Simplification

Simplification means making something easier to understand or interpret. As the name suggests, simplification makes things simpler. However, simplification is also an important topic in the quantitative section of the CLAT examination. About 35% of the quantitative section is made up of simplification questions. These questions check the ability of students to handle numbers.

Simplification questions aren’t very hard, but they could prove to be time consuming and lengthy. However, you can easily tackle these types of questions with the help of simplification formulas. The sub-topics that fall under simplification are percentages, digital sum, squares and cubes, approximation, etc.

Simplification

Simplification is making things less complicated. This technique comes in handy when one needs to perform a great number of calculations in less time. Hence, the simplification abilities of an aspirant are tested in the CLAT exam.

Simplification is a pretty easy topic but solving simplification questions is time-consuming. But learning a few tricks and simplifying formulas would help you solve many questions from the quantitative section of CLAT and leave you with enough time for other hard topics.

The simplification questions from any sub-category can be generalised into two types.

The two types are as follows:

In the first type of question, a problem and an answer are given, but one or more quantities from the problem side are missing. The students need to form equations and find out the missing quantity. Only a problem is given in the second type of question, and no quantities from the problem are missing. The student needs to simplify this problem and come up with an answer.

There are a few rules or formulas a student should keep in mind while solving simplification questions. These formulas help the aspirant simplify calculations and solve questions in less time.

Formulas for Simplification

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

For Example: Find ⅓ of 99.

Answer: 33

Explanation: 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.

Conclusion

Simplification means making things less complicated. The topic simplification covers about 35% of the quantitative section of the CLAT examining. Simplification questions are easy to solve however are time-consuming and lengthy. Simplification formulas and tricks could help solve these questions quicker and more accurately.

Simplification covers topics such as percentage, digital sum, square roots and cube roots, HCF, and LCM. An aspirant should have memorised squares and cubes at least up to 30. There are five basic rules in simplification that help evaluate the questions quicker. The PEMDAS law should be followed while solving any equations containing mathematical operations.