Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals - Concept map
Arithmetic Operations
Related concepts
Multiples and Factors
Sub concepts
- Prime Numbers
- Composite Numbers
- Prime Factorization
- LCM (Least Common Multiple)
- GCF (Greatest Common Factor)
- Divisibility Rules
- Relatively Prime Numbers
Relationship to central
Foundation for understanding number relationships and divisibility
Number System
Sub concepts
- Natural Numbers
- Whole Numbers
- Integers
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Complex Numbers
Relationship to central
Framework for classifying all numbers used in arithmetic
Properties of Real Numbers
Sub concepts
- Commutative Property
- Associative Property
- Distributive Property
- Identity Properties
- Inverse Properties
Relationship to central
Rules that govern arithmetic operations and simplify calculations
PEMDAS Order of Operations
Sub concepts
- Parentheses
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Relationship to central
Standard procedure for evaluating arithmetic expressions correctly
Fractions
Sub concepts
- Proper Fractions
- Improper Fractions
- Mixed Numbers
- Fraction Operations
- Equivalent Fractions
- Simplifying Fractions
Relationship to central
Representation of parts of whole numbers and rational number operations
Decimals
Sub concepts
- Place Value
- Terminating Decimals
- Repeating Decimals
- Decimal Operations
- Fraction-Decimal Conversion
- Rounding Decimals
Relationship to central
Alternative representation of fractions using base-10 system
Concept connections
- Prime FactorizationLCM and GCFPrime factorization is the most efficient method for finding LCM and GCF of large numbers
- Divisibility RulesPrime NumbersDivisibility rules help quickly identify factors and determine if a number is prime or composite
- FractionsGCFGCF is used to simplify fractions to their lowest terms
- FractionsLCMLCM is needed to add and subtract fractions with different denominators
- Properties of Real NumbersPEMDASNumber properties explain why PEMDAS order works and allow for strategic calculation shortcuts
- DecimalsFractionsDecimals are alternative representations of fractions, with conversion methods between both forms
- Number System ClassificationAll OperationsUnderstanding number types helps determine which operations and properties apply
- Rational NumbersFractions and DecimalsFractions and terminating/repeating decimals are different representations of rational numbers
- Prime NumbersNumber System SecurityPrime numbers form the foundation of modern cryptography and digital security systems
- Distributive PropertyMental Math StrategiesDistributive property enables quick mental calculations and algebraic manipulation
Diagrams
Complete Arithmetic Concepts Map
Comprehensive mind map showing all major arithmetic concepts and their hierarchical relationships, from basic number systems to advanced properties and operations
Prime Number Identification Process
Step-by-step flowchart for determining whether a given number is prime or composite, following the systematic approach taught for UPCAT preparation
PEMDAS Order of Operations Decision Tree
Decision tree showing the correct order for evaluating arithmetic expressions using PEMDAS rules, essential for solving complex mathematical problems accurately
LCM and GCF Calculation Methods
Comprehensive flowchart showing different methods for calculating LCM and GCF, including both listing methods and prime factorization approach with the key relationship formula
Distribution of Arithmetic Topics in UPCAT Exams
Statistical breakdown of how different arithmetic topics typically appear in UPCAT mathematics examinations, helping students prioritize their study time effectively