Introduction to Variables and Equations - Class 5 Basic Algebra Worksheet PDF

x + 5 = 12. Most children see this and immediately wonder what x has to do with maths they already know. The answer is: everything. Algebra is not a new subject — it is the same arithmetic, with one number temporarily replaced by a letter until you figure out what it is. That shift from "calculate" to "find the unknown" is what Class 5 Basic Algebra teaches, and it is one of the most important transitions in all of school maths.

Every equation in Class 6, 7, and beyond builds on whether this idea clicked in Class 5. This worksheet builds it from scratch — variables, expressions, equations, word problems, and the balance method — with 24 questions and a full answer key.

From Arithmetic to Algebra — What Actually Changed

Class 5 is the first time maths asks a child to think backwards. Every problem before this gave them numbers and asked for an answer. Algebra flips that — it gives the answer and asks for the number that got you there.

The reason this matters beyond Class 5 is that most real problems in maths, science, and everyday life are algebra problems, not arithmetic ones. You rarely know all the numbers. You usually know the result and need to work backwards. A shopkeeper calculating how many units to order, an engineer finding a missing measurement, a student figuring out what score they need to pass — all of it is the same thinking that x + 5 = 12 introduces.

What is Algebra?

Algebra is like a mathematical puzzle where we use letters (called variables) to represent unknown numbers.

Key Terms

Variable: A letter that represents an unknown number (like x, y, or n)

Expression: A combination of numbers, variables, and operations (like 3x + 5)

Equation: A mathematical statement where two expressions are equal (like x + 7 = 12)

Important Rules

To find the value of a variable, we need to isolate it on one side

Whatever we do to one side of the equation, we must do to the other side

We can add, subtract, multiply, or divide both sides by the same number

Solved Example

Problem: If x + 5 = 12, what is the value of x?

Solution:

Step 1: Write the equation → x + 5 = 12

Step 2: Subtract 5 from both sides → x + 5 - 5 = 12 - 5

Step 3: Simplify → x = 7

Answer: x = 7

Remember: Whatever you do to one side, do the same to the other side!

Sample Practice Problems

If x + 3 = 8, then x = ?

Solve: 3x + 4 = 19

Word Problem: Priya is thinking of a number. When she multiplies it by 4 and adds 7, she gets 31. What number is Priya thinking of?

A basket has some apples. Aarav puts 8 more apples in it. Then his sister takes away 5 apples. Now there are 15 apples in the basket. How many apples were there at first?

Word Problem: Rahul and Sneha together have ₹200. Rahul has ₹30 more than Sneha. How much money does Sneha have?

If 3(x - 4) + 5 = 20, find the value of x.

Picture Problem: A farmer has chickens and goats. The total number of legs is 26. The number of chickens is 3 more than the number of goats. How many goats does the farmer have?

In a class, there are some girls and boys. The number of boys is 5 less than twice the number of girls. If there are 35 students in total and 12 girls, verify if this is correct by forming an equation.

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Class 5 Basic Algebra Worksheet — Free PDF with Answer Key

This worksheet covers:

• What is a variable, expression, and equation
• One-step equations — addition and subtraction
• One-step equations — multiplication and division
• Two-step equations — combining operations
• The balance method — doing the same to both sides
• Word problems — finding unknown numbers from real-life situations
• Verification — substituting the answer back to check
• Full answer key on the last page

24 questions | 24 marks | Printable, A4 size | No sign-up needed

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How to Solve Any Equation — The Balance Method

An equation is like a weighing scale. Both sides are equal. The moment you do something to one side — add, subtract, multiply, divide — you must do the exact same thing to the other side, or the scale tips and the equation breaks.

Solving x + 5 = 12:

The scale has x + 5 on one side and 12 on the other. To find x, remove the 5 — but remove it from both sides.

x + 5 − 5 = 12 − 5

x = 7

Solving 3x = 21:

To find x, undo the multiplication by 3 — divide both sides by 3.

3x ÷ 3 = 21 ÷ 3

x = 3 × 7... wait — x = 7

Always verify: Put the answer back into the original equation. If both sides are equal, the answer is correct. If not, a step went wrong somewhere.

3 × 7 = 21 ✓

This one habit — checking by substitution — catches almost every algebra mistake before it costs a mark.