C. −10
D. 4
Correct Answer: A
Rationale: (−15) + 8 = −7, and subtracting (−3) is the same as adding +3, giving −7 + 3 = −4. Choice B mishandles
the sign of −3 by treating subtraction as addition of a negative; C forgets to convert the subtraction of a negative into
addition; D reverses the sign of the final answer.
Q7: Which property is illustrated by 7 × (3 + 8) = (7 × 3) + (7 × 8)?
A. Commutative Property
B. Associative Property
C. Distributive Property *[CORRECT]*
D. Identity Property
Correct Answer: C
Rationale: The distributive property states that a(b + c) = ab + ac, which exactly matches 7(3 + 8) = 7·3 + 7·8. The
commutative property reorders operands (a·b = b·a), the associative property regroups (a·(b·c) = (a·b)·c), and the
identity property involves 0 or 1 leaving a number unchanged.
Q8: Evaluate: 24 + √81
A. 25 *[CORRECT]*
B. 17
C. 89
D. 33
Correct Answer: A
Rationale: 24 = 2·2·2·2 = 16 and √81 = 9, so 24 + √81 = 16 + 9 = 25. Choice B treats 24 as 2 × 4 = 8; C treats √81 as
81 (omits the square root); D combines both errors by computing 2 × 4 + 9 + 16 in an ad-hoc way.
ANSWERS
PORTAGE LEARNING · 2026/2027 ACADEMIC YEAR
Total Questions: 50 | Suggested Time: 90 minutes | Cognitive Distribution: 30% Recall · 50% Application
· 20% Analysis
Instructions: This comprehensive Module 1 examination assesses your mastery of introductory college
mathematics as outlined in the Portage Learning MATH 110 curriculum. The exam contains 50 multiple-choice
questions distributed across five content areas: basic arithmetic, fractions/decimals/percentages, ratios and
proportions, basic algebra, and applied word problems. Each question has exactly one correct answer (marked
with *[CORRECT]*). Select the single best answer for each question. Show your work on scratch paper when
solving multi-step problems. Calculators are permitted for routine arithmetic, but you must demonstrate
conceptual understanding of order of operations (PEMDAS), properties of real numbers, equation-solving
techniques, and proportional reasoning.
Section 1: Basic Arithmetic & Number Operations 10 Questions
Q1: Evaluate: 847 + 236 + 195
A. 1,288
B. 1,278 *[CORRECT]*
C. 1,168
D. 1,277
Correct Answer: B
Rationale: Adding column by column from right to left: 847 + 236 = 1,083, then 1,083 + 195 = 1,278. Choice A adds
an extra carry in the hundreds column; C omits a carry in the tens; D is off by one in the units, a common copying slip.
Q2: Subtract: 5,004 − 1,876
A. 3,128 *[CORRECT]*
B. 3,228
C. 4,128
D. 3,118
Correct Answer: A
Rationale: Borrowing across the zeros gives 5,004 − 1,876 = 3,128 (verify: 3,128 + 1,876 = 5,004). Choice B fails to
borrow from the thousands column; C adds rather than subtracts; D mis-subtracts in the hundreds column.
Q3: Multiply: 47 × 36
A. 1,482
B. 1,792
C. 1,692 *[CORRECT]*
D. 1,582
Correct Answer: C
Rationale: Using the distributive property, 47 × 36 = 47 × 30 + 47 × 6 = 1,410 + 282 = 1,692. Distractor A omits the
cross-term partial product; B carries incorrectly in the tens column; D drops one partial product.
, Q4: Divide: 4,356 ÷ 12
A. 353
B. 363 *[CORRECT]*
C. 373
D. 366
Correct Answer: B
Rationale: Long division yields 4,356 ÷ 12 = 363 because 12 × 363 = 4,356. The distractors reflect common
subtraction errors inside the long-division algorithm: A drops a digit in the quotient; C over-carries; D miscalculates
the partial quotient.
Q5: Evaluate using the order of operations (PEMDAS): 8 + 4 × 32 − 6
A. 38 *[CORRECT]*
B. 174
C. 102
D. 30
Correct Answer: A
Rationale: Following PEMDAS: first evaluate the exponent (32 = 9), then multiply (4 × 9 = 36), then add and subtract
left to right (8 + 36 − 6 = 38). Choice B incorrectly groups (8+4)×32−6; C groups 4×(32−6) incorrectly; D works
strictly left-to-right ignoring PEMDAS.
Q6: Compute: (−15) + 8 − (−3)
A. −4 *[CORRECT]*
B. −20
C. −10
D. 4
Correct Answer: A
Rationale: (−15) + 8 = −7, and subtracting (−3) is the same as adding +3, giving −7 + 3 = −4. Choice B mishandles
the sign of −3 by treating subtraction as addition of a negative; C forgets to convert the subtraction of a negative into
addition; D reverses the sign of the final answer.
Q7: Which property is illustrated by 7 × (3 + 8) = (7 × 3) + (7 × 8)?
A. Commutative Property
B. Associative Property
C. Distributive Property *[CORRECT]*
D. Identity Property
Correct Answer: C
Rationale: The distributive property states that a(b + c) = ab + ac, which exactly matches 7(3 + 8) = 7·3 + 7·8. The
commutative property reorders operands (a·b = b·a), the associative property regroups (a·(b·c) = (a·b)·c), and the
identity property involves 0 or 1 leaving a number unchanged.
Q8: Evaluate: 24 + √81
A. 25 *[CORRECT]*
B. 17
C. 89
D. 33
Correct Answer: A
Rationale: 24 = 2·2·2·2 = 16 and √81 = 9, so 24 + √81 = 16 + 9 = 25. Choice B treats 24 as 2 × 4 = 8; C treats √81 as
81 (omits the square root); D combines both errors by computing 2 × 4 + 9 + 16 in an ad-hoc way.
