130 LearnersLast updated on July 25th, 2025
Arithmetic Operations
Mathematics has four basic arithmetic operations that form the basis of mathematics itself—addition, subtraction, multiplication, and division. These operations are used in our everyday lives for calculating bills, sharing things, interpreting data, etc.
What are Numbers and Symbols?
Numbers are symbols used to represent values and quantities. Today, we have different numbering systems like Hindu-Arabic, Roman, and Chinese. Even the basic arithmetic operations are symbolized as follows:
|
Operation |
Symbol |
|
Addition |
+ |
|
Subtraction |
- |
|
Multiplication |
× |
|
Division |
÷ |
|
Equal to |
= |
What are the Basic Operations of Arithmetic?
Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations. These operations can be applied to all kinds of numbers, like natural numbers, rational numbers, fractions, and even complex numbers.
Addition: Addition is used to find the sum of two or more numbers. The numbers that get added are called addends, and the symbol used to represent addition is the plus symbol (+). In the equation 10 + 5 = 15, 10 and 5 are addends and 15 is the sum.
Subtraction: Subtraction is represented by the minus symbol (-) and used to find the difference between two numbers. In the equation 10 - 6 = 4, 10 is the minuend, 6 is the subtrahend, and 4 is the difference.
Multiplication: Multiplication is the process of calculating the total of one number taken a specific number of times. The process is also called repeated addition. For e.g., 5 × 5 can be written as 5 + 5 + 5 + 5 + 5 = 25. Multiplication is represented by the symbol “×”.
Division: Division is the process of determining how many times one number is contained within another. It is the reverse operation of multiplication and is represented using the symbol “÷” or “/”. For example, 10 ÷ 2 means continuously subtracting 10 by 2,
10 - 2 = 8
8 - 2 = 6
6 - 2 = 4
4 - 2 = 2
2 - 2 = 0
As there are 5 steps, 10 ÷ 2 = 5.
What are Mathematical Operations?
As with the arithmetic operations, there are four mathematical operations. The mathematical operations include the arithmetic operations. The basic mathematical operations are:
- Percentages
- Ratio and Proportions
- Permutations
- Combinations
What are Arithmetic Properties?
Arithmetic properties are fundamental rules that regulate how numbers behave while performing the basic arithmetic operations. The arithmetic properties are given below:
- Closure Property:
- Commutative Property
- Associative Property
- Distributive Property
- Additive Identity
- Multiplicative Identity
- Additive Inverse
- Multiplicative Inverse
Closure Property: When we perform basic arithmetic operations on a set of numbers, the result always belongs to the same set. For example, when two integers p and q are added or subtracted, the result will always be an integer. This is called the closure property and can be written as:
p + q ∈ Z
p - q ∈ Z
p × q ∈ Z
Commutative Property: The commutative property states that the order of the values doesn't affect the result. It is applicable for both addition and multiplication. That is, a + b = b + a and a × b = b × a.
Associative Property: The associative property states that the way of grouping the numbers in addition and multiplication will not affect the result. Which means, a + (b + c) = (a + b) + c) and a × (b × c) = (a × b) × c).
Distributive Property: The distributive property states that multiplying a number by a sum is equal to multiplying the number by each term in the sum separately and then adding the products. That is, a × (b + c) = (a × b) + (a × c) and a × (b - c) = (a × b) - (a × c)
Additive Identity: The sum of any number with zero is the number itself; that is, a + 0 = a.
Multiplicative Identity: The product of any number with 1 is the number itself, a × 1 = a.
Additive Inverse: The additive inverse states that the sum of any number with the negative of the number itself is zero. That is a + (-a) = 0.
Multiplicative Inverse: The multiplicative inverse states that the product of a number with its reciprocal is 1. That is, a ×1/a = 1.
Real-world Applications of Arithmetic Operations
Addition, subtraction, multiplication, and division are the arithmetic operations, and these are the fundamental skills used in our everyday life. Let’s learn some applications of arithmetic operations.
- Basic arithmetic operations are used to manage household expenses, save money, pay bills, etc.
- When shopping, to calculate the discount percentage, we use arithmetic operations.
- In cooking, we use arithmetic operations to adjust the amount and number of ingredients based on the dish and the number of servings.
- In engineering, arithmetic operations are used in structural design, programming, and data analysis.
Common Mistakes and How to Avoid Them in Arithmetic Operations
Arithmetic operations are used extensively in our daily lives. Therefore, we cannot afford to make any mistakes while dealing with them. This makes it that much more important to go through some common mistakes given below so we can avoid them.
Mistake 1
Misaligning Place Values
In both addition and subtraction, place values play an important role in understanding the alignment of numbers. If the students make any error in understanding the place value of the digit, it can lead to errors. Always double-check the answer after the calculation.
Mistake 2
Skipping Steps in Multiplication
In multiplication, students often skip the steps or jump the steps for not wasting time. In this way, many students make wrong calculations by skipping steps. It is always advisable to make proper steps for counting in multiplication.
Mistake 3
Subtracting the Smaller Number from the Larger One
While subtracting, it is important to know that the subtrahend is always subtracted from the minuend. In basic subtraction, the minuend is always greater than the subtrahend.
Mistake 4
Mistaking Multiplication for Addition
Students tend to confuse addition with multiplication and vice versa. Every operation has its symbol, and it is important to recognize and interpret them correctly.
Mistake 5
Calculation Errors
Calculation errors can happen due to carelessness or when we are overwhelmed by numbers. To avoid this mistake, we should always try and stay alert and keep the calculations precise.
Solved Examples of Arithmetic Operations
problem 1
Find the sum of 489 and 563
The sum of 489 and 563 is 1052
Explanation
Step 1: Add the units, 9 + 3 = 12. Write down 2 and carry over 1.
Step 2: Add the tens: 8 + 6 = 14; add the carried over 1 to get 15. Write down 5 and carry over 1.
Step 3: Add the hundreds: 4 + 5 = 9; then add the carried over 1 to get 10.
Combine the numbers to get the result, 1052.
problem 2
Find the difference between 950 and 426?
The difference between 950 and 426 is 524
Explanation
Step 1: Subtract the units. Since 6 cannot be subtracted from 0, we need to borrow 1 from the tens place digit, which is 5. After borrowing, the 0 in the units place becomes 10 and the 5 in the tens place becomes 4. Now 6 can be subtracted from 10. So, 10 − 6 = 4.
Step 2: Subtract ten. After borrowing, 4 − 2 = 2.
Step 3: Subtract the hundreds: 9 − 4 = 5.
Combine the results to form 524.
problem 3
Find the product of 23 and 5?
The product of 23 and 5 is 115
Explanation
Step 1: Multiply the ones: 5 × 3 = 15. Write down 5 and carry over
Step 2: Multiply the tens: 5 × 2 = 10; then add the carried-over 1 to get 11
Combine these to get 115.
problem 4
Divide 165 by 5?
165 ÷ 5 = 33
Explanation
Step 1: Determine how many times 5 goes into 16 (the first two digits): 5 × 3 = 15 with a remainder of 1.
Step 2: Bring down the next digit (5) to get 15.
Step 3:15 × 3 = 15 fits exactly into 15.
The quotient is 33.
problem 5
Find the sum of 23, 56, and 89
The sum of 23, 56, and 89 is 168
Explanation
Step 1: Add the first two numbers: 23 + 56 = 79.
Step 2: Add the result to the third number: 79 + 89 = 168
The total sum is 168.
FAQs on Arithmetic Operations
1.What are the four basic arithmetic operations?
2.What is the product of a number and zero?
3.What is the associative property?
4.What is the difference between subtraction and addition?
5.What is the commutative property?
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
