Understanding the important formulas and theorems for the CBSE Class 6 Mathematics exams is crucial for a thorough understanding of the subject. Here is a detailed explanation of some key formulas and theorems that students should remember:

1. Basic Operations:
- Addition: a + b = b + a
- Subtraction: a - b ≠ b - a
- Multiplication: a × b = b × a
- Division: a ÷ b ≠ b ÷ a

2. Factors and Multiples:
- Factors: Any number that divides another number without leaving a remainder is called a factor.
- Multiples: A multiple is a product of a number and any whole number.
- Prime Numbers: A number that has only two factors, 1 and itself.

3. Number Line:
- The number line is a straight line on which numbers are marked at equal intervals.
- It helps in understanding the relative positions and operations of numbers.

4. Shapes and Geometry:
- Rectangle: Area = length × width, Perimeter = 2 × (length + width)
- Square: Area = side × side, Perimeter = 4 × side
- Circle: Area = π × radius^2, Circumference = 2 × π × radius

5. Fractions:
- A fraction represents a part of a whole or a ratio of two quantities.
- Numerator: The number above the line in a fraction.
- Denominator: The number below the line in a fraction.

6. Decimals:
- Decimal numbers represent parts of a whole and are separated by a decimal point.
- Place value: The value of a digit depending on its position in a number.

7. Algebra:
- Algebraic expressions: Expressions that contain variables, constants, and operators.
- Equations: Statements that show equality between two expressions.

8. Data Handling:
- Data: Information collected for analysis or reference.
- Mean: The average of a set of numbers.
- Mode: The number that appears most frequently in a set of numbers.
- Median: The middle number when the data is arranged in ascending or descending order.

9. Simple Equations:
- An equation is a statement that two expressions are equal.
- Solving equations: Finding the value of the variable that satisfies the equation.

10. Ratio and Proportion:
- Ratio: The quantitative relationship between two or more quantities.
- Proportion: An equation that states two ratios are equal.

Remembering and understanding these formulas and theorems will help students solve various mathematical problems and excel in their CBSE Class 6 Mathematics exams. Practice, regular revision, and solving sample papers will further enhance their understanding and problem-solving skills.