Simplification Questions for IBPS RRB PO and Clerk

Simplification Questions for IBPS RRB PO and Clerk

Simplification Questions for IBPS RRB PO and Clerk test your ability to quickly and accurately perform calculations and apply mathematical rules like BODMAS/BIDMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction).

In the context of mathematical operations and expressions, simplification using VBODMAS (also known as BODMAS or PEMDAS) refers to following a specific order of operations to ensure that calculations are performed correctly and consistently. Here is a breakdown of VBODMAS and its application in simplifying expressions:

VBODMAS Order of Operations

VBODMAS stands for:

V: Vinculum (operations inside vinculum or grouping symbols like parentheses, brackets, braces)
B: Brackets (operations inside brackets [])
O: Orders (operations involving exponents or powers)
D: Division (division operations)
M: Multiplication (multiplication operations)
A: Addition (addition operations)
S: Subtraction (subtraction operations)

Example of Simplification Using VBODMAS

1) Let's simplify the expression

Steps:

V (Vinculum): Evaluate operations inside parentheses first. 4 + 2 = 6
B (Brackets): No brackets remaining.
O (Orders): Perform operations involving exponents or powers (if any). None in this case.
D (Division): Perform division operations. 10/2 = 5
M (Multiplication): Perform multiplication operations. 3 × 6 = 18
A (Addition) and S (Subtraction): Perform addition and subtraction operations in sequence. 18 − 5 = 13

2) Simplify the expression:

Steps:

V (Vinculum): Evaluate operations inside parentheses first. 8 − 2 = 6

Now the expression becomes:

B (Brackets): No brackets remaining.
O (Orders): Perform operations involving exponents or powers (if any). None in this case.
D (Division): Perform division operations.

Now the expression is: 3 x 6 + 4
M (Multiplication): Perform multiplication operations. 3 x 6 = 18

Now the expression simplifies to: 18 + 4

A (Addition): Finally, perform addition operations. 18 + 4 = 22

Importance of VBODMAS

Consistency: Following VBODMAS ensures that every person will perform calculations in the same order, reducing confusion and errors.
Accuracy: Ensures that mathematical expressions are evaluated correctly and results are reliable.
Complexity Handling: Essential for handling complex expressions involving multiple operations and variables.

Basic BODMAS-based problems:

1) 15 × 15 + 8 - 12

Solution:

15 × 15 + 8 - 12 = 221

2) 20 ÷ 5 × 4 + 30 - 10

Solution:

20 ÷ 54 + 30 - 10 = 36

3) 64 of 8 ÷ 8 =?

Solution:

64 of 8 ÷ 8 = 64

Square, square root, cube, and cube root-based simplification

1. Simplification with Square Roots:

Basic Rules:

Example:

Simplify √36

Solution: √36 =6 (6×6=36).

Rationalization:

2. Simplification with Squares:

Basic Rules:

3. Simplification with Cube Roots

Basic Rules:

4. Simplification with Cubes

Basic Rules:

Tips for Simplifying Cubes and Cube Roots

Use Prime Factorization: For cube roots, factorize the number into its prime factors to simplify.
Apply Properties: Utilize properties of cubes and cube roots to break down complex expressions.
Check Perfect Cubes: Recognize perfect cubes to simplify cube root calculations quickly.
Practice Regularly: Regular practice helps in mastering these techniques and recognizing patterns.

Solved Examples:

SURDS & INDICES Based Simplification

1. Simplification with Indices

Basic Rules:

2. Simplification with Surds

Basic Rules:

Example:

Combined Indices and Surds-Based Example:

Solved Examples:

Percentage Based Simplification

Tricks:

Solved Examples:

Q1. ?=20% of 25% of 15% of 12000

Solution:

? = 12000 × 0.15 × 0.25 × 0.20 = 90

Q2. 15% of 20% of 600 + (22 × 6) = ? × 5

Solution

15% of 20% of 600 + (22 × 6) = ? × 5

0.15 × 0.2 × 600 + 132 = ? × 5

? × 5 = 18 + 132

? = 150 ÷ 5

Fraction Based SImplification

Simplification involving fractions requires understanding and applying basic arithmetic operations: addition, subtraction, multiplication, and division of fractions. Here's a detailed guide on how to approach these simplifications:

1. Simplifying Fractions

Reducing Fractions: Divide the numerator and the denominator by their greatest common divisor (GCD).
Example:

? = 30

2. Addition and Subtraction of Fractions

Common Denominator: To add or subtract fractions, convert them to have a common denominator.

Example:

3. Multiplication of Fractions

Multiply Numerators and Denominators:

4. Division of Fractions

Multiply by the Reciprocal:

5. Mixed Numbers

Convert to Improper Fractions:

Convert back to mixed numbers if necessary after calculations.

Example:

Solved Examples:

Decimal Based Simplification

1. Understanding Decimal Place Value

Decimal places: The position of a digit to the right of the decimal point represents tenths, hundredths, thousandths, etc.

Example: In 0.456, the digits 4, 5, and 6 are in the tenths, hundredths, and thousandths places, respectively.

2. Converting Decimals to Fractions

Basic Conversion:
- Write the decimal as a fraction with the appropriate power of 10 as the denominator.
- Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD).
- Example : Convert 0.75 to a fraction. 75/100 = 3/4

3. Addition and Subtraction of Decimals

Align Decimal Points: When adding or subtracting decimals, align the decimal points and proceed as with whole numbers.

Example: Add 2.35 and 4.6. 2.30+4.6=6.95

4. Multiplication of Decimals

Multiply as Whole Numbers: Ignore the decimal points and multiply the numbers as if they were whole numbers.
Place the Decimal Point: Count the total number of decimal places in both the numbers being multiplied. Place the decimal point in the result accordingly.
Example: Multiply 1.2 by 3.4.

Solution: 1.2 × 3.4 = 12 × 34 = 408 (ignore decimal points temporarily)

There are 2 decimal places in total (one in 1.2 and one in 3.4).

4084.08

So, 1.2 × 3.4 = 4.08

5. Division of Decimals

Convert to Whole Numbers: Move the decimal point to the right in both the dividend and the divisor until the divisor is a whole number.

Perform Division: Divide as with whole numbers, and place the decimal point in the quotient appropriately.

Example:

Solved Example:

Previous Year Questions Of Simplification Asked in Banking Exams

Tips and Tricks to Solve Simplification Problems

Master BODMAS Rule: Understand and apply the BODMAS rule consistently. This ensures that you perform operations in the correct order.
Work Inside-Out: When faced with complex expressions, start by simplifying expressions within brackets first, then proceed outward.
Priority to Division and Multiplication: In the absence of brackets, prioritize division and multiplication over addition and subtraction. This maintains accuracy in calculations.
Use Approximations: When dealing with large numbers, rounding off can simplify calculations. Be mindful of the level of accuracy required.
Cancel Common Factors: While dealing with fractions, cancel out common factors between the numerator and denominator to simplify.
Practice Mental Math: Develop mental calculation skills for basic arithmetic operations, making it quicker to handle simplification problems.
Solve Parentheses First: Always address operations within parentheses first to maintain the integrity of the expression.
Check Intermediate Steps: Verify your calculations at each step to catch errors early and ensure accuracy in the final result.
Focus on Speed and Accuracy: As simplification is often part of time-bound exams, strike a balance between speed and accuracy. Practice regularly to enhance both aspects.
Understand the Problem Context: For word problems, comprehend the context before attempting to simplify. Translate verbal information into mathematical expressions accurately.

By mastering the concept of simplification and employing these tips and tricks, candidates can enhance their problem-solving abilities and approach mathematical challenges with confidence. Regular practice and a clear understanding of fundamental principles are key to success in simplification problems.

Simplification Questions FAQs

Q1. What is Simplification in Quantitative Aptitude?

Ans. Simplification in Quantitative Aptitude involves reducing an expression or equation to its simplest form. This process makes it easier to work with and understand. Simplification can involve combining like terms, reducing fractions, and performing arithmetic operations to make the expression as concise as possible.

Q2. What is the formula of simplification?

Ans. Simplification in math is a process to make math problems simpler. It involves steps like combining terms or reducing fractions. The way you simplify depends on what type of math you're dealing with, like algebra or basic arithmetic. Just follow the order of operations (BODMAS/BIDMAS) for arithmetic – it helps you decide which math steps to do first. If you have a specific math problem, let me know for more help!

Q3. How do I multiply decimals?

Ans. To multiply decimals: Ignore the decimal points and multiply the numbers as whole numbers. Count the total number of decimal places in both numbers. Place the decimal point in the product so that it has the same number of decimal places.

Q4. What is the process for dividing decimals?

Ans. To divide decimals: Move the decimal point in the divisor to the right until it is a whole number. Move the decimal point in the dividend the same number of places to the right. Divide as with whole numbers, and place the decimal point in the quotient accordingly.

Q5. What are some common mistakes to avoid when simplifying expressions?

Ans. Not aligning decimal points properly in addition and subtraction. Forgetting to apply the distributive property when necessary. Not reducing fractions to their simplest form. Incorrectly handling negative signs. Failing to recognize and combine like terms.

VBODMAS Order of Operations

VBODMAS stands for:

V: Vinculum (operations inside vinculum or grouping symbols like parentheses, brackets, braces)
B: Brackets (operations inside brackets [])
O: Orders (operations involving exponents or powers)
D: Division (division operations)
M: Multiplication (multiplication operations)
A: Addition (addition operations)
S: Subtraction (subtraction operations)

Example of Simplification Using VBODMAS

1) Let's simplify the expression

Steps:

V (Vinculum): Evaluate operations inside parentheses first. 4 + 2 = 6
B (Brackets): No brackets remaining.
O (Orders): Perform operations involving exponents or powers (if any). None in this case.
D (Division): Perform division operations. 10/2 = 5
M (Multiplication): Perform multiplication operations. 3 × 6 = 18
A (Addition) and S (Subtraction): Perform addition and subtraction operations in sequence. 18 − 5 = 13

2) Simplify the expression:

Steps:

V (Vinculum): Evaluate operations inside parentheses first. 8 − 2 = 6

Now the expression becomes:

B (Brackets): No brackets remaining.
O (Orders): Perform operations involving exponents or powers (if any). None in this case.
D (Division): Perform division operations.

Now the expression is: 3 x 6 + 4
M (Multiplication): Perform multiplication operations. 3 x 6 = 18

Now the expression simplifies to: 18 + 4

A (Addition): Finally, perform addition operations. 18 + 4 = 22

Importance of VBODMAS

Consistency: Following VBODMAS ensures that every person will perform calculations in the same order, reducing confusion and errors.
Accuracy: Ensures that mathematical expressions are evaluated correctly and results are reliable.
Complexity Handling: Essential for handling complex expressions involving multiple operations and variables.

Basic BODMAS-based problems:

1) 15 × 15 + 8 - 12

Solution:

15 × 15 + 8 - 12 = 221

2) 20 ÷ 5 × 4 + 30 - 10

Solution:

20 ÷ 54 + 30 - 10 = 36

3) 64 of 8 ÷ 8 =?

Solution:

64 of 8 ÷ 8 = 64

Square, square root, cube, and cube root-based simplification

1. Simplification with Square Roots:

Basic Rules:

Example:

Simplify √36

Solution: √36 =6 (6×6=36).

Rationalization:

2. Simplification with Squares:

Basic Rules:

3. Simplification with Cube Roots

Basic Rules:

4. Simplification with Cubes

Basic Rules:

Tips for Simplifying Cubes and Cube Roots

Use Prime Factorization: For cube roots, factorize the number into its prime factors to simplify.
Apply Properties: Utilize properties of cubes and cube roots to break down complex expressions.
Check Perfect Cubes: Recognize perfect cubes to simplify cube root calculations quickly.
Practice Regularly: Regular practice helps in mastering these techniques and recognizing patterns.

Solved Examples:

SURDS & INDICES Based Simplification

1. Simplification with Indices

Basic Rules:

2. Simplification with Surds

Basic Rules:

Example:

Combined Indices and Surds-Based Example:

Solved Examples:

Percentage Based Simplification

Tricks:

Solved Examples:

Q1. ?=20% of 25% of 15% of 12000

Solution:

? = 12000 × 0.15 × 0.25 × 0.20 = 90

Q2. 15% of 20% of 600 + (22 × 6) = ? × 5

Solution

15% of 20% of 600 + (22 × 6) = ? × 5

0.15 × 0.2 × 600 + 132 = ? × 5

? × 5 = 18 + 132

? = 150 ÷ 5

Fraction Based SImplification

1. Simplifying Fractions

Reducing Fractions: Divide the numerator and the denominator by their greatest common divisor (GCD).
Example:

? = 30

2. Addition and Subtraction of Fractions

Common Denominator: To add or subtract fractions, convert them to have a common denominator.

Example:

3. Multiplication of Fractions

Multiply Numerators and Denominators:

4. Division of Fractions

Multiply by the Reciprocal:

5. Mixed Numbers

Convert to Improper Fractions:

Convert back to mixed numbers if necessary after calculations.

Example:

Solved Examples:

Decimal Based Simplification

1. Understanding Decimal Place Value

Decimal places: The position of a digit to the right of the decimal point represents tenths, hundredths, thousandths, etc.

Example: In 0.456, the digits 4, 5, and 6 are in the tenths, hundredths, and thousandths places, respectively.

2. Converting Decimals to Fractions

Basic Conversion:
- Write the decimal as a fraction with the appropriate power of 10 as the denominator.
- Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD).
- Example : Convert 0.75 to a fraction. 75/100 = 3/4

3. Addition and Subtraction of Decimals

Align Decimal Points: When adding or subtracting decimals, align the decimal points and proceed as with whole numbers.

Example: Add 2.35 and 4.6. 2.30+4.6=6.95

4. Multiplication of Decimals

Multiply as Whole Numbers: Ignore the decimal points and multiply the numbers as if they were whole numbers.
Place the Decimal Point: Count the total number of decimal places in both the numbers being multiplied. Place the decimal point in the result accordingly.
Example: Multiply 1.2 by 3.4.

Solution: 1.2 × 3.4 = 12 × 34 = 408 (ignore decimal points temporarily)

There are 2 decimal places in total (one in 1.2 and one in 3.4).

4084.08

So, 1.2 × 3.4 = 4.08

5. Division of Decimals

Convert to Whole Numbers: Move the decimal point to the right in both the dividend and the divisor until the divisor is a whole number.

Perform Division: Divide as with whole numbers, and place the decimal point in the quotient appropriately.

Example:

Solved Example:

Previous Year Questions Of Simplification Asked in Banking Exams

Tips and Tricks to Solve Simplification Problems

Master BODMAS Rule: Understand and apply the BODMAS rule consistently. This ensures that you perform operations in the correct order.
Work Inside-Out: When faced with complex expressions, start by simplifying expressions within brackets first, then proceed outward.
Priority to Division and Multiplication: In the absence of brackets, prioritize division and multiplication over addition and subtraction. This maintains accuracy in calculations.
Use Approximations: When dealing with large numbers, rounding off can simplify calculations. Be mindful of the level of accuracy required.
Cancel Common Factors: While dealing with fractions, cancel out common factors between the numerator and denominator to simplify.
Practice Mental Math: Develop mental calculation skills for basic arithmetic operations, making it quicker to handle simplification problems.
Solve Parentheses First: Always address operations within parentheses first to maintain the integrity of the expression.
Check Intermediate Steps: Verify your calculations at each step to catch errors early and ensure accuracy in the final result.
Focus on Speed and Accuracy: As simplification is often part of time-bound exams, strike a balance between speed and accuracy. Practice regularly to enhance both aspects.
Understand the Problem Context: For word problems, comprehend the context before attempting to simplify. Translate verbal information into mathematical expressions accurately.