Simplification Chapter Notes | Mathematics for Class 5 PDF Download

Introduction

•  Today, we’re diving into our math toolbox to discover simplification. 
•  Just like builders need the right tools to build a strong structure, simplification helps us break down complex problems into manageable pieces. 

• A combination of numbers joined by one or more symbols such as +, –, ×, and ÷ is known as a numerical expression.
• An example of a numerical expression is 16 x 8 ÷ 4 – 6.
• We will learn how to combine like terms and follow the order of operations to create strong solutions.
• Are you ready to improve your math skills? Let's begin!

What is Simplification?

• It may involve operations like addition, subtraction, multiplication, and division.
• For Example, $5+8÷\mathrm{4\; ,\; (10-2)+6\times 2\; etc}$
• $\mathrm{For\; solving\; questions\; related\; to\; simplification,\; we\; use\; BODMAS\; Rule.}$

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BODMAS Rule

To ensure we get the correct answer of the questions, we follow the BODMAS rule to decide which operation to do first.

BODMAS stands for

Order of priority

• Solve Brackets first (if any).
• Then perform Division and Multiplication from left to right.
• Finally, do Addition and Subtraction from left to right.

Different Types of Brackets

For the 'Bracket Off'  part, we have basically three types of brackets which are used in this chapter.
These brackets are mentioned as per the priority of solving the bracket
Priority 1: Round Brackets ( )
Priority 2: Curly Brackets { }
Priority 3: Square Brackets [ ]

If the problem contains more than one type of bracket, solve the innermost bracket first and move outward.

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Common Mistakes to Avoid 

•  Ignoring BODMAS
  For example, adding numbers before dividing can give the wrong answer.
• Not solving brackets first 
  Forgetting to prioritize brackets leads to errors.
• Rushing through calculations
  Always go step by step to avoid mistakes.

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BODMAS Examples

Let us understand this using BODMAS examples.

Example 1: Simplify the expression 5 + 8 ÷ 4
$\mathrm{<strong\; style="font-weight:\; 700;\; word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 20px;\; letter-spacing:\; inherit;\; color:\; black;">Ans:\; 7</strong>}$

Sol: According to the BODMAS rule,

• Division comes before addition.
• First: $8÷4=\; 2$
• Now the expression becomes: $5+2$
• =7.

Example 2: Simplify the expression 15 + (30 ÷ 2)
Ans: 30

Sol: Let us solve 15 + (30 ÷ 2) step by step using BODMAS Rule.

• Step 1: We need to solve the brackets first. 
• So, 15 + (30 ÷ 2) = 15 + 15
• Step 2: This will result in 15 + 15 = 30

Example 3: Simplify [2+{4×(6−2)}]÷2

Ans: 9

Sol: Step by Step solution of the same is given below

• Start with the innermost bracket: $\mathrm{<br\; style="word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 20px;\; letter-spacing:\; inherit;\; color:\; black;">}6\; -\; 2\; =\; 4$6−2=4.
• Now next bracket : $4\; \backslash times\; 4\; =\; 16$4×4=16.
• Now the expression becomes:$[2\; +\; 16]\; \backslash div\; 2$[2+16]÷2.
• Add: 2+16=18.
• Finally:18÷2=9.

Example 4: Simplify [30−(10−5×2)]÷5.
Ans: 6

Sol: Step by step solution of the same is given below

• Solve the multiplication inside the bracket first:
  $5\times 2=105\; \backslash times\; 2\; =\; 10$
• Now the bracket becomes:
  $10-10=010\; -\; 10\; =\; 0$
• Substitute back:
  $[30-0]÷5[30\; -\; 0]\; \backslash div\; 5$
• Now simplify:
  $30÷5=630\; \backslash div\; 5\; =\; 6$