Finding the Unknown - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Finding the Unknown turns arithmetic and expressions into equation-solving. An equation is like a balance: both sides must remain equal. Students learn to undo operations systematically and to translate real-life situations into mathematical statements.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Equation as balance

If the same operation is done to both sides of an equation, equality is preserved. This balance idea is the safest way to solve.

Inverse operations

Addition is undone by subtraction, multiplication by division, and vice versa. Solving means isolating the unknown.

Word problems

The hardest part is often forming the equation. Define the unknown clearly before writing the equation.

3. Rules and formulas to remember

• Addition equation: x + a = b -> x = b - a. Undo addition by subtraction.
• Subtraction equation: x - a = b -> x = b + a. Undo subtraction by addition.
• Multiplication equation: ax = b -> x = b/a. Undo multiplication by division.
• Two-step equation: ax + b = c -> ax = c - b -> x = (c - b)/a. Work one inverse step at a time.

4. Worked examples

Example 1: Solve x + 17 = 42.

Subtract 17 from both sides: x = 42 - 17 = 25.

Example 2: Solve 5x = 60.

Divide both sides by 5: x = 12.

Example 3: Solve 3x + 4 = 31.

Subtract 4: 3x = 27. Divide by 3: x = 9.

Example 4: Riya thinks of a number. Twice the number plus 6 is 38. Find it.

Let the number be x. 2x + 6 = 38, so 2x = 32, x = 16.

5. Activity corner

Use a physical balance model with counters. Add the same number of counters to both sides, remove the same number, and divide into equal groups. Students see why equation steps are legal.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Moving terms without understanding the inverse operation Fix: Write the same operation on both sides.
• Mistake: Forgetting to check the answer Fix: Substitute the value back into the original equation.
• Mistake: Not defining the variable in word problems Fix: Start with 'Let the number be x' or a similar clear statement.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Solve x - 9 = 14.
2. Solve 7x = 84.
3. Solve x/5 = 11.
4. Solve 4x - 3 = 29.
5. A number divided by 6 gives 13. Find the number.
6. How do you check an equation solution?

9. Answer key

1. Solve x - 9 = 14. Answer: x = 23.

2. Solve 7x = 84. Answer: x = 12.

3. Solve x/5 = 11. Answer: x = 55.

4. Solve 4x - 3 = 29. Answer: x = 8.

5. A number divided by 6 gives 13. Find the number. Answer: 78.

6. How do you check an equation solution? Answer: Substitute it into the original equation and see whether both sides match.

10. Quick revision

• Main themes: linear equations, unknowns, inverse operations, word problems.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.