Overview: Simplification | Quantitative Techniques for CLAT PDF Download

Simplification and Approximation

One of the simpler topics in the numerical ability area is simplification and approximation, and the only way to complete questions from this section quickly is by efficient calculation. The major goal of the questions on the approximation and simplification topic is to assess a candidate’s aptitude for working with numbers and doing simple computations.
Long decimal numbers and calculations are used in the questions to confound the applicants, however this is one of the areas where a candidate can perform best without making mistakes and yet receive a high score.
There are several fundamental strategies and techniques that can be used to answer the approximation and simplification questions in order to ensure that the candidate does not lose marks in this topic.

• Always use the BODMAS rule to solve situations involving approximation or simplification.
• Use a rounded-off value for numbers that are presented in decimal format. For instance, 35.72 can be read as 66, 16.10 as 15, etc.
• For applicants, learning the tables up to at least 20 can be very beneficial and time-saving.
• Keep in mind the fundamentally crucial formulas that might be used to this situation:
  • (a+b)² = a² + b² + 2ab
  • (a-b)² = a² + b² – 2ab
  • a² – b² = (a+b) (a-b)
  • a³ + b³ = (a+b) (a² – ab + b²)
  • (a+b)³ = a³ + b³ + 3ab (a+b)
  • (a-b)³ = a³ – b³ – 3ab (a-b)

What Is BODMAS?

BODMAS is an acronym for a math rule that represents the order of operations. Any simplification or approximation questions need to be solved in the following order:

• B – Brackets
• O – Of
• D – Division
• M – Multiplication
• A – Addition
• S – Subtraction

Different Ways of Asking Simplification Questions

There are two ways to phrase the questions about simplification:

• Missing numbers: Candidates must complete an equation that is either on the left-hand side (LHS) or the right-hand side (RHS) of the paper (Right-hand side). For instance, 18% of 125 x 9 % of 25 = _____ + 100. Candidates must complete the blanks.
• Making the equation simpler: The direct method of providing an equation and solving it to obtain the solution is the second way that the issues about simplification may be posed. As an example, 500 + 2000 ÷ 40 x 50 = ? Candidates must respond to these questions by choosing what appears in the place of the question mark (?).

Formulas for Simplification

Replace the “of” phrase in the question with division (÷) or multiplication (×).

Example: Find ⅓ of 99.
Sol: We substitute the “of” phrase in question by multiplication here.
Hence it becomes (⅓) × 99 = 33.

The PEMDAS Rule

• While simplifying a question with multiple operations, there is a rule which tells us which operation to solve first. It’s the PEMDAS rule.
• PEMDAS is an acronym for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
• We have to solve the parentheses first, then the exponents, followed by multiplication, and so on.
• Let us take an example that combines both of the above rules.
• Find (10-5) of 50.
• According to formula 1, we substitute the “of” with multiplication.
• The problem becomes (10-5) × 50.
• Now according to the PEMDAS rule, we need to solve the parentheses first, which will make the problem (5) × 50.
• Now after performing the multiplication, we get the answer to the question as 250.

The left- associativity of Multiplication and Division

• This is an important addition to the PEMDAS rule. While solving simplification questions, MD of PEMDAS does not mean that you have to solve all the multiplication before division. You solve whichever operator comes first from the left side. This is called left associativity.
• For example: Simplify 8÷4×5.
• Here we don’t perform multiplication first just because M appears before D in PEMDAS.
• We solve division first as it is the first operation from the left.
• So, the problem becomes 2×5, and now the answer is 10.

The left-associativity of Addition and Subtraction:

• Just like multiple action and division, left-associativity applies to addition and subtraction operations. You solve whichever one you encounter first from the left.

For example: Simplify 10-5+2.

• Subtraction appears first, so after solving that, our problem becomes 5+2, which is equal to 7.

Rounding a fraction to the nearest integer:

• This is the last of five basic simplification formulas. Sometimes while performing a calculation, we end up with fractional numbers. Fractional numbers complicate further calculations. So, if a fractional number is really close to an integer, you can round it to that integer.

Example: 15.96 × 2.87 could become 15 × three, and the answer will be 45.
These were the basic simplification formulas.

Other Topics in Simplification

Simplification also covers several other topics. Let’s take a look at them.

Number system: Under the number system, simplification questions could be about the classification of numbers, divisibility test for number, the rules for division and remainder, etc.
Let’s look at the classification of numbers.

Natural number: The numbers that are used for counting that start with one and end with infinity are natural numbers.

• Whole numbers: Natural numbers along with the number 0.
• Prime numbers: A prime number isn’t divisible by any other number besides itself.
• Composite numbers: Any numbers which aren’t prime are said to be composite.
• Even numbers: Numbers who are completely divisible by 2
• Odd numbers: Numbers who leave remainder 1 when divided with 2.

Strategies for Solving Simplification Problems

• Follow Order of Operations: Adhere to order of operations (PEMDAS/BODMAS) for accurate simplification.
• Step-by-Step Approach: Break down expressions into steps, solving each part systematically.
• Mind Signs: Pay attention to positive and negative signs.
• Calculator Usage: While calculators help, understand steps to avoid blindly relying on them.
• Regular Practice: Practice various simplification problems.

Conclusion

Simplification is essential, enhancing math problem-solving and laying foundation for advanced topics. Master order of operations and practice problems to handle expressions confidently. Prepare for CLAT with strategies mentioned. With practice, solve simplification problems, boosting performance in Quantitative Aptitude.