Simplification Important Notes - Class 5 Mathematics - Complete Learning Material PDF

Introduction

• Today we explore the idea of simplification in mathematics.
• Just as builders use tools to make a strong structure, simplification helps us break down a complex numerical expression into simple steps to get one correct answer.

• A combination of numbers joined by one or more symbols such as +, -, ×, and ÷ is called a numerical expression.
• An example of a numerical expression is 16 × 8 ÷ 4 - 6.
• We will learn how to follow the order of operations and simplify expressions step by step.
• Are you ready to improve your math skills? Let us begin.

What is Simplification?

Simplification means solving a numerical expression by following rules in a correct order so that we get a single final answer.

• Simplification may involve addition, subtraction, multiplication, and division.
• Examples of expressions we simplify: 5 + 8 ÷ 4, (10 - 2) + 6 × 2.
• To get the correct answer, we follow the BODMAS rule (order of operations).

BODMAS Rule

The BODMAS rule tells us which operation to do first so that everyone gets the same correct answer.

BODMAS stands for

• B - Brackets
• O - Orders (powers and square roots; for Class 5 this is rarely used but it means exponents or square roots if present)
• D - Division
• M - Multiplication
• A - Addition
• S - Subtraction

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.

When division and multiplication appear together, do whichever comes first from the left. The same rule applies to addition and subtraction.

Different Types of Brackets

We use three common types of brackets in expressions:

• Round brackets: ( )
• Curly brackets: { }
• Square brackets: [ ]

When different brackets are used together, we always solve the innermost bracket first and then move outward. For example, in [2 + {4 × (6 - 2)}] ÷ 2, the round bracket (6 - 2) is innermost and is solved first.

Common Mistakes to Avoid

• Ignoring BODMAS - Doing addition before division or multiplication can give the wrong answer.
• Not solving brackets first - Always look for brackets and finish them before other operations.
• Rushing through calculations - Work step by step to avoid small errors in arithmetic.

BODMAS Examples

Let us learn by working through examples using BODMAS.

Example 1: Simplify the expression 5 + 8 ÷ 4
$\mathrm{<strong>Ans:\; 7</strong>}$

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="box-sizing:border-box;font-family:lato,sans-serif\; !important;letter-spacing:inherit\; !important;word-break:break-word;font-size:18px\; !important;line-height:1.8"><br>}$6−2=4.
• Now next bracket : 4×4=16.
• Now the expression becomes:[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:
  $5\times 2=10$
• Now the bracket becomes:
  $10-10=0$
• Substitute back:
  $[30-0]÷5$
• Now simplify:
  $30÷5=6$

Tips for Simplification

• Read the entire expression first and spot brackets and any division or multiplication signs.
• Mark the order: brackets first, then D and M left to right, then A and S left to right.
• When brackets are nested, always start with the innermost bracket.
• Work neatly and write each intermediate result on a new line to avoid mistakes.