**Pre-Requisites**

- Class 4

## Learning Objective

On successful completion of this lesson, students will be able to:

- demonstrate basic knowledge of simplification, types of brackets.
- analyze the rule of BODMAS.
- develop problem-solving skills.
- apply in real life.

**Dictionary**

**Number**: 1, 2, 3 etc.**Simplification**: Making Easier**Simplify**: To make simple**Bracket**: Grouping**>**: Greater than**<**: Lesser than**=**: Equal to**Ascending**: Increasing**Descending**: Decreasing**Order**: Sequence

**4.1 Introduction**

=> **Numerical Expression**: It is a combination of numbers connected by one or more of the symbols **/**,** x**, **–**, **+** and **Of**.

e.g:

- 8/2 x 3 + 5
- 5 x 6 + 7
- 10/5 x 5 + 10 – 20

=> When we simplify the Numerical Expression , we obtained a value of the expression.

e.g1. **Solve 12 / 2 + 2.**

**Sol.** 12 / 2 + 2=6+2= 8.

Therefore , **8** is the value of the expression 12/2+2.

=> When we find the value of the expression , we do some operations is called **Simplification** of the expression.

=> **Simplification**: The process of making something easier or simpler to understand.

=> In order to get a unique value of a given Numerical Expression , we have to perform the operations strictly in a definite order given below:

**Division (D)****Multiplication (M)****Addition (A)****Subtraction (S)**

i.e **DMAS**.

=> **Don’t change the order of these operations.**

=> Remember the word **DMAS**.

#### Solved Examples

Ex1. **Simplify 40 – 10 / 5 x 2 + 5.**

**Sol**. We have:

40 – 10 / 5 x 2 + 5 = 40 – 2 x 2 + 5

= 40 – 4 + 5

= 45 – 4

= 41 **ans**.

**4.2 Use of Brackets **

=> **Brackets**: Grouping symbols

=> Brackets are used to separate various parts of an expression.

**4.3 Types of Brackets**

=> **4 types of brackets**:

**Bar**or**Vinculum****———-****Round**bracket or**Small**brackets**( )****Curly**bracket or**Braces**{ }**Square**bracket or**Big**bracket [ ]

**4.4 Order of Operations**

**Bar**or**Vinculum**———-**Round**bracket or**Small**brackets ( )**Curly**bracket or**Braces**{ }**Square**bracket or**Big**bracket [ ]

=> When we simplify an expression , the terms in the brackets are taken as independent units.

=> Brackets terms are solved separately.

=> Remember the word **BODMAS**.

=> **BODMAS** stands for ” **Brackets , Of, Division , Multiplication , Addition & Subtraction** respectively.

=> We take Multiplication Sign when there is no sign before a bracket.

#### Solved Examples

Ex1. **Simplify 6 – [20 / { 8 – 2 ( 9 – 5 – 2)}]**

**Sol**. We have:

6 – [20 / { 8 – 2 ( 9 – 5 – 2)}]

= 6 – [20 / { 8 – 2 ( 2)}]

= 6 – [20 / { 8 – 2 x 2}]

= 6 – [20 / { 8 – 4}]

= 6 – [20 / 4]

= 6 – 5

= 11 **ans**.

**Sol**. We have:

6 – [20 / { 8 – 2 ( 9 – 5 – 2)}]

= 6 – [20 / { 8 – 2 ( 9 – 3)}]

= 6 – [20 / { 8 – 2 x 6}]

= 6 – [20 / { 8 – 12}]

= 6 – [20 / -4]

= 6 – [-5]

= 6+5

= 11 **ans**.

**4.5 Practice Sets **

- Fill Type
- Match Type
- Order Type
- Conversion Type
- Compare Type
- Error Type
- Statement Type
- True/False Type
- Related Type
- Day-to-Day Type
- Miscellaneous Type

#### Set-1

**1. Simpl**y

**2. **Tick (✔️) the correct answer.

**3. Which of the following are meaningless?**

**4. Compare and put symbol >, < or =in the placeholder.**

**5. Fill in the blanks.**

**6. Cross (x) the Roman numerals which are not written correctly.**

**7. Write the following Roman numerals in ascending order.**

**8. Write the following Roman numerals in descending order.**

**9. Solve & write the answer in Roman numerals.**

**10. Complete the following table.**

11. State whether each of the following statements is true or false.

#### Set-2

#### Set-3

#### Set-4

#### Set-5

**4.6 Quiz**

** **

**4.7 Test**

**4.8 Exam**

The exam will be conducted after the completion of the course.

**4.9 Ask Question**

Ask your doubts **here**

#### …..The End…..

**Other Notes**

- Counting from one to hundred: एक से लेकर सौ तक गिनती
- Punctuation Mark: विराम चिन्ह
- Roman Numerals : 1 to 3000
- Testing
- Words Start with letter G
- Words Start with letter F
- Words Start with letter E
- Words Start with letter D
- Words Start with letter C
- Words Start with letter B