Civil Service Exam (Subprofessional) Numerical Ability — Integers, PEMDAS & DivisibilitySlides
Visual slide deck for Integers, PEMDAS & Divisibility. Perfect for reviewers who prefer seeing concepts laid out with diagrams and bullet points rather than long paragraphs. Built specifically for Civil Service Exam (Subprofessional) Numerical Ability aspirants preparing for the 2026 cycle.
Exam context
Civil Service Commission (CSC) runs the Career Service Examination — Subprofessional Level on Bi-annual — March and August 2026. Its Numerical Ability section sits under a "~25% weightage" weighting, and Integers, PEMDAS & Divisibility is the 1st chapter in the 9-chapter Civil Service Exam (Subprofessional) Numerical Ability rotation. The Civil Service Exam (Subprofessional) passing mark is 80%, and the most recent 2026 paper drew about 17 questions from Numerical Ability.
Integers, PEMDAS & Divisibility - Slides
This chapter covers fundamental numerical concepts essential for success in Philippine college entrance exams and civil service examinations. You'll master operations with integers, the order of operations (PEMDAS), and divisibility rules - skills that form the foundation of numerical ability testing.
Slides
Welcome to Integers, PEMDAS & Divisibility
This chapter builds your numerical fluency through three interconnected topics that appear frequently in standardized tests across the Philippines.
Notes
Introduction slide establishing the importance and scope of the chapter
Topic
Chapter Overview
Slide Id
S1
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mermaid
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1
Mermaid Diagram
Code
mindmap root((Numerical Ability)) Integers Positive Numbers Negative Numbers Zero Properties Operations PEMDAS Parentheses Exponents Multiplication Division Addition Subtraction Divisibility Rules 2 5 10 Rules 3 6 9 Rules 4 8 11 Prime Composite
Type
mermaid_mindmap
Description
Overview of the three main topics and their subtopics in numerical ability
Understanding Integers
Integers form the foundation of number systems. They extend counting numbers to include negative values and zero, creating a complete system for mathematical operations.
Notes
Foundation slide introducing the concept and properties of integers
Topic
Integer Fundamentals
Slide Id
S2
Visual Type
mermaid
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2
Mermaid Diagram
Code
flowchart LR A[Negative Integers] --> B[Zero] B --> C[Positive Integers] A --> D[-3 -2 -1] B --> E[0] C --> F[1 2 3] D --> G[Less than zero] E --> H[Neither positive nor negative] F --> I[Greater than zero]
Type
mermaid_flowchart
Description
Visual representation of the integer number line showing negative, zero, and positive integers
Types of Integers
Integers can be classified into different types based on their properties. Understanding these classifications helps in applying appropriate mathematical rules and operations.
Notes
Detailed classification of integers to establish clear understanding of different types
Topic
Integer Classification
Slide Id
S3
Visual Type
mermaid
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3
Mermaid Diagram
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flowchart TD A[fa:fa-calculator Integers] --> B[Positive] A --> C[Zero] A --> D[Negative] A --> E[Even] A --> F[Odd] B --> G[1 2 3 4 5] C --> H[0] D --> I[-1 -2 -3 -4 -5] E --> J[Divisible by 2] F --> K[Not divisible by 2]
Type
mermaid_flowchart
Description
Classification of integers showing different types and their characteristics
Addition of Integers - Like Signs
When adding integers with the same sign, add their absolute values and keep the common sign. This rule makes addition straightforward for like signs.
Notes
First rule for integer addition - like signs
Topic
Integer Addition - Like Signs
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S4
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mermaid
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4
Mermaid Diagram
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flowchart TD A[Like Signs Addition] --> B[Both Positive] A --> C[Both Negative] B --> D[Add absolute values] C --> E[Add absolute values] D --> F[Result is Positive] E --> G[Result is Negative] F --> H[5 + 3 = 8] G --> I[-5 + -3 = -8]
Type
mermaid_flowchart
Description
Process for adding integers with the same sign
Addition of Integers - Unlike Signs
When adding integers with different signs, subtract the smaller absolute value from the larger absolute value. The result takes the sign of the integer with the larger absolute value.
Notes
Second rule for integer addition - unlike signs
Topic
Integer Addition - Unlike Signs
Slide Id
S5
Visual Type
mermaid
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Slide Number
5
Mermaid Diagram
Code
flowchart TD A[Unlike Signs Addition] --> B{Compare absolute values} B --> C[Positive larger] B --> D[Negative larger] B --> E[Equal values] C --> F[Result is Positive] D --> G[Result is Negative] E --> H[Result is Zero] F --> I[15 + -8 = 7] G --> J[-15 + 8 = -7] H --> K[15 + -15 = 0]
Type
mermaid_flowchart
Description
Decision process for adding integers with different signs
Subtraction of Integers
Integer subtraction is simplified by converting it to addition. Change the subtraction sign to addition and change the sign of the second number, then apply addition rules.
Notes
Systematic approach to integer subtraction using addition conversion
Topic
Integer Subtraction
Slide Id
S6
Visual Type
mermaid
Image Prompt
Slide Number
6
Mermaid Diagram
Code
flowchart TD A[fa:fa-minus Subtraction Problem] --> B[Change minus to plus] B --> C[Change sign of second number] C --> D[Apply addition rules] D --> E[Get final answer] A --> F[Example: 8 - 5] F --> G[8 + -5] G --> H[3]
Type
mermaid_flowchart
Description
Step-by-step process for converting subtraction to addition
Multiplication and Division of Integers
Multiplication and division of integers follow simple sign rules. When signs are the same, the result is positive. When signs are different, the result is negative.
Notes
Universal sign rules for integer multiplication and division
Topic
Integer Multiplication and Division
Slide Id
S7
Visual Type
mermaid
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Slide Number
7
Mermaid Diagram
Code
flowchart TD A[fa:fa-times Integer Multiplication Division] --> B{Signs same?} B -->|Yes| C[Result is Positive] B -->|No| D[Result is Negative] C --> E[+ × + = +] C --> F[- × - = +] D --> G[+ × - = -] D --> H[- × + = -]
Type
mermaid_flowchart
Description
Sign rules for multiplication and division of integers
Introduction to PEMDAS
PEMDAS ensures everyone gets the same answer when solving mathematical expressions. It provides a standard order for performing operations, preventing confusion and errors in calculations.
Notes
Introduction to the PEMDAS rule and its importance
Topic
PEMDAS Introduction
Slide Id
S8
Visual Type
mermaid
Image Prompt
Slide Number
8
Mermaid Diagram
Code
flowchart TD A[fa:fa-calculator Mathematical Expression] --> B[P: Parentheses] B --> C[E: Exponents] C --> D[M/D: Multiplication Division] D --> E[A/S: Addition Subtraction] E --> F[fa:fa-check Final Answer] B --> G[Work inside out] C --> H[Powers first] D --> I[Left to right] E --> J[Left to right]
Type
mermaid_flowchart
Description
The sequential order of operations in PEMDAS
PEMDAS Step-by-Step Example
Complex expressions require systematic application of PEMDAS. Work from innermost grouping symbols outward, then follow the order strictly.
Notes
Detailed example showing step-by-step PEMDAS application
Topic
PEMDAS Example
Slide Id
S9
Visual Type
mermaid
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Slide Number
9
Mermaid Diagram
Code
sequenceDiagram participant E as Expression participant P as Parentheses participant Ex as Exponents participant M as Multiply/Divide participant A as Add/Subtract E->>P: (-3 + 5) = 2 P->>Ex: (2)² = 4 Ex->>M: 3 × 4 = 12, then 4 - 12 = -8 M->>A: 4 ÷ 2 × 6 = 12 A->>E: 2 - (-8) + 12 - 3 = 19
Type
mermaid_sequence
Description
Sequential steps in solving a complex PEMDAS expression
Common PEMDAS Mistakes
Understanding common errors helps avoid them. Many students struggle with the left-to-right rule for operations of equal priority and proper handling of negative signs.
Notes
Prevention-focused slide highlighting common student errors
Topic
PEMDAS Common Errors
Slide Id
S10
Visual Type
mermaid
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10
Mermaid Diagram
Code
flowchart TD A[fa:fa-warning Common PEMDAS Mistakes] --> B[Skip Parentheses] A --> C[Wrong Order] A --> D[Ignore Left to Right] A --> E[Sign Errors] B --> F[Always do groupings first] C --> G[Follow PEMDAS sequence] D --> H[Same priority: left to right] E --> I[Be careful with negatives]
Type
mermaid_flowchart
Description
Common mistakes in PEMDAS and how to avoid them
Divisibility Rules Overview
Divisibility rules are shortcuts that let you quickly determine if a number is divisible by another without performing actual division. These are crucial for efficiency in standardized tests.
Notes
Introduction to divisibility rules and their practical importance
Topic
Divisibility Overview
Slide Id
S11
Visual Type
mermaid
Image Prompt
Slide Number
11
Mermaid Diagram
Code
mindmap root((Divisibility Rules)) Quick Tests Check Last Digit Sum Digits Pattern Recognition Common Rules 2 5 10 3 6 9 4 8 11 Benefits Save Time Mental Math Exam Efficiency
Type
mermaid_mindmap
Description
Overview of divisibility rules, methods, and benefits
Divisibility Rules: 2, 5, and 10
The easiest divisibility rules focus on the last digit. These patterns emerge from the base-10 number system and are foundational for more complex rules.
Notes
Basic divisibility rules focusing on the last digit
Topic
Divisibility: 2, 5, 10
Slide Id
S12
Visual Type
mermaid
Image Prompt
Slide Number
12
Mermaid Diagram
Code
flowchart TD A[Check Last Digit] --> B{Ends in 0?} B -->|Yes| C[Divisible by 2, 5, and 10] B -->|No| D{Ends in 2, 4, 6, 8?} D -->|Yes| E[Divisible by 2 only] D -->|No| F{Ends in 5?} F -->|Yes| G[Divisible by 5 only] F -->|No| H[Not divisible by 2, 5, or 10]
Type
mermaid_flowchart
Description
Decision tree for testing divisibility by 2, 5, and 10
Divisibility Rules: 3, 6, and 9
These rules require adding all digits in the number. The digital root (repeated digit sum) reveals divisibility patterns. Rule for 6 combines two simpler rules.
Notes
Digit sum method for divisibility testing
Topic
Divisibility: 3, 6, 9
Slide Id
S13
Visual Type
mermaid
Image Prompt
Slide Number
13
Mermaid Diagram
Code
flowchart TD A[fa:fa-plus Add All Digits] --> B{Sum divisible by 9?} B -->|Yes| C[Divisible by 3, 6, and 9] B -->|No| D{Sum divisible by 3?} D -->|Yes| E{Original number even?} D -->|No| F[Not divisible by 3, 6, or 9] E -->|Yes| G[Divisible by 3 and 6] E -->|No| H[Divisible by 3 only]
Type
mermaid_flowchart
Description
Process for testing divisibility by 3, 6, and 9 using digit sums
Divisibility Rules: 4, 8, and 11
These rules require examining specific digit positions. Rule 11 uses alternating addition/subtraction pattern. These are more complex but very useful for factorization.
Notes
Advanced divisibility rules requiring specific digit pattern checks
Topic
Divisibility: 4, 8, 11
Slide Id
S14
Visual Type
mermaid
Image Prompt
Slide Number
14
Mermaid Diagram
Code
flowchart TD A[Divisibility Test] --> B[For 4: Last 2 digits] A --> C[For 8: Last 3 digits] A --> D[For 11: Alternating sum] B --> E{Divisible by 4?} C --> F{Divisible by 8?} D --> G{Difference is 0 or multiple of 11?} E -->|Yes| H[Number divisible by 4] F -->|Yes| I[Number divisible by 8] G -->|Yes| J[Number divisible by 11]
Type
mermaid_flowchart
Description
Testing process for divisibility by 4, 8, and 11
Factors and Multiples
Factors and multiples are fundamental concepts in number theory. Understanding their relationship helps with fraction simplification, finding common denominators, and solving word problems.
Notes
Foundation concepts of factors and multiples with clear examples
Topic
Factors and Multiples
Slide Id
S15
Visual Type
mermaid
Image Prompt
Slide Number
15
Mermaid Diagram
Code
flowchart TD A[Number 12] --> B[Factors] A --> C[Multiples] B --> D[1 × 12 = 12] B --> E[2 × 6 = 12] B --> F[3 × 4 = 12] C --> G[12 × 1 = 12] C --> H[12 × 2 = 24] C --> I[12 × 3 = 36] D --> J[Factors: 1, 2, 3, 4, 6, 12] G --> K[Multiples: 12, 24, 36, 48...]
Type
mermaid_flowchart
Description
Relationship between factors and multiples using 12 as an example
Finding GCF and LCM
GCF and LCM are essential for working with fractions and solving real-world problems involving cycles and patterns. Multiple methods exist, each with advantages depending on the numbers involved.
Notes
Systematic approach to finding GCF and LCM using multiple methods
Topic
GCF and LCM
Slide Id
S16
Visual Type
mermaid
Image Prompt
Slide Number
16
Mermaid Diagram
Code
flowchart TD A[Two Numbers: 18 and 24] --> B[Find GCF] A --> C[Find LCM] B --> D[List factors] B --> E[Prime factorization] B --> F[Continuous division] C --> G[List multiples] C --> H[Prime factorization] C --> I[Continuous division] D --> J[GCF = 6] G --> K[LCM = 72]
Type
mermaid_flowchart
Description
Methods for finding GCF and LCM of two numbers
Prime and Composite Numbers
Prime and composite classification is fundamental in number theory. Primes are building blocks for all other numbers through multiplication, making them crucial for factorization and divisibility.
Notes
Clear distinction between prime and composite numbers with examples
Topic
Prime and Composite Numbers
Slide Id
S17
Visual Type
mermaid
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17
Mermaid Diagram
Code
flowchart TD A[Natural Number] --> B{Number of factors?} B -->|Exactly 2| C[Prime Number] B -->|More than 2| D[Composite Number] B -->|Only 1| E[Neither prime nor composite] C --> F[Examples: 2, 3, 5, 7, 11] D --> G[Examples: 4, 6, 8, 9, 10] E --> H[Only number 1]
Type
mermaid_flowchart
Description
Classification of numbers as prime, composite, or neither
Practical Applications
These concepts appear throughout Philippine standardized testing and have practical applications in daily life. Mastery enables quick problem-solving and builds confidence in mathematical reasoning.
Notes
Connecting theoretical concepts to practical applications and exam contexts
Topic
Practical Applications
Slide Id
S18
Visual Type
none
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Slide Number
18
Mermaid Diagram
Type
none
Problem-Solving Strategies
Effective problem-solving combines understanding concepts with strategic thinking. Time management is crucial in standardized tests, so developing efficient methods is essential for success.
Notes
Strategic approach to problem-solving with emphasis on systematic thinking
Topic
Problem-Solving Strategies
Slide Id
S19
Visual Type
mermaid
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Slide Number
19
Mermaid Diagram
Code
flowchart TD A[fa:fa-book Problem] --> B[Read carefully] B --> C[Identify key information] C --> D[Choose appropriate method] D --> E{Multiple operations?} E -->|Yes| F[Apply PEMDAS] E -->|No| G[Apply single rule] F --> H[fa:fa-check Verify answer] G --> H H --> I[Check using divisibility if applicable]
Type
mermaid_flowchart
Description
Step-by-step approach to solving numerical problems systematically
Chapter Summary
This chapter provided essential numerical skills that form the foundation for advanced mathematics and standardized test success. Regular practice with these concepts will build both speed and accuracy.
Notes
Comprehensive summary emphasizing the practical value and interconnected nature of the concepts
Topic
Chapter Summary
Slide Id
S20
Visual Type
mermaid
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Slide Number
20
Mermaid Diagram
Code
mindmap root((Chapter Mastery)) Integer Operations Addition Rules Subtraction Method Multiplication Division Signs PEMDAS Application Parentheses First Exponents Second Left to Right MD AS Divisibility Mastery Quick Recognition Pattern Identification Exam Speed Problem Solving Real World Applications Exam Success Mental Math Fluency
Type
mermaid_mindmap
Description
Summary of key chapter concepts and their interconnections
References
- BRAINBOX UPCAT AND OTHER COLLEGE ENTRANCE - Mathematics Proficiency.pdf
- NEW CURRICULUM CIVIL SERVICE 2026 EDITION - Numerical.pdf
- NCV CIVIL SERVICE - Numerical Ability.pdf
- Philippine Department of Education K-12 Mathematics Curriculum
- UPCAT and College Entrance Exam Preparation Materials
In summary
Mastery of integers, PEMDAS, and divisibility rules provides the foundation for success in Philippine standardized exams and advanced mathematics. These concepts appear frequently in UPCAT, Civil Service, and other entrance examinations. Regular practice with these fundamentals will build the numerical fluency essential for academic and professional success. Remember to apply these skills systematically, check your work using divisibility rules when possible, and maintain accuracy while building speed through consistent practice.
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