WBBSE Notes For Class 6 Maths Chapter 1 Simplification

Simplification Maths Class 6

Chapter 1 Simplification

Simplification of a mathematical quantity means that a simplified form is obtained after the application of different mathematical processes on it such that no further mathematical process can be applied to this simplified form.
Suppose that you have to simplify “10 + 2”—here you have to obtain a simplified form on two real numbers 10 and 2 and there is a mathematical operation “+” (addition) in between them.

We get a simplified real number 12 as a result of the mathematical operation “+” is applied on 10 and 2 and there you can not apply any other mathematical operation on 12.
So the simplification of the mathematical quantity (10 + 2)—we get 12, i.e., 10+ 2 = 12.
Similarly, 20 – 5 = 15, a simplification process. 4 x 5 = 20, 30 -r 5 = 6, etc. are examples of simplification.

It is to be noted that by a “mathematical process or operation” we mean.
Addition, Subtraction, Multiplication, Division, etc. and we express them as +, -, x, ÷, etc. respectively.
Other than these operations, we also use the mathematical symbols ( ), { }, [ ], of, etc.

These mathematical symbols denote also definite
mathematical processes or operations like +, x, -, ÷, etc.
For example, the mathematical operation “2 of 8” means 8 x 2 and the result of this quantity after the operation has been done is 16.

Similarly, the symbols ( ), { }, [ ], etc. represent definite mathematical operations or processes.
So we get the following mathematical operations: “+” means addition ; means subtraction ; “x” means multiplication, “÷” means division, “of’ means multiplication ; means first bracket ; “{ }” means second bracket ; “[ ]” means third bracket ;
“—” means vinculum.

Now if it is said that only one mathematical operation is to be done in a mathematical quantity, then we generally do not say that “Simplify” it, we say that you make the process directly,
For example
Add : 15 + 3

or, Multiply: 12 x 5, etc. so to say “Simplify”—we mean generally do more than one mathematical process or operations,

Class 6 Math Solution WBBSE English Medium

For example:

Simplify 10 ÷ 2 x 5 + 3-1. Here all four mathematical operations or processes “÷”, “x”, “+” and “-’’ are to be done.

Now the question is:

Whether all the operations can be done simultaneously or not?
If not, then which process or operation can be done at first, and which process can be done afterward?
This must be known clearly, otherwise, the result will be different in different procedures.

For this you observe the following simplification :

24 + 6 + 2

= 4 + 2

= 6.

WBBSE Notes For Class 6 Maths Chapter 1 Simplification

Understanding BODMAS

Here we have done the division (+) process first and then the addition (+) process has been done.
Again, ,24 + 6 + 2 = 24 + 8 = 3. Here we have done an addition.
(+) the process at first and then the division process has been done.

As a result of which we get the answer 6 in the first case and 3 in the second case.
So in the simplification of the same problem, we get different results in the different processes if we do not obey a definite rule. But this is not reasonable.
For this Mathematicians have decided on a definite rule of an operational procedure for simplification which we should follow always.

A = Addition
S = Subtraction
So for simplification, you have to start with, the operations vinculum, then the first bracket, 2nd bracket, 3rd bracket, of, and at last division, multiplication, addition, and subtraction correspondingly.

It is to be noted that if any one of the mathematical operations is absent, then perform the next mathematical operation and so on and this rule can not be violated in any way.
Sometimes in any of the simplifications, there may exist no definite mathematical operation between any two numbers or quantities

WBBSE Class 6 Simplification Notes

For example

12÷2 (5-3) in this simplification there is no mathematical operation between 2 and (5−3). In this case, the process i.e., the operation “x” between 2 and (5-3) is absent, you will always assume that there is “x” i.e., the product operation between these two quantities but you can not put directly “x”-sign between these two quantities. Because in that case, the answer may not be correct. For example, in the same simplification, we get 12÷2 (5-3) = 122 (2) = 12 ÷ 4 = 3
This is the correct answer. But if you put the “x” sign between 2 and (5-3), then the simplification becomes
12÷2 (5-3)
= 12÷2 x (5-3)
= 12÷ 2 x 26 x 2
= 12 which is not the correct answer.

Here we have done the division process first and then multiplication (whenever you put the “x” sign in the specified place) and the result of the simplification is wrong correspondingly. You will always be alert in this matter.

Simplification Questions For Class 6

Alertness regarding the withdrawal of the Vinculum sign:

The students often make a mistake about the operation “Vinculum”, especially there is a “—” sign before the sign “Vinculum”. For example:
\(22 \div 11-\overline{7-3}\) here” — ” sign exists before the sign Vinculum. Some students write this after the operation of Vinculum as 22 ÷ 11-7-3, which is totally wrong Because in this case,
22 ÷11-7-3
= 2-7-3
= -5-3
= -8.
But the correct value of the simplification is \(22 \div 11-\overline{7-3}\)
= 22÷11-4
= 2-4
= -2.

So if there is a “—” sign before the sign Vinculum, then after the withdrawal of the vinculum sign, one must take care of the sign as follows
The “+” sign becomes the “—” sign and the “—” sign becomes the “+” sign.
Then only the correct value of the simplification will be obtained.