Simplification-Approximation

What is Simplification?

Simplification is defined as the process of simplifying complex solutions. In, easy words simplification is the process to make our life easy, this process helps us by showing us an easy way of solving difficult, complex solutions with certain rules to follow.

Certain rules of Simplification are-

Rule1- Wherever you read an ‘of’ in mathematical word problems, it must be replaced with a multiplication sign ‘x’.

Example for Rule1- Find 5 of 10, Replace ‘of’ with ‘the multiplication signs’ and thus we get a new question as 5×10 that is equal to 50. 

Rule2- The second rule of Simplification is that one must replace all the ‘/’ signs with the ‘division’ sign (÷).

Example for Rule2- Find 20/5, Replace the ‘/’ symbol in the question with the division sign, we get a new question as 20 ÷ 5 that is equal to 4.

Rule3- The third rule for Simplification is to follow the ‘BODMAS’ rule. The solution of an equation or problem must be done in the below-mentioned order from B to S.

B stands for Bracket, (), [], {}, etc.

O stands for Of (Multiplication).

D stands for Division (÷).

M stands for Multiplication (x).

A stands for Addition (+).

S stands for Subtraction (-).

Example- Solve  4 (10 + 15 ÷ 5 x 4 – 2 x 2)

= 4 (10 + 15 ÷ 5 x 4 – 2 x 2)    …. Bracket of.

= 4 (10 + 3 x 4 – 2 x 2)             …. Division.

= 4 (10 + 12 – 4)                       …. Multiplication.

= 4 (22 – 4)                                …. Addition.

= 4 (18)                                       …. Subtraction.

= 4 x 18

= 72.

Rule4-  Multiplication and Division both have the same importance for solution purposes but at times when there are both the operations to be performed in a problem, we must perform the operation which is on the left first.

According to the rules of BODMAS, the solution of division comes before multiplication but in some instants, we can perform any operation which is on the left. 

Example- Find 10 x 2 / 5

Solution- First solve the multiplication that is 10 x 2 because it is on the left and then the division.

= 10 x 2 / 5

= 20 / 5 = 4.

Rule5-  Addition and Subtraction have the same importance but at times when there are both the operations to be performed in a problem, we must perform the operation which is on the left first.

According to the rules of BODMAS, the solution of addition comes before subtraction but sometimes we can perform any operation which is on the left. 

Example- Find 40 – 20 + 10

Solution- First solve the subtraction that is 40- 20 because it is on the left and then the addition.

= 40 – 20 + 10

= 20 + 10

= 30.

Rule6-  Rounding off the decimal numbers to the nearest integer is also allowed in some instances. 

Most of the numbers in decimals are rounded off to their nearest integer number to make it easy the solution of such difficult problems.

Example- (29.9 + 55.9)

The nearest integer to 29.9 is 30, so we replace 29.9 with 30 and the nearest integer to 55.9 is 56, so we replace 55.9 with 56

Therefore,

= (29.9 + 55.9)

= (30 + 56)

= 86.

What is Approximation?

An approximation is defined as a value/quantity that is very near but not equal to a similar original value. 

An approximation is often used to find an approximate solution to a given problem. It is because of the help of approximation that a chef adds salt to the food he/she prepares. 

An approximation is denoted with a symbol – (≈).

The symbol that denotes approximation means that it ‘is approximately equal to’

If given a number 64298 we can take its approximate value by correcting it to the nearest hundred which is 64300. Similarly, if we want its approximation to its nearby thousandth number it will be 64000.

Example 1

Approximate 266 to the nearest 10’s value

In the given example you must pay attention to the tens and unit digits. The hundreds digit is not required for now. We need to decide on our own if 66 will be rounded up to 70 or 60.

We know that the unit’s digit is 6, which is more than 5, so you round it up not down. Thus, the required and correct answer is 270.

Conclusion

With an increase in difficulty levels of the mathematical problems, solutions do take a lot of time, with the help of approximations and simplifications we can now find an easy path to find a solution for the difficult sums. 

With ease due to these two topics, mathematical equation solutions have become very easy to go on with.