Expressions Using Letter-Numbers - 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

Letter-numbers, or variables, allow mathematics to describe a whole pattern at once. Instead of writing separate rules for 1 table, 2 tables, and 10 tables, we can write a rule for n tables. This is the first serious move from arithmetic to algebra.

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

What a variable means

A variable is a symbol that can stand for a number. It is not a decoration or a hidden answer; it represents a changing or unknown quantity.

Building expressions

If a pencil costs p rupees, 6 pencils cost 6p rupees. If a number is n, the next number is n + 1 and twice the number is 2n.

Substitution

To evaluate an expression, replace the letter with the given number and then calculate carefully.

3. Rules and formulas to remember

• Consecutive number: n, n + 1, n + 2. Used for patterns and sequences.
• Perimeter of square: 4s. If side length is s.
• Perimeter of rectangle: 2(l + b). If length is l and breadth is b.
• Substitution: If x = 5, then 3x + 2 = 17. Replace the variable before calculating.

4. Worked examples

Example 1: Write an expression for 8 more than a number x.

x + 8.

Example 2: Write an expression for the cost of 5 notebooks if one notebook costs n rupees.

5n rupees.

Example 3: Evaluate 4a - 7 when a = 6.

4 x 6 - 7 = 24 - 7 = 17.

Example 4: A pattern has 3n + 1 dots in stage n. How many dots are in stage 8?

3 x 8 + 1 = 25 dots.

5. Activity corner

Use matchsticks to make a row of squares. One square needs 4 sticks, two joined squares need 7, three need 10. Students record the table and generalise the nth case as 3n + 1.

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: Treating 5x as 5 + x Fix: 5x means 5 multiplied by x.
• Mistake: Changing the variable while substituting Fix: Use the same given value wherever the letter appears.
• Mistake: Writing word phrases backwards Fix: Three less than x is x - 3, not 3 - x.

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. Write twice a number decreased by 9.
2. Evaluate 7p + 4 when p = 3.
3. Write the perimeter of a regular pentagon with side a.
4. If one mango costs m rupees, write the cost of 12 mangoes.
5. For pattern rule 2n + 5, find term 10.
6. Why are variables useful?

9. Answer key

1. Write twice a number decreased by 9. Answer: 2x - 9.

2. Evaluate 7p + 4 when p = 3. Answer: 25.

3. Write the perimeter of a regular pentagon with side a. Answer: 5a.

4. If one mango costs m rupees, write the cost of 12 mangoes. Answer: 12m.

5. For pattern rule 2n + 5, find term 10. Answer: 25.

6. Why are variables useful? Answer: They let one expression describe many possible numbers or cases.

10. Quick revision

• Main themes: variables, algebraic expressions, substitution, patterns.
• 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.