Write Equations with Unknowns – All Operations | Printable Worksheet PDF

 A Quick Look at the History

The idea of using letters to represent unknown values in math began over 400 years ago with French mathematician François Viète. He introduced the concept of using symbols (like x) to stand in for numbers we don’t know — a revolutionary idea that led to the development of algebra as we know it today.

Since then, writing equations with unknowns has become a key skill in solving real-world problems.

 Introduction to the Topic

This worksheet helps students practice writing equations using +, −, ×, and ÷ to model real-life situations. Each problem includes a number story, and students must write an equation using a letter variable like x to represent the unknown quantity.

It’s not just about solving — it’s about understanding how numbers connect in a situation, and building the foundation for algebraic thinking.

Solved Example from the Worksheet

Problem:
Emma had 45 candies. She gave 15 to her friend. How many are left?
 Equation: 45−x=30

45-30=x                       
Solve: $15$

This shows students how subtraction can model “giving away” or “taking from” — and how to spot the unknown in the equation.

We use equations with unknowns all the time:

• “I had some money, spent $15, and now have $30 — how much did I start with?”

• “There are 48 marbles split into 6 bags — how many in each?”

• “Each movie ticket costs $9. I spent $45 — how many tickets did I buy?”

These are real math moments, and this worksheet gives students the tools to handle them.

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