CEUET Mathematics — Arithmetic — Multiples, Factors, PEMDAS, Fractions & DecimalsMisconception Buster
If you have been missing Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals questions on your CEUET mocks, the cause is almost always a misconception. This page lists the ones Centro Escolar University exploits most often in the CEUET Mathematics subtest and shows how to correct them before exam day.
Exam context
Centro Escolar University runs the Centro Escolar University Entrance Test on Q3–Q4 2026. Its Mathematics section sits under a "Core" weighting, and Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals is the 1st chapter in the 9-chapter CEUET Mathematics rotation. The CEUET passing mark is Competitive overall score, and the most recent 2026 paper drew about a meaningful share of questions from Mathematics.
Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals - Misconception buster
Understanding arithmetic misconceptions is crucial for UPCAT success because these fundamental concepts appear in 30-40% of exam questions. Many students lose easy marks not because they don't know the concepts, but because they hold common misconceptions that lead to systematic errors. This guide reveals the most dangerous wrong beliefs that can cost you precious points in college entrance exams.
Summary
The key to avoiding these arithmetic misconceptions is understanding the underlying logic, not just memorizing rules. Practice with trap questions that specifically target these wrong beliefs. Remember: PEMDAS operations have equal priority within MD and AS groups, fractions need common denominators before adding, and 1 is neither prime nor composite by mathematical definition. Always verify your answers using the correct methods, and don't rely on intuition alone—especially with decimals and negative numbers.
Misconceptions
PEMDAS means you always do operations from left to right in the order P-E-M-D-A-S
Tags
- common_error
- formula_confusion
- procedural_mistake
Topic
PEMDAS/Order of Operations
Severity
critical
Exam Impact
This misconception causes wrong answers in 60-70% of order-of-operations problems, typically worth 3-5 marks per question in UPCAT.
The Reality
PEMDAS gives the hierarchy of operations, but multiplication and division have EQUAL priority (work left to right), and addition and subtraction have EQUAL priority (work left to right). The correct order is: Parentheses, Exponents, then Multiplication/Division (left to right), then Addition/Subtraction (left to right).
Trap Question
Question
Calculate: 20 - 3 × 2 + 8 ÷ 4
Explanation
Following PEMDAS correctly: First do multiplication and division (left to right): 3 × 2 = 6 and 8 ÷ 4 = 2. Then do addition and subtraction (left to right): 20 - 6 + 2 = 14 + 2 = 16
Wrong Answer
34 (doing operations left to right: 20 - 3 = 17, 17 × 2 = 34, 34 + 8 = 42, 42 ÷ 4 = 10.5) or other incorrect values
Correct Answer
16
Misconception Id
M1
Correct Vs Incorrect
Correct Approach
For 8 ÷ 2 × 4: Multiplication and division have equal priority, so work left to right: 8 ÷ 2 = 4, then 4 × 4 = 16. Answer: 16 (This example gives same result, but consider 12 ÷ 3 × 2 = 4 × 2 = 8, not 12 ÷ 6 = 2)
Incorrect Approach
For 8 ÷ 2 × 4: Do division first (8 ÷ 2 = 4), then multiplication (4 × 4 = 16). Answer: 16
Why Students Believe It
Students memorize PEMDAS as a strict sequence and think multiplication always comes before division, and addition always comes before subtraction. The acronym seems to suggest a rigid order.
If a number is divisible by 6, it must be divisible by 12
Tags
- conceptual_gap
- logical_error
Topic
Divisibility Rules
Severity
major
Exam Impact
This appears in number theory questions worth 2-3 marks each. Students often eliminate correct answer choices or select wrong multiples.
The Reality
A number divisible by 6 is divisible by both 2 and 3, but to be divisible by 12, it must be divisible by 4 (not just 2) and 3. For example, 18 is divisible by 6 but not by 12 because 18 ÷ 4 = 4.5.
Trap Question
Question
Which of the following numbers is divisible by both 6 and 12? A) 18 B) 30 C) 42 D) 36
Explanation
Check each: 18÷12=1.5✗, 30÷12=2.5✗, 42÷12=3.5✗, 36÷12=3✓. Only 36 works because it's divisible by both 3 and 4 (36÷3=12, 36÷4=9).
Wrong Answer
A, B, C, and D (thinking all numbers divisible by 6 are divisible by 12)
Correct Answer
D) 36
Misconception Id
M2
Correct Vs Incorrect
Correct Approach
For divisibility by 12, check divisibility by both 3 and 4: 30 ÷ 3 = 10 ✓, but 30 ÷ 4 = 7.5 ✗. Therefore, 30 is not divisible by 12.
Incorrect Approach
Since 30 is divisible by 6, it must be divisible by 12. Check: 30 ÷ 12 = 2.5 (wrong!)
Why Students Believe It
Students see that 6 is a factor of 12, so they think divisibility by 6 automatically means divisibility by 12. They confuse the direction of the divisibility relationship.
The LCM of two numbers is always larger than both numbers
Tags
- conceptual_gap
- definition_misunderstanding
Topic
LCM (Least Common Multiple)
Severity
major
Exam Impact
This misconception causes students to unnecessarily calculate larger multiples, wasting time and often leading to computational errors worth 2-4 marks.
The Reality
When one number is a multiple of another, the LCM equals the larger number. For example, LCM(6,18) = 18, not some number larger than 18.
Trap Question
Question
Find the LCM of 15 and 45.
Explanation
Since 45 = 15 × 3, the number 15 is a factor of 45. When one number divides another evenly, the LCM is simply the larger number. Check: 45 ÷ 15 = 3 and 45 ÷ 45 = 1.
Wrong Answer
90 (thinking it must be larger than both numbers)
Correct Answer
45
Misconception Id
M3
Correct Vs Incorrect
Correct Approach
LCM(8,24): Since 24 = 8 × 3, the number 8 divides 24 evenly. Therefore, LCM = 24 (the larger number)
Incorrect Approach
LCM(8,24): List multiples: 8→16,24,32,48... 24→48,72... So LCM = 48
Why Students Believe It
Students think 'least common multiple' means finding a number bigger than both original numbers. They don't consider cases where one number is a multiple of another.
When adding fractions, add numerators and add denominators: a/b + c/d = (a+c)/(b+d)
Tags
- common_error
- procedural_mistake
- conceptual_gap
Topic
Fraction Addition
Severity
critical
Exam Impact
This is one of the most common errors in fraction problems, appearing in 70-80% of fraction questions worth 3-6 marks each in college entrance exams.
The Reality
Fractions must have common denominators before adding. The correct method is: a/b + c/d = (ad + bc)/(bd) after finding a common denominator, or convert to equivalent fractions with LCD first.
Trap Question
Question
Calculate: 2/5 + 1/3
Explanation
Find LCD of 5 and 3, which is 15. Convert: 2/5 = 6/15 and 1/3 = 5/15. Add: 6/15 + 5/15 = 11/15.
Wrong Answer
3/8 (adding numerators and denominators directly)
Correct Answer
11/15
Misconception Id
M4
Correct Vs Incorrect
Correct Approach
1/3 + 1/4: Find LCD = 12. Convert: 1/3 = 4/12, 1/4 = 3/12. Add: 4/12 + 3/12 = 7/12
Incorrect Approach
1/3 + 1/4 = (1+1)/(3+4) = 2/7
Why Students Believe It
Students apply the pattern they see in whole number addition to fractions. It seems logical to add 'tops to tops' and 'bottoms to bottoms'.
1 is a prime number because it only has one factor
Tags
- definition_misunderstanding
- conceptual_gap
Topic
Prime Numbers
Severity
major
Exam Impact
This misconception affects prime factorization problems, prime counting problems, and number classification questions worth 2-3 marks each.
The Reality
By mathematical definition, a prime number must have EXACTLY two distinct factors: 1 and itself. Since 1 only has one factor (itself), it is neither prime nor composite.
Trap Question
Question
How many prime numbers are there between 1 and 10 inclusive?
Explanation
Prime numbers between 1 and 10 are: 2, 3, 5, 7. The number 1 is neither prime nor composite by definition. The number 4, 6, 8, 9, 10 are composite.
Wrong Answer
5 (counting 1, 2, 3, 5, 7)
Correct Answer
4
Misconception Id
M5
Correct Vs Incorrect
Correct Approach
List the first 5 prime numbers: 2, 3, 5, 7, 11 (1 is excluded by definition)
Incorrect Approach
List the first 5 prime numbers: 1, 2, 3, 5, 7
Why Students Believe It
Students think the definition of prime is 'having very few factors' and since 1 only divides by itself, it seems prime. The factor counting seems to match.
0.5 × 0.5 = 0.25 is wrong because multiplying makes numbers bigger
Tags
- conceptual_gap
- intuition_error
Topic
Decimal Multiplication
Severity
major
Exam Impact
This misconception causes students to doubt correct decimal calculations and choose wrong answers in word problems involving percentages and probability.
The Reality
When multiplying numbers between 0 and 1, the result is smaller than both original numbers. This is because you're taking a fraction OF a fraction. 0.5 × 0.5 = 0.25 is correct.
Trap Question
Question
If 0.3 of students wear glasses and 0.4 of those who wear glasses are girls, what fraction of all students are girls who wear glasses?
Explanation
Multiply the fractions: 0.3 × 0.4 = 0.12. This represents 12% of all students, which makes sense as it should be smaller than either original percentage.
Wrong Answer
0.7 (adding 0.3 + 0.4, thinking multiplication would make it bigger)
Correct Answer
0.12
Misconception Id
M6
Correct Vs Incorrect
Correct Approach
0.5 × 0.5 means 'half of a half' = 1/2 × 1/2 = 1/4 = 0.25, which is smaller than both factors
Incorrect Approach
0.5 × 0.5 should equal something bigger than 0.5, so maybe 1.0 or 2.5
Why Students Believe It
Students learn early that multiplication makes numbers bigger, based on whole number examples. They expect 0.5 × 0.5 to be larger than 0.5.
GCF is always smaller than LCM
Tags
- conceptual_gap
- special_case
Topic
GCF and LCM Relationship
Severity
minor
Exam Impact
This rarely affects calculations but can cause confusion in multiple choice questions where students eliminate correct answers.
The Reality
When the two numbers are the same, GCF = LCM = the number itself. For example, GCF(12,12) = LCM(12,12) = 12. The GCF can never be larger than either original number, but the LCM can equal the larger number.
Trap Question
Question
What is the relationship between GCF(15,15) and LCM(15,15)?
Explanation
When finding GCF and LCM of identical numbers, both equal the number itself. GCF(15,15) = 15 and LCM(15,15) = 15.
Wrong Answer
GCF < LCM (thinking they must be different)
Correct Answer
GCF = LCM = 15
Misconception Id
M7
Correct Vs Incorrect
Correct Approach
Usually GCF ≤ both numbers ≤ LCM, but when a = b, then GCF(a,b) = LCM(a,b) = a = b
Incorrect Approach
For any two numbers a and b, GCF(a,b) < LCM(a,b) always
Why Students Believe It
Students think 'greatest common factor' means a big number and 'least common multiple' means an even bigger number. The words 'greatest' and 'least' confuse them about relative size.
To check divisibility by 6, just check if the last digit is even
Tags
- procedural_mistake
- incomplete_rule
Topic
Divisibility Rules
Severity
major
Exam Impact
This appears frequently in divisibility questions worth 2-3 marks. Students often mark numbers as divisible by 6 when they're only divisible by 2.
The Reality
For divisibility by 6, the number must be divisible by BOTH 2 AND 3. Check if it's even (divisible by 2) AND if the sum of digits is divisible by 3.
Trap Question
Question
Which number is divisible by 6? A) 22 B) 34 C) 46 D) 48
Explanation
Check each: A) 22: even ✓ but 2+2=4 (not divisible by 3) ✗. B) 34: even ✓ but 3+4=7 ✗. C) 46: even ✓ but 4+6=10 ✗. D) 48: even ✓ and 4+8=12 (divisible by 3) ✓.
Wrong Answer
All of them (since all are even)
Correct Answer
D) 48
Misconception Id
M8
Correct Vs Incorrect
Correct Approach
Is 14 divisible by 6? Check both: 14 is even ✓, but 1+4=5 (not divisible by 3) ✗. So 14 is not divisible by 6.
Incorrect Approach
Is 14 divisible by 6? Last digit is 4 (even), so yes.
Why Students Believe It
Students remember that divisibility by 2 involves checking the last digit, and since 6 = 2 × 3, they think checking for 2 is sufficient.
When converting fractions to decimals, the decimal always terminates
Tags
- conceptual_gap
- pattern_recognition
Topic
Fraction to Decimal Conversion
Severity
minor
Exam Impact
This affects decimal conversion problems and can cause confusion when students get repeating decimals and think they made an error.
The Reality
A fraction in lowest terms has a terminating decimal only if the denominator has no prime factors other than 2 and 5. Fractions like 1/3, 1/7, 1/9 have repeating decimals.
Trap Question
Question
Convert 2/9 to a decimal.
Explanation
Since 9 = 3², and 3 is not 2 or 5, this fraction produces a repeating decimal: 2÷9 = 0.222... The digit 2 repeats forever.
Wrong Answer
0.22 (stopping at two decimal places thinking it should terminate)
Correct Answer
0.222... or 0.2̄
Misconception Id
M9
Correct Vs Incorrect
Correct Approach
1/3 = 0.333... = 0.3̄ (repeating decimal, never terminates)
Incorrect Approach
1/3 should equal something like 0.33 exactly
Why Students Believe It
Students practice with simple fractions like 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75 that all terminate, so they expect all fractions to have terminating decimal forms.
Negative numbers cannot be multiples
Tags
- definition_misunderstanding
- sign_confusion
Topic
Multiples and Factors
Severity
minor
Exam Impact
This mainly affects advanced number theory problems but can cause confusion when dealing with integer sets.
The Reality
Multiples include negative numbers. For example, multiples of 3 include: ..., -9, -6, -3, 0, 3, 6, 9, ... The definition works for all integers.
Trap Question
Question
Is -15 a multiple of 3?
Explanation
-15 = 3 × (-5), so -15 is indeed a multiple of 3. Multiples can be negative, zero, or positive.
Wrong Answer
No (thinking multiples must be positive)
Correct Answer
Yes
Misconception Id
M10
Correct Vs Incorrect
Correct Approach
Multiples of 4: ..., -12, -8, -4, 0, 4, 8, 12, 16... (all integers)
Incorrect Approach
Multiples of 4: 4, 8, 12, 16, 20... (only positive)
Why Students Believe It
Students learn multiples using positive counting examples (3, 6, 9, 12...) and think the definition only applies to positive results.
Quick Self Check
Multiplication has higher priority than subtraction in PEMDAS. Do 4 × 2 = 8 first, then 10 - 8 = 2.
Statement
In the expression 10 - 4 × 2, you should subtract first because subtraction comes before multiplication in PEMDAS
The number must be divisible by LCM(4,6) = 12, not necessarily 24. For example, 12 is divisible by both 4 and 6 but not by 24.
Statement
If a number is divisible by 4 and by 6, it must be divisible by 24
You cannot add numerators and denominators directly. The correct answer is 7/35 + 5/35 = 12/35.
Statement
The sum 1/5 + 1/7 equals 2/12
By definition, 1 is excluded from both prime and composite classifications because it has only one factor (itself).
Statement
The number 1 is neither prime nor composite
Multiplying fractions means taking a fraction OF a fraction, which always gives a smaller result. For example, 0.5 × 0.3 = 0.15.
Statement
When you multiply two decimals less than 1, the result is always smaller than both original numbers
Only fractions whose denominators (in lowest terms) have factors of only 2 and/or 5 terminate. Others like 1/3 repeat forever.
Statement
Every fraction can be converted to a terminating decimal
When two numbers are different, the GCF (largest common factor) is always smaller than the LCM (smallest common multiple).
Statement
For any two different positive numbers, the GCF is always less than the LCM
You must check divisibility by BOTH 2 AND 3. A number divisible by 6 must be divisible by both of its prime factors.
Statement
To check if a number is divisible by 6, you only need to check if it's divisible by 2
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