Introduction to Vedic Mathematics

Simplification of Numerical Expressions

Simplifying numerical expressions is a key mathematical skill that streamlines complex calculations into manageable steps. Whether you're solving equations or evaluating formulas, simplification ensures accuracy and efficiency.

What is Simplification?

Simplification involves reducing a mathematical expression to its simplest form. This often means performing operations like addition, subtraction, multiplication, and division in the correct order, as defined by the BODMAS or PEMDAS rule:

• BODMAS: Brackets, Orders (exponents), Division and Multiplication, Addition and Subtraction.
• PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Steps to Simplify Numerical Expressions

1. Solve Inside Parentheses: Simplify expressions within parentheses or brackets first.
   Example: 
   $(8 + 4) \times 2 = 12 \times 2 = 24$

2. Address Exponents: Calculate powers or roots next.
   Example: 
   $2^3 + 4 = 8 + 4 = 12$

3. Perform Multiplication and Division: Work from left to right, handling these operations as they appear.
   Example: 
   $16 \div 4 \times 2 = 4 \times 2 = 8$

4. Complete Addition and Subtraction: Finish by performing these operations from left to right.
   Example: 
   $10 + 5 - 3 = 15 - 3 = 12$

Tips for Accurate Simplification

• Be Methodical: Follow the order of operations step-by-step. Skipping steps can lead to errors.
• Recheck Your Work: A quick review helps identify mistakes.
• Use Visual Aids: For beginners, tools like number lines or diagrams can clarify processes.

Example

Simplify 

$(5 + 3) \times 2^2 - 6 \div 3$

1. Parentheses: 
   $(5 + 3) = 8$
2. Exponents: 
   $2^2 = 4$
3. Multiplication and Division: 
   $8 \times 4 = 32$$6 \div 3 = 2$
4. Addition and Subtraction: 
   $32 - 2 = 30$

Result: 

$30$