This chapter focuses on understanding and mastering the fundamental operations of mathematics: addition, subtraction, multiplication, and division. These operations are the building blocks for solving complex problems and are essential for day-to-day activities. Below, we delve into each operation, including methods, examples, and tips for accuracy.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. The numbers being added are called addends, and the result is the sum.

Key Points

• Addition is commutative: a + b = b + a
• Addition is associative: (a + b) + c = a + (b + c)
• Adding zero to a number does not change its value: a + 0 = a

Example

If you have 235 apples and you buy 128 more, the total number of apples is:

235 + 128 = 363

Subtraction

Subtraction is the process of finding the difference between two numbers. The number from which another number is subtracted is the minuend, the number subtracted is the subtrahend, and the result is the difference.

Key Points

• Subtraction is not commutative: a - b ≠ b - a
• Subtraction is not associative: (a - b) - c ≠ a - (b - c)
• Subtracting zero from a number does not change its value: a - 0 = a

Example

If you have 500 rupees and spend 185 rupees, the remaining amount is:

500 - 185 = 315

Multiplication

Multiplication is a shortcut for repeated addition. The numbers being multiplied are called factors, and the result is the product.

Key Points

• Multiplication is commutative: a × b = b × a
• Multiplication is associative: (a × b) × c = a × (b × c)
• Multiplication by 1 does not change the value: a × 1 = a
• Multiplication by 0 results in 0: a × 0 = 0

Example

If a box contains 12 pens and there are 15 such boxes, the total number of pens is:

12 × 15 = 180

Division

Division is the process of splitting a number into equal parts. The number being divided is the dividend, the number by which it is divided is the divisor, and the result is the quotient. Any leftover part is called the remainder.

Key Points

• Division is not commutative: a ÷ b ≠ b ÷ a
• Division is not associative: (a ÷ b) ÷ c ≠ a ÷ (b ÷ c)
• Division by 1 does not change the value: a ÷ 1 = a
• Division by 0 is undefined.

Example

If you have 56 candies and divide them equally among 8 children, each child gets:

56 ÷ 8 = 7

Order of Operations

When solving mathematical expressions involving multiple operations, follow the BODMAS rule:

• Brackets
• Orders (powers and roots)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Example

Simplify the expression: 8 + (3 × 2) ÷ 6

Solution:

1. Calculate inside brackets: 3 × 2 = 6
2. Perform division: 6 ÷ 6 = 1
3. Add the result: 8 + 1 = 9

Tips for Accurate Computation

• Write numbers clearly to avoid errors.
• Double-check your calculations, especially with subtraction and division.
• Use estimation to verify if your answer is reasonable.
• Practice mental math to improve speed and confidence.

Practice Problems

1. Find the sum of 456 and 789.
2. Subtract 298 from 645.
3. Multiply 34 by 19.
4. Divide 144 by 12.
5. Simplify: 25 + (18 ÷ 3) × 2.

Conclusion

Mastering computation operations is essential for solving mathematical problems effectively. Practice regularly and apply these operations in real-life scenarios to strengthen your understanding and accuracy.