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CBSE • Class 6 • Mathematics • Ch 11

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Algebra

In CBSE Class 6 Mathematics, "Algebra" introduces generalized arithmetic with variables (letters like $x, y, n$) representing unknown quantities. Students explore matchstick geometric patterns, algebraic expressions ($2n + 1, 3x - 5$), equations, and finding solutions via the trial and error method.

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Overview Core Concepts Formulas & Identities Solved Examples Common Traps Summary Self Check Take MCQ Test

🔤 Have You Ever Wondered?

How do video game programmers write one formula for jumping that works for any character regardless of weight?

Variables are letters standing for numbers! Welcome to Algebra, the crowning gateway from plain numbers to universal mathematical problem-solving.

Why This Chapter Matters

Before You Begin (Prerequisites)

Arithmetic operations
Number patterns

What You Will Learn (Core Objectives)

Understand variables as letters that can take various numerical values.
Derive general rules from matchstick patterns ($2n$ for L, $3n$ for C).
Translate English word statements into algebraic expressions and vice versa.
Define an Equation as a condition on a variable with an equality sign ($=$).
Solve simple equations using the Trial and Error substitution method.

Chapter Roadmap & Progression

1 1. Matchstick Patterns & The Idea o...

2 2. Algebraic Expressions

3 3. Equations & Trial and Error Meth...

Complete Concept Guide (100% Curriculum Coverage)

1. Matchstick Patterns & The Idea of a Variable

To make the letter L with matchsticks, 1 "L" requires 2 sticks, 2 "L"s require 4 sticks, 3 "L"s require 6 sticks. In general, for $n$ "L"s, the number of matchsticks required is $2n$.

Here, $n$ is a variable (its value can vary: $n = 1, 2, 3, \dots$). Constants have fixed values (like 2, 5, 10); variables change value (like $x, y, z, m, n$).

2. Algebraic Expressions

Combining variables and constants using arithmetic operations ($+, -, \times, \div$) creates algebraic expressions:

$y + 5$: 5 added to $y$.
$t - 7$: 7 subtracted from $t$.
$10a$: $a$ multiplied by 10.
$\frac{x}{3}$: $x$ divided by 3.
$2p + 1$: 1 added to product of 2 and $p$.

3. Equations & Trial and Error Method

An Equation is a statement of equality between two algebraic expressions containing at least one variable. It must have an equal sign ($=$):

$$2x + 3 = 11$$

The expression on the left of $=$ is the LHS (Left Hand Side); on the right is the RHS (Right Hand Side).
The value of the variable that makes $\text{LHS} = \text{RHS}$ is the solution of the equation.
Trial and Error: Substitute sequential test values ($x = 1, 2, 3, 4\dots$) until LHS matches RHS. For $2x + 3 = 11$: when $x = 4$, $2(4) + 3 = 8 + 3 = 11 = \text{RHS}$. Hence $x = 4$ is the solution.

Key Formulas, Identities & Theorems

Linear Equation Form

$$ax + b = c \implies x = \frac{c - b}{a}$$

Single variable linear equation.

Conceptual Solved Examples & Case Studies

Example 1

State which of the following are equations: (a) x + 20 = 70, (b) 2p < 30, (c) 8 × 3 = 24.

Step-by-Step Solution:

(a) Equation with variable (has variable x and $=$ sign).
(b) Not an equation (inequality with $<$ sign).
(c) Numerical equation (has $=$ sign but no variable; in Class 6 algebra, equations must contain variables).

Example 2

Solve by trial and error: 5m = 30.

Step-by-Step Solution:

Test values for m:
For $m = 4$: $5(4) = 20 \ne 30$
For $m = 5$: $5(5) = 25 \ne 30$
For $m = 6$: $5(6) = 30 = \text{RHS}$.
Therefore, the solution is $\mathbf{m = 6}$.

Common Misconceptions & Examiner Traps

Common Misconception

Treating expressions like x + 5 as equations.

Scientific Reality & Correction

An expression has no equality sign ($=$); an equation MUST have an equals sign ($=$) balancing LHS and RHS.

Visual Learning & Conceptual Map

Anatomy of an Algebraic Equation

LHS = RHS Balance Concept

LHS

2x + 3

RHS

Solution: x = 4 balances the scale!

Chapter Summary & 10 Key Takeaways

Takeaway 1

Variables are symbols (letters) representing unknown values.

Takeaway 2

Algebraic expressions combine variables and constants with operations.

Takeaway 3

An equation is an equality with an equals sign ($=$).

Takeaway 4

The solution satisfies $\text{LHS} = \text{RHS}$.

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Write the algebraic expression for: "7 subtracted from -m".

Reveal Answer & Explanation

Answer: $-m - 7$.
Start with -m and subtract 7.

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