CEUET Mathematics — Arithmetic — Multiples, Factors, PEMDAS, Fractions & DecimalsSlides
Visual slide deck for Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals. Perfect for reviewers who prefer seeing concepts laid out with diagrams and bullet points rather than long paragraphs. Built specifically for CEUET Mathematics aspirants preparing for the 2026 cycle.
Exam context
The Centro Escolar University Entrance Test is conducted by Centro Escolar University and is scheduled for Q3–Q4 2026. The Mathematics subtest is marked as "Core" in the official pattern, and Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals appears in position 1st of 9 in the CEUET Mathematics review rotation. Passing mark: Competitive overall score. Recent CEUET 2026 papers have drawn roughly a meaningful share of questions from this subject.
Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals - Slides
This chapter covers fundamental arithmetic concepts essential for UPCAT and other college entrance exams. You will learn about multiples and factors, prime factorization, LCM and GCF calculations, divisibility rules, order of operations (PEMDAS), and operations with fractions and decimals. These skills form the foundation for advanced mathematical problem-solving.
Slides
Understanding Multiples and Factors
Understanding the relationship between multiples and factors is crucial for solving arithmetic problems. Think of multiples as the 'counting by' pattern (5, 10, 15, 20...) and factors as the numbers that divide evenly into another number.
Notes
Remember: Every integer has 1 as its smallest factor and itself as its largest factor. The smallest multiple of any integer is the integer itself.
Topic
Multiples and Factors
Slide Id
S1
Visual Type
mermaid
Image Prompt
Slide Number
1
Mermaid Diagram
Code
flowchart TD A[Given two numbers m and n] --> B{Does m divide n without remainder?} B -->|Yes| C[m is a factor of n] B -->|No| D[m is not a factor of n] C --> E[Therefore n is a multiple of m] D --> F[No multiple relationship]
Type
mermaid_flowchart
Description
Decision tree for determining factor and multiple relationships between two numbers
Prime and Composite Numbers
Prime numbers are the building blocks of all integers. Understanding them helps in factorization and solving complex arithmetic problems. Composite numbers can be broken down into prime factors.
Notes
To check if a large number n is prime, only test divisibility by primes up to √n. This saves time and effort in calculations.
Topic
Prime and Composite Numbers
Slide Id
S2
Visual Type
mermaid
Image Prompt
Slide Number
2
Mermaid Diagram
Code
mindmap root((Numbers)) Prime Exactly 2 factors Examples: 2, 3, 5, 7 Only even prime: 2 Composite More than 2 factors Examples: 4, 6, 8, 9 Can be factorized Special Cases 0: Neither prime nor composite 1: Neither prime nor composite
Type
mermaid_mindmap
Description
Classification of numbers into prime, composite, and special cases
Testing for Prime Numbers - Step by Step
This systematic approach saves time when testing large numbers for primality. You only need to check prime divisors up to the square root because any factor larger than √n would have a corresponding factor smaller than √n.
Notes
This method is much faster than testing all numbers. For example, to test if 100 is prime, you only need to check divisibility by 2, 3, 5, 7 instead of all numbers up to 100.
Topic
Prime Number Testing
Slide Id
S3
Visual Type
mermaid
Image Prompt
Slide Number
3
Mermaid Diagram
Code
flowchart TD A[Start with number n] --> B[Calculate square root of n] B --> C[List all primes up to square root] C --> D[Test first prime] D --> E{Does prime divide n evenly?} E -->|Yes| F[n is COMPOSITE] E -->|No| G{More primes to test?} G -->|Yes| H[Test next prime] H --> E G -->|No| I[n is PRIME]
Type
mermaid_flowchart
Description
Algorithm for testing if a number is prime or composite
Prime Factorization Using Factor Trees
Prime factorization breaks down any composite number into its prime building blocks. The factor tree method provides a visual way to systematically find all prime factors. No matter which factors you choose first, you'll always get the same final result.
Notes
The choice of initial factors doesn't matter - you'll always get the same prime factorization. This is called the Fundamental Theorem of Arithmetic.
Topic
Prime Factorization
Slide Id
S4
Visual Type
mermaid
Image Prompt
Slide Number
4
Mermaid Diagram
Code
flowchart TD A[100] --> B[4] A --> C[25] B --> D[2] B --> E[2] C --> F[5] C --> G[5] D --> H[fa:fa-check Prime] E --> I[fa:fa-check Prime] F --> J[fa:fa-check Prime] G --> K[fa:fa-check Prime] L[Result: 100 = 2² × 5²]
Type
mermaid_flowchart
Description
Factor tree showing the prime factorization of 100
Least Common Multiple (LCM) - Two Methods
The LCM is essential for fraction operations and word problems involving repeated events. The prime factorization method is more efficient for larger numbers, while listing multiples works well for smaller numbers.
Notes
For large numbers, the prime factorization method is much more efficient. Remember: LCM × GCF = product of the two original numbers.
Topic
Least Common Multiple
Slide Id
S5
Visual Type
mermaid
Image Prompt
Slide Number
5
Mermaid Diagram
Code
flowchart TD A[Find LCM of two numbers] --> B{Choose Method} B -->|Method 1| C[List multiples of each number] B -->|Method 2| D[Find prime factorization] C --> E[Identify smallest common multiple] D --> F[Take highest power of each prime] F --> G[Multiply all highest powers] E --> H[LCM Found] G --> H
Type
mermaid_flowchart
Description
Two methods for finding the Least Common Multiple of two numbers
Greatest Common Factor (GCF) - Finding the Largest Common Divisor
The GCF helps simplify fractions and solve problems involving equal groups. Understanding both methods gives you flexibility in choosing the most efficient approach based on the numbers involved.
Notes
When one number is a factor of another, the smaller number is automatically the GCF. For example, GCF of 12 and 36 is 12.
Topic
Greatest Common Factor
Slide Id
S6
Visual Type
mermaid
Image Prompt
Slide Number
6
Mermaid Diagram
Code
flowchart TD A[Find GCF of two numbers] --> B{Choose Method} B -->|Method 1| C[List factors of each number] B -->|Method 2| D[Find prime factorization] C --> E[Identify largest common factor] D --> F[Take lowest power of each common prime] F --> G[Multiply all lowest powers] E --> H[GCF Found] G --> H
Type
mermaid_flowchart
Description
Two methods for finding the Greatest Common Factor of two numbers
Divisibility Rules - Quick Tests for Common Divisors
Divisibility rules help you quickly determine if one number divides another without performing actual division. These shortcuts are invaluable for factorization, simplifying fractions, and solving arithmetic problems efficiently.
Notes
For divisibility by 6, a number must satisfy both the rule for 2 AND the rule for 3. For larger numbers, you can repeat the digit sum process until you get a single digit.
Topic
Divisibility Rules
Slide Id
S7
Visual Type
mermaid
Image Prompt
Slide Number
7
Mermaid Diagram
Code
mindmap root((Divisibility Rules)) By 2 Ends in 0,2,4,6,8 Even numbers By 3 Sum of digits divisible by 3 Repeat sum if needed By 5 Ends in 0 or 5 Simple check By 6 Divisible by both 2 and 3 Combined rule By 9 Sum of digits divisible by 9 Repeat sum if needed By 10 Ends in 0 Easiest rule
Type
mermaid_mindmap
Description
Overview of common divisibility rules for quick mental math
PEMDAS - Order of Operations
PEMDAS ensures everyone gets the same answer when evaluating mathematical expressions. Without a standard order, the same expression could have multiple interpretations. Remember that multiplication/division have equal priority, as do addition/subtraction.
Notes
Common mistake: Students often do multiplication before division or addition before subtraction. Remember that operations of equal priority are done from left to right!
Topic
Order of Operations
Slide Id
S8
Visual Type
mermaid
Image Prompt
Slide Number
8
Mermaid Diagram
Code
flowchart TD A[Mathematical Expression] --> B[P: Solve Parentheses first] B --> C[E: Calculate Exponents] C --> D[MD: Multiplication and Division left to right] D --> E[AS: Addition and Subtraction left to right] E --> F[fa:fa-check Final Answer]
Type
mermaid_flowchart
Description
Step-by-step process for applying the order of operations (PEMDAS)
PEMDAS Practice - Complex Expression
Complex expressions require careful attention to detail and systematic application of PEMDAS. Breaking down the problem into smaller steps helps prevent mistakes and makes the solution clearer.
Notes
When dealing with brackets and parentheses, work from the innermost grouping symbols outward. Always recalculate the expression after each step to avoid carrying forward errors.
Topic
PEMDAS Practice
Slide Id
S9
Visual Type
mermaid
Image Prompt
Slide Number
9
Mermaid Diagram
Code
flowchart TD A[2[3 + 4(5² - 3 × 7)] - 8 ÷ 2²] --> B[Inner parentheses: 5² - 3 × 7] B --> C[25 - 21 = 4] C --> D[2[3 + 4(4)] - 8 ÷ 2²] D --> E[2[3 + 16] - 8 ÷ 4] E --> F[2[19] - 2] F --> G[38 - 2 = 36]
Type
mermaid_flowchart
Description
Step-by-step solution of a complex PEMDAS expression
Understanding Fractions - Parts of a Whole
Fractions represent parts of a whole or ratios between quantities. Understanding the relationship between numerator and denominator is crucial for all fraction operations. Visual representations help solidify these concepts.
Notes
To convert mixed numbers to improper fractions: multiply whole number by denominator, add numerator, keep same denominator. Example: 2 3/5 = (2×5+3)/5 = 13/5
Topic
Introduction to Fractions
Slide Id
S10
Visual Type
mermaid
Image Prompt
Slide Number
10
Mermaid Diagram
Code
pie title Fraction 3/4 Representation "Shaded Parts (3)" : 75 "Unshaded Parts (1)" : 25
Type
mermaid_pie
Description
Visual representation of the fraction 3/4 showing three-quarters shaded
Adding and Subtracting Fractions - Same Denominators
When fractions have the same denominator, you're working with the same-sized pieces, so you can directly add or subtract the number of pieces. With different denominators, you must first convert to equivalent fractions with a common denominator.
Notes
Always check if your final answer can be simplified by dividing both numerator and denominator by their GCF. For example, 6/12 = 1/2 after dividing by GCF of 6.
Topic
Fraction Addition and Subtraction
Slide Id
S11
Visual Type
mermaid
Image Prompt
Slide Number
11
Mermaid Diagram
Code
flowchart TD A[Adding/Subtracting Fractions] --> B{Same denominators?} B -->|Yes| C[Add/subtract numerators] B -->|No| D[Find LCD] C --> E[Keep same denominator] D --> F[Convert to equivalent fractions] F --> G[Add/subtract numerators] E --> H[Simplify if possible] G --> H
Type
mermaid_flowchart
Description
Decision process for adding and subtracting fractions
Multiplying and Dividing Fractions
Fraction multiplication is straightforward - multiply straight across. Division uses the 'keep, change, flip' rule: keep the first fraction, change division to multiplication, flip the second fraction. Canceling common factors early prevents working with large numbers.
Notes
When canceling, you can cancel a factor in any numerator with the same factor in any denominator. This makes calculations much easier with large numbers.
Topic
Fraction Multiplication and Division
Slide Id
S12
Visual Type
mermaid
Image Prompt
Slide Number
12
Mermaid Diagram
Code
flowchart TD A[Fraction Operation] --> B{Multiplication or Division?} B -->|Multiplication| C[Multiply numerators] B -->|Division| D[Keep Change Flip] C --> E[Multiply denominators] D --> F[Multiply by reciprocal] E --> G[Cancel common factors] F --> G G --> H[Simplify final answer]
Type
mermaid_flowchart
Description
Process for multiplying and dividing fractions
Converting Between Fractions and Decimals
Converting between fractions and decimals is essential for comparing numbers and solving real-world problems. Understanding place values helps in accurate conversion. Some fractions produce terminating decimals, while others repeat infinitely.
Notes
Memorize common fraction-decimal equivalents: 1/2=0.5, 1/4=0.25, 3/4=0.75, 1/5=0.2, 2/5=0.4, 3/5=0.6, 4/5=0.8. These appear frequently on exams.
Topic
Fractions and Decimals Conversion
Slide Id
S13
Visual Type
mermaid
Image Prompt
Slide Number
13
Mermaid Diagram
Code
flowchart TD A[Number Conversion] --> B{Fraction to Decimal or Decimal to Fraction?} B -->|Fraction to Decimal| C[Divide numerator by denominator] B -->|Decimal to Fraction| D[Write as fraction over power of 10] C --> E[Result: Decimal form] D --> F[Simplify by dividing by GCF] F --> G[Result: Simplified fraction]
Type
mermaid_flowchart
Description
Process for converting between fractions and decimals
Decimal Operations - Addition, Subtraction, Multiplication
Decimal operations follow similar rules to whole number operations with special attention to decimal point placement. Proper alignment and careful counting of decimal places ensures accurate results.
Notes
When adding or subtracting decimals, you can add zeros to the right of the decimal point to make alignment easier. For example, 12.3 + 5.67 can be written as 12.30 + 5.67.
Topic
Decimal Operations
Slide Id
S14
Visual Type
mermaid
Image Prompt
Slide Number
14
Mermaid Diagram
Code
flowchart TD A[Decimal Operation] --> B{Type of Operation?} B -->|Add/Subtract| C[Align decimal points] B -->|Multiply| D[Ignore decimals, multiply] B -->|Divide| E[Move decimal to make divisor whole] C --> F[Perform operation] D --> G[Count total decimal places] E --> H[Divide normally] F --> I[Final Answer] G --> I H --> I
Type
mermaid_flowchart
Description
Process for performing operations with decimal numbers
Problem-Solving with Arithmetic Concepts
Real-world problems often combine multiple arithmetic concepts. Success depends on recognizing which concepts apply and applying them in the correct sequence. Always verify your answer makes sense in the context of the problem.
Notes
Practice identifying keywords: 'total' suggests addition, 'difference' suggests subtraction, 'times' or 'of' suggests multiplication, 'per' or 'each' suggests division.
Topic
Problem-Solving Applications
Slide Id
S15
Visual Type
mermaid
Image Prompt
Slide Number
15
Mermaid Diagram
Code
flowchart TD A[Word Problem] --> B[Read carefully] B --> C[Identify key information] C --> D[Determine arithmetic concepts needed] D --> E[Set up calculations] E --> F[Apply rules and formulas] F --> G[Calculate step by step] G --> H[Check reasonableness] H --> I[fa:fa-check Final Answer]
Type
mermaid_flowchart
Description
Problem-solving strategy for arithmetic word problems
References
- BRAINBOX UPCAT AND OTHER COLLEGE ENTRANCE - Mathematics Proficiency
- Department of Education Mathematics Curriculum Guide
- UPCAT Mathematics Review Materials
In summary
Mastering these arithmetic fundamentals - multiples, factors, PEMDAS, fractions, and decimals - provides the foundation for success in UPCAT and other college entrance exams. Practice these concepts regularly, focusing on accuracy and speed. Remember to check your work and verify that your answers make sense in context. These skills will serve you well not only on exams but also in advanced mathematical coursework and real-world applications.
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