Arithmetic Operations formulas properties and solved examples
The concept of arithmetic operations plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding how to perform arithmetic operations quickly and accurately helps students succeed in various subjects and is essential for solving word problems, managing money, and preparing for competitive exams.
What Is Arithmetic Operations?
An arithmetic operation is defined as a fundamental mathematical process used to manipulate numbers. The four main arithmetic operations are addition (+), subtraction (−), multiplication (×), and division (÷). You’ll find this concept applied in areas such as basic calculations, number patterns, and problem-solving in subjects like physics and computer science.
Key Formula for Arithmetic Operations
Here are the standard expressions:
| Operation | Symbol | Example | Result |
|---|---|---|---|
| Addition | + | 7 + 5 | 12 |
| Subtraction | − | 16 − 9 | 7 |
| Multiplication | × | 6 × 3 | 18 |
| Division | ÷ | 20 ÷ 4 | 5 |
Types & Properties of Arithmetic Operations
The four types of arithmetic operations—addition, subtraction, multiplication, and division—come with important properties that make calculations easier:
- Commutative Property (Addition & Multiplication): Order does not affect result. E.g., 3 + 5 = 5 + 3, 2 × 4 = 4 × 2
- Associative Property (Addition & Multiplication): Grouping does not affect result. E.g., (2 + 3) + 4 = 2 + (3 + 4)
- Distributive Property (Multiplication over Addition): E.g., 2 × (3 + 4) = 2 × 3 + 2 × 4
Order of Arithmetic Operations (BODMAS Rule)
When a calculation includes different arithmetic operations, the BODMAS rule decides what to solve first. BODMAS stands for Brackets, Orders, Division/Multiplication, Addition/Subtraction. Always compute brackets and orders (powers, roots) first, then division/multiplication from left to right, and finally addition/subtraction from left to right.
Example: 3 + 6 × (5 + 4) ÷ 32 − 7
1. Solve inside the brackets: 5 + 4 = 92. Calculate orders: 32 = 9
3. Multiply: 6 × 9 = 54
4. Divide: 54 ÷ 9 = 6
5. Add/Subtract: 3 + 6 − 7 = 2
Correct solution per BODMAS: 2
Step-by-Step Illustration
- Given: \( 8 + 4 \times 2 \)
- Then add: 8 + 8 = 16
Examples in Real Life
| Situation | Arithmetic Operation | Explanation |
|---|---|---|
| Shopping | Addition | Total price = sum of all items |
| Bank Withdrawal | Subtraction | Balance = Old balance − Amount withdrawn |
| Splitting a bill | Division | Share per person = Total bill ÷ Number of friends |
| Finding area (rectangle) | Multiplication | Area = Length × Breadth |
Speed Trick or Vedic Shortcut
Here’s a quick shortcut for multiplying numbers ending with 5:
Example Trick: To calculate 25 × 25:
- Take the first digit (2). Add 1 to it: 2 + 1 = 3.
- Multiply the result by the first digit: 2 × 3 = 6.
- Place 25 at the end. Final answer: 625.
Tricks like this help you work faster, especially in MCQs and school math competitions. Vedantu’s teachers share more time-saving tips during live sessions!
Try These Yourself
- Add 123 and 456.
- Subtract 89 from 150.
- Multiply 13 by 7.
- Divide 84 by 6.
- Solve: 4 × (5 + 3) − 2.
Frequent Errors and Misunderstandings
- Forgetting the BODMAS/PEMDAS order while solving mixed questions.
- Incorrect sign usage for subtraction and division with negatives.
- Adding instead of multiplying repeated additions.
- Division mistakes when divisor is zero (cannot divide by zero!).
Relation to Other Concepts
The idea of arithmetic operations connects closely with topics such as Decimal Number System and Fractions and Percentages. Mastering arithmetic makes it easier to solve equations, tackle word problems, and learn higher-level topics like algebra and number theory.
Classroom Tip
A quick way to remember the BODMAS rule is to use the phrase “Brackets Over Division, Multiplication, Addition, Subtraction.” Teachers on Vedantu use colorful charts and hands-on puzzles to make these rules stick in your memory!
We explored arithmetic operations—from definition, formulas, step-by-step solutions, speed tricks, and common errors, to how they link with other subjects. Continue practicing on Vedantu to become confident and fast in using these operations while solving maths problems every day!
Explore related concepts on Vedantu:
BODMAS Rule |
Commutative Property |
Fraction to Percent |
Decimal Number System
FAQs on Understanding Arithmetic Operations in Mathematics
1. What are arithmetic operations in maths?
Arithmetic operations are the basic mathematical operations used to combine numbers: addition, subtraction, multiplication, and division.
These operations form the foundation of arithmetic and are used to perform calculations in everyday life and higher mathematics.
- Addition (+): Combining numbers
- Subtraction (−): Finding the difference
- Multiplication (×): Repeated addition
- Division (÷): Equal sharing or grouping
2. What is the order of arithmetic operations (BODMAS or PEMDAS)?
The order of arithmetic operations follows the rule BODMAS/PEMDAS, which determines the correct sequence of calculations.
- B – Brackets (Parentheses)
- O – Orders (Powers/Exponents)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction
Example: 6 + 2 × 3 = 6 + 6 = 12.
3. What is addition in arithmetic?
Addition is the arithmetic operation of combining two or more numbers to find their total or sum.
The symbol for addition is +, and the result is called the sum.
Example:
7 + 5 = 12
Addition follows important properties:
- Commutative property: a + b = b + a
- Associative property: (a + b) + c = a + (b + c)
4. What is subtraction in arithmetic?
Subtraction is the arithmetic operation used to find the difference between two numbers.
The symbol for subtraction is −, and the result is called the difference.
Example:
15 − 8 = 7
Unlike addition, subtraction is not commutative because 15 − 8 ≠ 8 − 15.
5. What is multiplication in arithmetic?
Multiplication is the arithmetic operation of repeated addition of equal groups.
The symbol for multiplication is × or *, and the result is called the product.
Example:
4 × 3 means 4 added 3 times: 4 + 4 + 4 = 12.
Key properties:
- Commutative: a × b = b × a
- Associative: (a × b) × c = a × (b × c)
- Distributive: a(b + c) = ab + ac
6. What is division in arithmetic?
Division is the arithmetic operation of splitting a number into equal parts or finding how many times one number fits into another.
The symbol for division is ÷ or /, and the result is called the quotient.
Example:
20 ÷ 4 = 5
Division by zero is undefined because no number multiplied by 0 gives a non-zero result.
7. What is the difference between multiplication and division?
Multiplication combines equal groups, while division splits a quantity into equal parts.
- Multiplication: Finds the total (e.g., 6 × 4 = 24)
- Division: Finds how many groups (24 ÷ 4 = 6)
8. How do you solve arithmetic expressions step by step?
To solve arithmetic expressions correctly, follow the order of operations (BODMAS/PEMDAS) step by step.
Steps:
- Solve brackets first
- Calculate exponents (if any)
- Perform division and multiplication (left to right)
- Perform addition and subtraction (left to right)
12 ÷ 3 + 2 × 4 = 4 + 8 = 12.
9. What are the basic properties of arithmetic operations?
The basic properties of arithmetic operations include the commutative, associative, distributive, identity, and inverse properties.
- Commutative: a + b = b + a; a × b = b × a
- Associative: (a + b) + c = a + (b + c)
- Distributive: a(b + c) = ab + ac
- Identity: a + 0 = a; a × 1 = a
- Inverse: a − a = 0; a ÷ a = 1 (a ≠ 0)
10. What are common mistakes in arithmetic operations?
Common mistakes in arithmetic operations usually involve ignoring the order of operations or miscalculating basic facts.
- Not following BODMAS/PEMDAS
- Confusing multiplication and addition (e.g., 2 + 3 × 4)
- Dividing by zero
- Sign errors with negative numbers
