Gain Clarity on Simplification

Various competitive examinations are conducted to recruit employees for honorable job positions as well as many higher education entrance examinations to use quantitative aptitude questions based on simplification to test the aspirants. These simplification problems carry a significant weightage on the paper and the examinees must prepare well beforehand to score the maximum marks out of those questions. Due to their common set pattern, individuals are prone to make mistakes from overconfidence or carelessness. Thus one must be calm and composed while solving simplification problems. 

The idea of Simplification Questions 

Simplification accounts for only a limited set of questions within the mathematical analysis section of an examination paper. These problems are easy and quick to resolve but at the same time very rewarding. The purpose of such simplification queries is to initiate critical thinking of the examinees and to test their basic numerical abilities. Candidates often get overwhelmed when the question tries to distract them with long strings of decimal places or an array of mathematical operators. To eliminate such complex situations we should learn to simplify them. This will minimize the possibility of any error. 

Types of Simplification Problems 

There are two common ways to present numerical problems which require further simplification. In the first pattern, we need to fill a blank space of a given equation. After the blank has been filled with a number it must satisfy the provided equation. Depending on the examiner the blank can be placed either on the left-hand side or the right-hand side of an equation. Let us take an example to elaborate on the case. 

7 x 8 – 54 = 99 – ____ x 2. Here, we have to find out the missing number. This is a simple question that tests out basic numerical abilities. 

The second common variation of simplification problems is the direct approach of asking the solution to a given expression. Here, we have to apply the BODMAS technique to solve an expression that includes an array of mathematical operators. 

Example of this kind of simplification is 5 x (6 + 29 x 5) – 10 = y. Find the value of y. 

Simplification formulas 

Teachers guide the students more cautiously on solving the simplification problems. They provide useful tips to the candidates so that they can solve complex mathematical expressions flawlessly every time.

 It is recommended to use the BODMAS rule while solving quantitative aptitude questions that require simplification. The abbreviation or mnemonic stands for brackets of division, multiplication, addition, and subtraction. It is a generalized method that has been accepted to resolve complex mathematical questions. 

For example, let us consider the expression 7 x (54 – 44) ÷ 2. Here, we need to perform the subtraction before division and multiplication although it comes after them in the chain of priority as per the BODMAS. This is because the minus operation is residing within the brackets. Brackets are the foremost priority in the BODMAS rule. After doing simplification once, the above-mentioned problem will look like 7 x 10 ÷ 2. Next, we will get the answer as 35 after multiplying the quotient by 7.

A quite similar method having the acronym PEMDAS is used less frequently to solve arithmetic problems that have more than one operator. It gives foremost importance to the parenthesis or brackets. Then the exponents or numerical powers follow. Next, we perform any one of the operations – multiplication, division, subtraction, or addition depending on what encounters us first while moving towards the right side. 

Example : 24 – 42 + 3. 5 = 24 – 16 + 3. 5 = 24 – 16 + 15 = 8 + 15 = 4

Applications that necessitate the PEMDAS rule are rare in modern examinations. But just for the sake of learning, we can refer to it. 

Mathematics teachers also encourage their students to memorize basic algebraic formulas. Those formulas extensively simplify algebraic problems when they correctly replace their equivalent complex expressions. 

A few algebraic formulas that we should remember are :

(x – y)3 = x3 – y3 – 3 xy(x – y)

Another trick to solve the simplification sums is to learn the multiplication tables by heart. Remembering tables till 20 helps the aspirants to save time during the assessment. 

We also come across simplification problems that involve decimal numbers. We can simply round off these numbers in the case of MCQ papers where we can guess the correct answer by evaluating its closest solution. For example, 10.7 can be considered as 11 to ease the calculation. 

Conclusion 

Simplification helps us to sharpen our numerical abilities which we develop gradually through cognitive learning in our primary schools. Mastering a few basic rules helps the candidates gain a competitive advantage over others in the exams.