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352 LearnersLast updated on December 6, 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?
Arithmetic operations refer to the four fundamental processes used to add, subtract, multiply, or divide two or more quantities. They involve understanding numbers and the order of operations, which is essential for all other areas of mathematics, including algebra, data handling, and geometry. No mathematical problem can be solved accurately without following these arithmetic rules. The four primary operations, such as addition, subtraction, multiplication, and division, each have specific symbols, as shown in the image below.
|
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 types of numbers, including natural numbers, rational numbers, fractions, and 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 example, 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 repeatedly subtracting 2 from 10 until zero is reached.
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?
Mathematical operations include arithmetic operations and also extend to:
- Percentages
- Ratio and proportions
- Permutations
- Combinations
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What are Arithmetic Properties?
Arithmetic properties are fundamental rules that regulate how numbers behave while performing the basic arithmetic operations. The fundamental arithmetic properties include:
- 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, where Z represents the set of all integers.
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, \(a ×1/a = 1\).
Arithmetic Operations with Whole Numbers
Whole numbers allow us to carry out the four basic arithmetic operations easily. These numbers begin at 0 and extend infinitely, without any fractional or decimal parts. When we add two or more whole numbers, the result is always greater than the sum of the addends.
For example, adding 4, 5, and 6 gives,
4 + 5 + 6 = 9 + 6 = 15, and here, 15 is larger than all three numbers.
Adding 0 to any whole number leaves it unchanged, and adding 1 to a whole number gives its following consecutive number, also known as its successor. Its following consecutive number, also known as its successor. For whole numbers, subtraction is performed by taking a smaller number from a larger one, yielding a difference that is less than the minuend. Subtracting 0 from any number leaves it unchanged, and subtracting 1 gives the number’s predecessor.
Multiplication of whole numbers can be done using multiplication tables. The product is typically greater than both numbers, except when multiplying by 1 or 0. Any number multiplied by 0 gives 0, while multiplying by 1 returns the same number. When dividing whole numbers, the result may or may not be a whole number. If the quotient is a whole number, it means the dividend is a multiple of the divisor. Otherwise, the quotient will be a decimal.
Arithmetic Operations with Rational Numbers
Arithmetic operations on rational numbers follow the same rules as those for whole numbers. The key difference is that rational numbers are written in the form p/q, where p and q are integers and q ≠ 0. When adding or subtracting rational numbers, we must first find the LCM of the denominators.
Tips and Tricks to Master Arithmetic Operations
Follow these tips and tricks to master the arithmetic operations such as addition, subtraction, multiplication and division.
- While performing addition, you can round the numbers to the nearest 10 multiple and then make adjustments. For example, 49 + 28 ≈ (50 + 30) - 3 = 77.
- While performing subtraction, use the borrow strategy. Rewrite the given subtraction problem vertically and borrow carefully.
- For mastering multiplication, memorize all the tables till 12.
- While dividing, use the place value. Perform the division step by step for thousands, hundreds, tens and ones.
- Keep on practicing mental math every day to build fluency. Play math games like Sudoku, math puzzles etc...
- Parents can encourage students to use puzzle-based learning methods.
- Teachers can conduct classroom activities to strengthen mental math skills.
- Children can use rounding or breaking numbers to solve problems faster.
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 simple subtraction examples, the minuend is typically greater than the subtrahend to avoid negative results.
Mistake 4
Mistaking multiplication for addition
Students often 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 often occur due to carelessness or being overwhelmed by numbers. To avoid this mistake, we should always try and stay alert and keep the calculations precise.
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.
- In banking, we use addition for deposits, subtraction for withdrawals, multiplication for interest calculations and division for splitting payments.
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 1.
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: 5 goes into 15 exactly 3 times. Final quotient remains 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.
