Simplification

Learning Outcomes:

After studying this post, readers will be able to: 

1- Know that the following four(4) kinds of brackets 

______ vinculum, (ونی کلم۔بار)

( ) parentheses or curved Brackets or round brackets, (خم دار بریکٹس)

{ } braces or curly brackets, (کرلی بریکٹس۔بریسس)

[ ] square brackets or box brackets, (باکس بریکٹس۔ مربعہ نما بریکٹس)

2- Readers  Know the order of preference as, 

______ , ( ), { } and [ ] , to remove (simplify) them from an expression.

3- Readers are able to  recognize BODMAS rule to follow the order (ترتیب) in which the operations, to simplify mathematical expressions, are performed.

4-  Simplify mathematical expressions involving fractions (کسر عام)and decimals(کسر اعساریہ) grouped with brackets using BODMAS rule.

اوپر بریکٹس کی چار اقسام بیان کی گیں ہیں۔ہم انکو اسی ترتیب کے ساتھ حل کرتے ہیں۔ مطلب سب سے پہلے بار والی یا ونی کلم والی رقم حل کریں گے اور اس کے بعد خم دار بریکٹس پھر کرلی برکٹس اور آخر میں باکس بریکٹس کو حل کرتے ہیں۔

Introduction:

We have already learnt simplification of an expression involving two  or more of four operations but sometimes it becomes more important to simplify some operations before the others in an expression. For this purpose, we use brackets which indicate the order of simplification. There are four types o f brackets. 

1- ________  is called a bar or viniculum

 2-  ( ) is called a round or curved brackets or parentheses. 

 4- [ ] is called box brackets or square brackets. 

Some Rules

There are some rules to simplify (حل کرنا) an expression containing brackets. 

Rule 1:  When an expression (حسابی جملہ)contains only addition and Subtraction: work from left to right within the brackets. 

Rule 2:  When an expression contains only multiplication(ضرب) and division: work from left to right within the brackets. 

Rule 3:  When an expression contains (مشتمل) any three or all four operations: use the BODMAS rules.

BODMAS Rule:

Every one of us know that addition, subtraction, multiplication and division are the four (4) basic operations (بنیادی عوامل) of math. An expression which contains all these operations we use simplification rule(اختصار کا قانون). This rule tells us that we performed this simplification rule in the following order but after removing (Simplify) the brackets.

BODMAS

BO for Brackets Of
D for Division
M for Multiplication
A for Addition
S for Subtraction

So this simplification rule is called BODMAS Rule.

ہم جانتے ہیں کہ ریاضی میں چار بنیادی عوامل ہیں۔ جمع ۔تفریق۔ضرب اور تقسیم ۔ اس قانون کےمطابق یہ چاروں عوامل بریکٹس ہٹانے کے بعد ہم جسں ترتیب کے ساتھ حل کرتے ہیں وہ ترتیب ذیل میں درج ہے۔ سب سے پہلےتقسیم کا عمل پھر ضرب کا عمل پھر جمع کا عمل اور آخر میں تفریق کا عمل کیا جاتا ہے۔

Some Examples:

Example 01:

Example 02:

Example 03:

Example 04:

 

Example 05:

Example 06:

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Have a nice day.