CBSE Class 7 · Mathematics
Expressions using Letter-Numbers
Official NCERT chapter from Ganita Prakash Part I (book code gegp1). ExamMaster notes are original teaching at CBSE Class 7 depth.
This lesson follows the official chapter “Expressions using Letter-Numbers” in Ganita Prakash Part I. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 7
- Easy level
- 8 concepts
1The Notion of Letter-Numbers
A letter-number holds a place for a number you have not named yet, or a number that can change: 5 more than n is n + 5. The letter is not a decoration.
Writing n because the problem said “number” and then forgetting it is a sticker, not a letter-number.
Figure. x is the place that makes x + 3 = 8 true. That place is 5 on the line, not a decoration beside the plus.
How it works
- Name what can vary or is unknownA length, a count.
- Give it a lettern, or l.
- Write the relation with that lettern + 5, or 2n.
2Revisiting Arithmetic Expressions
An arithmetic expression becomes algebraic when a letter sits where a number sat: 3 + 2 × 5 can become 3 + 2 × a. The order of operations stays.
The letter does not cancel the ×-before-+ rule.
Figure. 7 + x = 18 is an arithmetic sentence with a hole. Undo the +7 on both sides; x is 11.
How it works
- Keep the same orderBrackets, ×÷, +−.
- Treat the letter as a number you will fill laterA holder.
- If you are given a = 5, evaluate as before3 + 10 = 13.
3Simplification of Algebraic Expressions
Simplify by collecting like terms: 2a + 3a is 5a. 2a + 3 is not 5a — the 3 has no a. Like means the same letter-part.
Adding the numbers and ignoring the letter is the miss.
Figure. Like terms share the same letter-power. 2x and 3x collect to 5x; the 4 is a different pile and stays.
How it works
- Spot terms with the same letter-part2a and 3a.
- Add or subtract those coefficients5a.
- Leave unlike terms written separately5a + 3.
Collect 2a + 3a + 4
Simplify 2a + 3a + 4.
- Like a-terms2a + 3a = 5a
- Unlike+ 4
- Simplified5a + 4
Pro tip. The 4 has no a. Do not swallow it into 9a.
4Pick Patterns and Reveal Relationships
A pattern in a table can become a letter-rule: term n is 3n + 1. The letter reveals the relationship the list was hiding.
A pretty list with no sentence is not yet the relationship.
Figure. Name the shortest chunk that restarts — here A-A-B. The next tile is A, not a guess.
How it works
- Write a few termsEvidence.
- Try a sentence with n3n, or n + 4.
- Check every term you haveThen claim the rule.
5A definition is a test you can run
“Letter-number” means you can substitute a number and get a value, or collect like terms. If you cannot run either test, you have a decoration.
A letter in a title with no expression is not this notion.
Figure. A definition is a test: put the candidate in and both sides must match. 10 + 3 and 13 agree, so x = 10 stays.
How it works
- Write an expression with a letterThe definition’s object.
- Substitute or collectThe test.
- If neither is possible, it is not yet a letter-number jobRun a test.
6Name the given before the unknown
The given may be the expression, or a value for the letter. The unknown may be the simplified form, or the value after substitute. Name which is which.
Treating every letter as 1 without being told is a silent given.
Figure. Name the given +4 and 14 before you hunt x. Starting at the letter is how the sentence turns into handwriting.
How it works
- Circle the given writing or valueThis expression, or a = 4.
- Name what is askedSimplify, or evaluate.
- Then workGiven first.
7One worked case is enough at this class
One substitution or one collection is enough to show the move. A page of the same 2a+3a does not deepen the idea.
Cloning 5a + 4 ten times is not a new relationship.
Figure. One honest undo is enough at this class: x + 8 = 14 becomes x = 6. A second worked case is not a new idea.
How it works
- Do one clear caseThe worked case.
- A second case only to checkChange a number.
- StopThis class.
8A miss: swapping the school name for the picture
A picture of n apples is a setting. The letter-number is n, or 2n. Doing the picture-count and skipping the letter is the swap-miss.
Eight drawn apples do not simplify 2a + 3a.
Figure. The letter is a place in a sentence, not a drawing of an x. Treating x as art swaps the school name for the picture.
How it works
- Keep the picture as a storyApples, steps.
- Write the letter expressionThe maths.
- Work on the writingDo not swap.
2a + 3a + 4 simplifies to
- 5a + 4
- 9a
- 5a
Collect like a-terms; leave 4.
Notes
- The official chapter title is “Expressions using Letter-Numbers”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Formulas
- 2a + 3a = 5a
- 2a + 3 stays 2a + 3
Recap
Hold these pegs from the official chapter “Expressions using Letter-Numbers”. The wording is ExamMaster’s teaching, not a textbook recap.
- The Notion of Letter-Numbers
- A letter-number holds a place for a number you have not named yet, or a number that can change: 5 more than n is n + 5.
- Revisiting Arithmetic Expressions
- An arithmetic expression becomes algebraic when a letter sits where a number sat: 3 + 2 × 5 can become 3 + 2 × a.
- Simplification of Algebraic Expressions
- Simplify by collecting like terms: 2a + 3a is 5a.
- Pick Patterns and Reveal Relationships
- A pattern in a table can become a letter-rule: term n is 3n + 1.
- A definition is a test you can run
- “Letter-number” means you can substitute a number and get a value, or collect like terms.
- Name the given before the unknown
- The given may be the expression, or a value for the letter.
Practise Expressions using Letter-Numbers
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device