Cl-5 (Math) | Ch-4 | Simplification

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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. Simply

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.

Show Ans