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Expressions using Letter-Numbers – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 4. Notes, key terms, important questions with answers and MCQs.

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Chapter overview

Letters can stand for numbers. Algebraic expressions describe patterns and rules in a short, general way.

Letters as numbers

  • If a pen costs ₹p, then 5 pens cost ₹5p.
  • Perimeter of a square of side s is 4s.
  • Like terms (3x, 7x) can be added: 3x + 7x = 10x; unlike terms (3x, 2y) cannot.

Using expressions

  • Evaluate by substituting: if n = 4, 3n + 2 = 14.
  • Patterns: matchsticks for n squares in a row = 3n + 1.
  • Simplify by combining like terms: 5a + 2b − 3a + b = 2a + 3b.

Key terms

Variable
a letter that can take different values
Algebraic expression
an expression with numbers and letters
Like terms
terms with the same letter part

Formulas

  • Perimeter of rectangle = 2(l + b)

Important questions with answers

Write an expression: "5 more than three times a number n".2 marks

Three times n is 3n; 5 more gives 3n + 5.

The perimeter of a rectangle with length l and breadth b is 2(l + b). Find it when l = 12 cm and b = 7 cm.3 marks

2(12 + 7) = 2 × 19 = 38 cm.

A matchstick pattern uses 4 sticks for 1 square, 7 for 2 squares, 10 for 3 squares in a row. Find the rule for n squares, the sticks for 20 squares, and how many squares can be made with 61 sticks.5 marks

Each new square adds 3 sticks to the first 4, so sticks = 3n + 1. For n = 20: 61 sticks. With 61 sticks: 3n + 1 = 61, n = 20 squares.

Quick revision

  • Letters stand for numbers.
  • Add only like terms.
  • Substitute to find a value.

Exam tips

  • 5x means 5 × x; do not write it as x5.
  • Check a pattern rule by testing small values (n = 1, 2, 3).

Practice MCQs

  1. If one book costs ₹b, then 7 books cost

    1. ₹7b
    2. ₹7 + b
    3. ₹b/7
    4. ₹b − 7
    Show answer

    Answer: (a) ₹7b. 7 × b.

  2. 4x + 5x equals

    1. 9x
    2. 20x
    3. 9x²
    4. 9
    Show answer

    Answer: (a) 9x. Like terms.

  3. Value of 2m + 3 when m = 5 is

    1. 10
    2. 13
    3. 25
    4. 8
    Show answer

    Answer: (b) 13. 10 + 3.

  4. Simplify 6a + 4 − 2a + 3

    1. 8a + 7
    2. 4a + 7
    3. 4a + 1
    4. 11a
    Show answer

    Answer: (b) 4a + 7. (6a − 2a) + (4 + 3).

  5. Simplify 5x + 3 − 2x + 7

    1. 3x + 10
    2. 7x + 10
    3. 3x + 4
    4. 13x
    Show answer

    Answer: (a) 3x + 10. Combine like terms.

  6. Matchsticks needed for n triangles in a row (sharing sides) is

    1. 3n
    2. n + 2
    3. 2n + 1
    4. 3n − 1
    Show answer

    Answer: (c) 2n + 1. 3 for the first, then 2 more each: 2n + 1.

  7. Ravi is x years old. His father is 4 years more than three times Ravi's age. Father's age is

    1. x + 12
    2. 4x + 3
    3. 3(x + 4)
    4. 3x + 4
    Show answer

    Answer: (d) 3x + 4. Three times x plus 4.

  8. If a = 3 and b = −2, the value of 2a² − 3b is

    1. 24
    2. 12
    3. 18
    4. 0
    Show answer

    Answer: (a) 24. 18 + 6.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.