A Thorough Guide on Simplification

Simplification means determining the solution by reducing or simplifying it from the complex calculation. Simplification helps to reduce a fraction by cancelling it to the lowest common factor(LCM) for both the numerator and the denominator to its lowest term. It also helps to reduce an algebraic expression by grouping and combining similar terms. Simplifying makes an algebraic equation easy to understand. There are certain rules to simplify a problem based on simplification, also known as the “BODMAS” rule. Simplification helps in eliminating unnecessary variables. It is one of the most important topics studied for the bank and insurance exams.

Simplification

Simplification makes an expressionless complicated and easy to understand or solve. Here are some advantages of solving the problems or equations by simplifying them: 

•  It helps to solve the problems in fewer steps
• By following the rules of simplification, we can reduce complex problems into easier forms
• It is less time-consuming

Relation Between Simplification and Approximation

Simplification means simplifying the expression by reducing it to a simpler form. Approximation means simplifying the mathematical expression to its nearest value, which is not exactly correct. To find the approximate value, we round off the digits in the equations to the nearest value, and simplify the equation using the ‘BODMAS’ rule. The relation between simplification and approximation is that while solving an expression, we simplify the expression and then find the approximate value. Simplification and approximation together help to solve complex problems easily in less time. 

Some important terms under simplification and approximation:

• Vinculum – it is a horizontal line used in mathematical expressions; the line indicates that the expression is grouped together
• Brackets – while solving expression related to simplification, we use three types of brackets, round brackets ( ), curly brackets{ } and box brackets [ ]. The brackets are used in the following order ( ), { } and [ ]
• Surds – to simplify the surd, we express the number under the root sign. Surd is an irrational number
• Indices – it is a power or an exponent which is raised to a number of variables. For example, 4^2, 3^3

Tips and Tricks to Solve Simplification and Approximation

• For the expressions containing decimals, we can find the approximate value, first convert the decimals into integers, and then solve the expression
• In case of problems related to simplification and approximation, always follow the BODMAS rule
• In case of problems, if all the denominators in the fraction are common, then the integer part and the fraction part can be calculated separately
• To save extra time, memorise the tables, at least till 20
• Round off the numbers to simplify the problems
• Always follow the priority order according to the BODMAS rule
• Remember fractional values to solve the questions
• Learn the rules of divisibility to save extra time

Basics of Simplification

The basics of simplification is to use the ‘BODMAS’ rule. The rule is remembered in order to follow it while solving an expression. ‘BODMAS’ stands for:

B – brackets.

O – Order of operation.

D – division.

M – multiplication.

A – addition.

S – subtraction.

It means that while solving an expression, follow the BODMAS rule from left to right, that is, first solve the brackets, then power or roots, then division or multiplication, then addition or subtraction.

Problems Based on Simplification

Q1. 8 + 4 ÷ 2 × 5 = ? 

Using the BODMAS rule, 

Solution: 8 + 4 ÷ 2 × 5 

= 8 + 2 × 5

= 8 + 10 = 18.

The correct answer for the above expression is 18.

Q2. 36 – [18 – {14 – (15 – 4 ÷ 2 × 2) } ]. Simplify the expression.

Using the BODMAS rule,

Solution: 36 – [18 – {14 – (15 – 4 ÷ 2 × 2) } ]

= 36 – [18 – {14 – (15 – 2 × 2)}]

= 36 – [18 – {14 – (15-4)}]

= 36 – [18 – {14 – 11}]

= 36 – [18 – 3]

= 36 – 15 = 21.

The correct answer for the above expression is 21.

Q3. 19 – [4 + {16 – (12 – 2)}]. Simplify the expression.

Using the BODMAS rule,

Solution: 19 – [4 + {16 – (12 – 2)}]

= 19 – [4 + {16 – 10}]

= 19 – [4 +6]

= 19 – 10 = 9.

The correct answer is 9.

Q4. 45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]. Simplify the expression.

Using the BODMAS rule,

Solution: 45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}].

= 45 – [38 – {60 ÷ 3 – 3 ÷3}].

= 45 – [38 – {20 – 1}].

= 45 – [38 – 19.]

= 45 – 19 = 26.

The correct answer is 26.

Conclusion 

Simplification is a process of turning complex expressions into simpler forms. It determines the solution by reducing or simplifying the expression. The rule used for simplifying an equation is called the BODMAS rule. The rule is remembered and is used while solving complex expressions, it is followed from left to right. Simplification is usually used for solving two types of problems: the first type is finding the missing numbers, and the second type is the relation between the numbers and simplifying it using the BODMAS rule. Simplification helps to solve a question in fewer steps, thereby helping to reduce time while solving complex expressions. The important parts of simplification are digital sum, number system, reciprocal, approximation, percentage, surds, indices, fraction, etc.