Algebra & Simple Equations Class 6 Worksheet — Free PDF Download with Answers

Algebra is the branch of mathematics where letters (called variables) stand in for unknown numbers. Instead of asking "what number plus $5$ equals $12$?" and guessing, algebra lets you write $x + 5 = 12$ and solve it systematically: $x = 7$.

This simple idea — using a letter to represent an unknown — is one of the most powerful tools in all of mathematics. It lets you express general rules (the perimeter of any rectangle is $2(l + b)$), describe patterns (the $n$th even number is $2n$), and solve problems that would be impossibly tedious by trial and error.

In Class 6, students are introduced to variables, learn to write algebraic expressions from word statements, and solve simple one-step equations. This is the gateway to the formal algebra that dominates Classes 7 through 10, so building a clear conceptual foundation now is essential.

* Variable — A letter (commonly $x, y, n, a$) used to represent an unknown or changing quantity.
* Constant — A fixed number, like $5$ or $-3$.
* Algebraic expression — A combination of variables, constants, and operations. E.g., $3x + 7$, $2n - 5$.
* Term — Each part of an expression separated by $+$ or $-$. In $4x + 3y - 2$, the terms are $4x$, $3y$, and $-2$.
* Coefficient — The numerical factor of a term. In $4x$, the coefficient is $4$.
* Equation — A statement that two expressions are equal. E.g., $x + 5 = 12$.
* Solving an equation — Finding the value of the variable that makes the equation true.
* Balancing method — Perform the same operation on both sides to isolate the variable:
$x + 5 = 12 \Rightarrow x = 12 - 5 = 7$.
* Trial and error method — Substitute different values until the equation balances. Useful for simple equations but not scalable.
* Forming equations from words:
- "$5$ more than a number" $\to x + 5$.
- "Twice a number decreased by $3$" $\to 2x - 3$.
- "The sum of a number and $7$ is $15$" $\to x + 7 = 15$.

1. Print the PDF — Download from the links below.

2. Start with Level 1 (Easy) — 20 questions on writing expressions, identifying terms/coefficients, and solving one-step equations.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the included answer key. Always verify by substituting back.

5. Revise mistakes — For equation-solving errors, redo the problem step by step, writing each operation on both sides.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Write an algebraic expression for "$8$ more than a number $n$."
Solution: $n + 8$.

2. Identify the coefficient of $y$ in $9y - 4$.
Solution: $9$.

3. Solve: $x + 6 = 14$.
Solution: $x = 14 - 6 = 8$.

Level 2 — Medium

1. Form an equation and solve: "Three times a number minus $4$ equals $17$."
Solution: $3x - 4 = 17 \Rightarrow 3x = 21 \Rightarrow x = 7$.

2. Solve: $\dfrac{x}{5} = 9$.
Solution: $x = 9 \times 5 = 45$.

3. Write an expression for the perimeter of a rectangle with length $(x + 3)$ and breadth $4$.
Solution: $P = 2[(x+3) + 4] = 2(x + 7) = 2x + 14$.

Level 3 — Hard

1. Solve: $5x + 3 = 2x + 18$.
Solution: $5x - 2x = 18 - 3 \Rightarrow 3x = 15 \Rightarrow x = 5$.

2. The sum of three consecutive numbers is $54$. Find the numbers.
Solution: Let the numbers be $n, n+1, n+2$. Then $3n + 3 = 54 \Rightarrow n = 17$. Numbers: $17, 18, 19$.

3. Ravi's age is $3$ years more than twice Sita's age. If Ravi is $19$, find Sita's age.
Solution: Let Sita's age $= x$. Then $2x + 3 = 19 \Rightarrow 2x = 16 \Rightarrow x = 8$. Sita is $8$ years old.

CBSE (NCERT — Ganita Prakash / Math Magic)
CBSE introduces algebra informally in the Class 6 Ganita Prakash textbook through pattern generalisation and simple equation-forming. The emphasis is on understanding what a variable represents rather than formal solving techniques. Formal algebra becomes a major focus from Class 7 onwards.

ICSE (Selina / ML Aggarwal)
ICSE has two dedicated chapters: "Algebra Introduction" (expressions, terms, coefficients) and "Simple Equations" (forming and solving). ICSE covers more ground at Class 6 than CBSE, including two-step equations and equations with the variable on both sides.

IB MYP (Mathematics Framework)
The MYP "Algebraic Thinking" unit encourages students to see algebra as generalised arithmetic. Students express patterns algebraically, form equations from real-world situations, and justify their solutions. The IB emphasis is on reasoning and communication.

Key Differences:
* CBSE: Informal introduction; pattern-based; formal algebra from Class 7.
* ICSE: Two dedicated chapters; two-step equations covered.
* IB: Pattern generalisation; emphasis on reasoning and justification.

Download your free Algebra & Simple Equations worksheets:

* Algebra Introduction ICSE Worksheet — 60 questions on expressions and terms
* Simple Equations ICSE Worksheet — 60 questions on forming and solving equations

Practise online:

* Practice Online — ICSE Algebra
* Practice Online — ICSE Equations
* Practice Online — IB Algebraic Thinking

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Stuck on an equation? Get a step-by-step solution.
* Spark Coach — AI tutor that guides your thinking with hints.
* Free Worksheets for All Classes — Browse worksheets from Class 1 to 10.
* Play Mode for Class 1-4 — Fun algebra readiness games for younger learners.

Continue your Class 6 practice:

* Integers Class 6 Worksheet
* Patterns in Mathematics Class 6 Worksheet
* Ratio and Proportion Class 6 Worksheet
* Fractions & Decimals Class 6 Worksheet
* Whole Numbers Class 6 Worksheet