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

First algebra worksheet for Class 5 students. Learn variables, expressions, and simple equations with 24 problems. Includes balance method, word problems, and step-by-step solutions for beginners.

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.

Scoring Guide

20-24 correct: Excellent! You're an algebra champion! Try solving equations with fractions and more complex word problems.

15-19 correct: Very Good! Great progress! Practice more multi-step equations and word problems with two variables.

10-14 correct: Good Effort! Keep practicing! Focus on understanding the concept of balancing equations and isolating variables.

0-9 correct: Keep Trying! Review the concept section carefully. Practice simple one-step equations daily before moving to harder ones.

Tips for Improvement

Balance the equation: Whatever you do to one side, do to the other side

Work step by step: Don't try to solve everything in one step

Isolate the variable: Get the letter alone on one side of the equation

Use inverse operations: Addition ↔ Subtraction, Multiplication ↔ Division

Check your answer: Substitute your answer back into the original equation

Draw pictures: Visual representations help understand word problems better

Common Mistakes to Avoid

Forgetting to do the same operation on both sides

Making calculation errors (use a rough notebook to show work)

Not simplifying inside brackets first

Mixing up addition and subtraction or multiplication and division

Not checking if your answer makes sense in the original problem