Class 7 Maths · Original EZT practice
Expressions Using Letter-Numbers (Class 7 Chapter 4): summary and practice
Letters begin to stand for numbers: writing expressions with letter-numbers, dropping the multiplication symbol, reading terms as like or unlike, substituting values, and simplifying by collecting like terms - then using expressions to describe patterns. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 22 October 2026:
1. The notion of letter-numbers
A letter stands for a number that can change or is not yet known. The perimeter of a square of side s is 4s - one short expression covering every square.
2. Omitting the multiplication symbol
4 x s is written 4s, and a x b as ab. The symbol hides only between a number and a letter (or between letters) - never between two numbers.
3. Terms, like and unlike
An expression splits into terms joined by + or -. Like terms carry the same letter part (3x and 2x); unlike terms do not (3x and 4). Only like terms combine.
4. Simplification and patterns
Collect like terms to simplify, substitute values to evaluate, and use expressions to describe and explain patterns - the chapter's closing theme.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Write an expression for a rule
Choose the method: Name the changing quantity with a letter, then write the rule with it.
EZT practice question
Write the perimeter of a square of side s, and find it for s = 7 cm.
Show the worked solution
- A square has 4 equal sides, so perimeter = 4 x s = 4s.
- Substitute s = 7.
- 4 x 7 = 28 cm.
Answer: Perimeter 4s; for s = 7 cm, 28 cm.
Check: Direct count: 7 + 7 + 7 + 7 = 28. The expression and the arithmetic agree.
Watch for this: 4s means 4 TIMES s - the multiplication symbol is hidden, not the operation.
Now try it yourself
Perimeter of an equilateral triangle of side a, at a = 9 cm?
Check your answer
3a; 27 cm.
3 equal sides.
Substitute a value
Choose the method: Replace the letter by the given number, then compute.
EZT practice question
Find the value of n + 5 at n = 12.
Show the worked solution
- Replace n by 12.
- 12 + 5.
- = 17.
Answer: 17.
Check: n + 5 always sits 5 above n - 17 is exactly 5 above 12.
Watch for this: Substitution replaces the letter EVERYWHERE it appears - in 2n + 5 at n = 12, both the multiplication and the addition happen.
Now try it yourself
Value of 2n + 5 at n = 12?
Check your answer
29.
2 x 12 + 5.
Simplify by collecting like terms
Choose the method: Add or subtract the coefficients of like terms; leave unlike terms untouched.
EZT practice question
Simplify 3x + 2x + 4.
Show the worked solution
- 3x and 2x are like terms - same letter part x.
- 3x + 2x = 5x.
- The constant 4 has no partner, so it stays: 5x + 4.
Answer: 5x + 4.
Check: Test at x = 1: original gives 3 + 2 + 4 = 9, simplified gives 5 + 4 = 9 - same value, simpler form.
Watch for this: 3x + 4 is NOT 7x - the 4 has no x, so it cannot join the x terms.
Now try it yourself
Simplify 2a + 3a - 1.
Check your answer
5a - 1.
2a + 3a = 5a; -1 stands alone.
Like versus unlike terms
Choose the method: Compare the letter parts, not the coefficients.
EZT practice question
Which terms in 4a + 3b + 2a + 5 can be combined, and what is the simplified expression?
Show the worked solution
- Letter parts: a, b, a, (none).
- Like pair: 4a and 2a combine to 6a.
- 3b and 5 have no partners: result 6a + 3b + 5.
Answer: 6a + 3b + 5.
Check: Count the families: a-terms, b-terms, constants - three families, three terms in the answer. Nothing was lost.
Watch for this: Do not merge different letters: 6a + 3b is not 9ab - a and b count different things.
Now try it yourself
Simplify 5x + x + 2y.
Check your answer
6x + 2y.
5x + x = 6x; 2y stays.
Expressions from word situations
Choose the method: Translate the situation: unit rate x quantity.
EZT practice question
A pen costs Rs 15. Write the cost of p pens, and find it for p = 8.
Show the worked solution
- Each pen adds Rs 15, so cost = 15 x p = 15p.
- Substitute p = 8.
- 15 x 8 = 120.
Answer: Cost 15p rupees; 8 pens cost Rs 120.
Check: Doubling the pens doubles the cost: 4 pens cost 60, 8 pens cost 120 - the expression scales correctly.
Watch for this: Keep the units straight: 15p is in rupees only because 15 was rupees per pen.
Now try it yourself
Cost of q notebooks at Rs 40 each, for q = 5?
Check your answer
40q; Rs 200.
40 x 5.
Describe a pattern with an expression
Choose the method: Find what changes per step - that becomes the letter's coefficient.
EZT practice question
A row of triangles uses 3 matchsticks for the first triangle and 2 more for each added triangle. Write the matchsticks for t triangles (sharing sides), and check t = 2.
Show the worked solution
- First triangle: 3 sticks.
- Each further triangle shares one side, adding 2 sticks.
- Total = 3 + 2(t - 1) = 2t + 1.
Answer: 2t + 1; for t = 2, 5 sticks.
Check: Two shared-side triangles really use 5 sticks (3 + 2) - draw it and count.
Watch for this: 3 + 2(t - 1), not 3 + 2t - the first triangle is already counted in the 3.
Now try it yourself
Sticks for t = 5 triangles?
Check your answer
11.
2 x 5 + 1.
Try a mixed set
Choose a method or explanation before opening each answer.
1. What does 4s mean?
Show answer and reason
4 times s.
The multiplication symbol is omitted.
2. Like terms?
Show answer and reason
Terms with the same letter part, like 3x and 2x.
Only they can combine.
3. Simplify 3x + 2x.
Show answer and reason
5x.
Add the coefficients of like terms.
4. Can 3x + 4 be simplified further?
Show answer and reason
No - 3x and 4 are unlike terms.
A constant cannot join an x term.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Simplify 2a + 3a - 1.
- Cost of q notebooks at Rs 40 each, for q = 5.
- Perimeter of an equilateral triangle of side a, at a = 9 cm.
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Questions about this practice page
- What does a letter-number stand for?
- A number that can change or is not known yet. Writing the perimeter of a square as 4s covers every possible side length at once - that generality is the whole point of algebra.
- How do like terms combine?
- By adding or subtracting their coefficients: 3x + 2x = 5x. The letter part stays exactly as it was - combining changes how MANY of the term you have, not what the term is.
- Why is 3x + 4 not 7x?
- Because 3x counts x's and 4 counts ones - unlike things. Only like terms (same letter part) combine; 3x + 4 is already fully simplified.
- When can the multiplication symbol be omitted?
- Between a number and a letter (4 x s becomes 4s) or between letters (a x b becomes ab) - never between two numbers, where 23 would be misread as twenty-three.
- Are these the NCERT exercise questions for Expressions Using Letter-Numbers (Class 7)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.