Simplification All Concepts & Tricks | BODMAS | Unit Digit | Digit Sum | Surds & Indices | Fraction

Introduction

This tutorial provides a comprehensive guide to simplifying mathematical expressions using various methods, including BODMAS, unit digit, digit sum, surds, indices, and fractions. Understanding these concepts is essential for efficiently solving problems in competitive exams and improving your math skills.

Step 1: Understand BODMAS Rules

BODMAS is an acronym that helps remember the order of operations in mathematics:

• Brackets
• Orders (i.e., powers and roots)
• Division
• Multiplication
• Addition
• Subtraction

Practical Tips

• Always solve operations inside brackets first.
• For orders, calculate powers and roots before moving to multiplication and division.

Step 2: Apply Unit Digit Method

This method simplifies calculations by focusing only on the unit digits of numbers.

Steps

1. Identify the unit digit of each number in the operation.
2. Perform the operation using only these unit digits.
3. Determine the unit digit of the result.

Example

For the multiplication of 23 and 47:

• Unit digit of 23 is 3
• Unit digit of 47 is 7
• Calculate 3 × 7 = 21
• The unit digit is 1.

Step 3: Utilize Digit Sum Method

This method is helpful for simplifying large numbers by adding their digits.

Steps

1. Add the digits of the number together.
2. If the result is a multi-digit number, sum the digits again.
3. Continue until you achieve a single-digit number.

Example

For the number 987:

• 9 + 8 + 7 = 24
• 2 + 4 = 6

Step 4: Learn Square and Square Roots

Knowing perfect squares and their roots can speed up calculations.

Key Squares to Remember

• 1² = 1
• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 10² = 100

Practical Tip

• For quick estimates, round numbers to the nearest perfect square.

Step 5: Master Surds and Indices

Surds are irrational numbers that can't be simplified to remove the root. Indices represent powers.

Concepts

• Simplify surds by factoring out perfect squares.
• Use the laws of indices for multiplication and division.

Example

To simplify √50:

• √50 = √(25 × 2) = √25 × √2 = 5√2

Step 6: Simplify Percentages

When working with percentages, convert them into fractions or decimals for easier calculations.

Steps

1. Convert the percentage to a fraction (e.g., 25% = 25/100 = 1/4).
2. Perform calculations using the fraction.

Example

To find 20% of 50:

• Convert 20% to 1/5.
• Multiply: 50 × 1/5 = 10.

Step 7: Handle Fraction Simplification

Simplifying fractions can make calculations straightforward.

Steps

1. Find the greatest common divisor (GCD) of the numerator and denominator.
2. Divide both by the GCD.

Example

To simplify 8/12:

• GCD of 8 and 12 is 4.
• 8 ÷ 4 = 2, 12 ÷ 4 = 3, so 8/12 = 2/3.

Step 8: Simplify Decimals

Converting decimals to fractions can help in simplifications.

Steps

1. Write the decimal as a fraction (e.g., 0.75 = 75/100).
2. Simplify the fraction as shown in the previous step.

Conclusion

By mastering these simplification techniques—BODMAS, unit digits, digit sums, squares, surds, percentages, fractions, and decimals—you can enhance your mathematical skills and improve efficiency in exams. Practice these methods with various examples to gain confidence and proficiency in simplifications.