Fundamental Arithmetical Operations
What is Fundamental Arithmetical Operations?
The largest positive integer that divides two or more integers without leaving a remainder.
Key formula / rule: HCF and LCM relation
Key points
- Perform basic arithmetic operations accurately and efficiently.
- Apply divisibility rules to quickly check divisibility.
- Calculate HCF and LCM for given numbers.
- Solve problems involving the order of operations.
Common exam trap
Incorrect application of BODMAS/PEMDAS rule.
Definitions
- Term
HCF (Highest Common Factor)
- Meaning
The largest positive integer that divides two or more integers without leaving a remainder.
- Term
LCM (Least Common Multiple)
- Meaning
The smallest positive integer that is a multiple of two or more integers.
- Term
Divisibility Rule
- Meaning
A rule used to determine whether a number is divisible by another number without performing the division.
Learning objectives
Perform basic arithmetic operations accurately and efficiently.
Apply divisibility rules to quickly check divisibility.
Calculate HCF and LCM for given numbers.
Solve problems involving the order of operations.
Understand different types of numbers and their properties.
Formulae
- Name
HCF and LCM relation
- Note
Applies to two numbers.
- Expression
HCF(a, b) * LCM(a, b) = a * b
- Name
BODMAS Rule
- Note
Order of operations for simplifying expressions.
- Expression
B - Brackets, O - Of, D - Division, M - Multiplication, A - Addition, S - Subtraction
Prerequisites
Basic understanding of numbers
Familiarity with basic arithmetic symbols
Common mistakes
Incorrect application of BODMAS/PEMDAS rule.
Errors in applying divisibility rules, especially for 7, 11, 13.
Calculation errors in HCF and LCM, particularly for larger numbers.
Misinterpreting the question, e.g., finding the sum instead of the product.
Speed-related errors due to lack of practice.
Keywords
Arithmetic Operations
Number System
Divisibility Rules
HCF
LCM
BODMAS
PEMDAS
Integers
Fractions
Remainders
Practice preview
Simplify: 15 + 3 * (8 - 2) / 2…
easy
The ratio of two numbers is 3:5. If their sum is 80, what is the larger number?…
medium
What is the value of 1234 + 5678 - 3456?…
easy