Loading...

About Algebraic Expressions — Class 7 CBSE

Form and evaluate algebraic expressions using variables and constants. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 4). On this page you can practice 61 questions across three difficulty levels — 20 easy, 20 medium, and 21 hard — each with a visual step-by-step solution, plus a timed 36-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Algebraic Expressions

  • Unit 1: Introduction to Algebraic Expressions
  • Unit 2: Terms, Factors, and Coefficients
  • Unit 3: Forming Algebraic Expressions from Statements
  • Unit 4: Simplifying Algebraic Expressions (Combining Like Terms)
  • Unit 5: Evaluating Algebraic Expressions

Interactive lesson · about 15 minutes · checkpoint question after every unit

Algebraic Expressions — solved examples for Class 7 CBSE

Example 1easy

Which of the following statements correctly describes a variable in an algebraic expression?
  1. A)It is a fixed numerical value.
  2. B)It is an unknown value that can change or take different values.
  3. C)It is always the number zero.
  4. D)It is a mathematical operation sign, like + or -.

Step-by-step solution

  1. A variable is a symbol, usually a letter, that represents an unknown quantity or a quantity that can change.
  2. Unlike a constant, which has a fixed value, a variable's value can vary.

Answer: It is an unknown value that can change or take different values.

Example 2medium

In the algebraic expression 5x²y - 3xy + 7, what is the coefficient of the term 'xy'?
  1. A)5
  2. B)3
  3. C)-3
  4. D)7

Step-by-step solution

  1. The given expression is 5x²y - 3xy + 7.
  2. The terms in the expression are 5x²y, -3xy, and 7.
  3. The term containing 'xy' is -3xy. The numerical factor in this term is -3.
  4. Therefore, the coefficient of xy is -3.

Answer: -3

Example 3hard

The sum of three consecutive odd integers is represented by an algebraic expression. If the smallest odd integer is '2n - 1', what is the expression for the sum of the three integers?
  1. A)6n - 3
  2. B)6n + 3
  3. C)6n + 9
  4. D)6n - 1

Step-by-step solution

  1. Let the smallest odd integer be '2n - 1'.
  2. The next consecutive odd integer will be (2n - 1) + 2 = 2n + 1.
  3. The third consecutive odd integer will be (2n + 1) + 2 = 2n + 3.
  4. The sum of the three integers is (2n - 1) + (2n + 1) + (2n + 3) = 2n + 2n + 2n - 1 + 1 + 3 = 6n + 3.

Answer: 6n + 3

Practice questions on Algebraic Expressions

  1. Q1.easy

    The cost of one apple is ₹'a' and the cost of one banana is ₹'b'. What is the total cost of 5 apples and 3 bananas?
    1. A)a + b
    2. B)5a + 3b
    3. C)5a × 3b
    4. D)5 + a + 3 + b
    Show answer

    Answer: 5a + 3b

    Hint: To find the total cost, consider the cost of each item multiplied by its quantity, and then add them together.

  2. Q2.easy

    In the expression 7x²y - 4xy + 9, identify the coefficient of the term 'xy'.
    1. A)7
    2. B)x²
    3. C)-4
    4. D)9
    Show answer

    Answer: -4

    Hint: The coefficient is the numerical factor that multiplies the variable part of a term. Pay close attention to the sign.

  3. Q3.easy

    Which of the following pairs represents 'like terms'?
    1. A)6x, 6y
    2. B)9ab, 4ba
    3. C)3p², 3p
    4. D)2m, 2mn
    Show answer

    Answer: 9ab, 4ba

    Hint: Like terms must have the exact same variables raised to the same powers. Remember that the order of multiplication does not change the product.

  4. Q4.medium

    Form an algebraic expression for '7 times the sum of x and y'.
    1. A)7x + y
    2. B)7(x + y)
    3. C)x + 7y
    4. D)7xy
    Show answer

    Answer: 7(x + y)

    Hint: Pay close attention to the order of operations. 'Sum' means addition, and '7 times' means multiplication applied to the entire sum.

  5. Q5.medium

    Which of the following pairs represents like terms?
    1. A)3x, 3y
    2. B)5x², 5x
    3. C)7ab, -2ba
    4. D)4p, 4q
    Show answer

    Answer: 7ab, -2ba

    Hint: Like terms have the same algebraic factors, meaning the same variables raised to the same powers, regardless of the order of variables.

  6. Q6.medium

    Add the expressions: (3x + 5y) and (2x - 2y).
    1. A)x + 3y
    2. B)5x + 7y
    3. C)x + 7y
    4. D)5x + 3y
    Show answer

    Answer: 5x + 3y

    Hint: To add expressions, group the like terms together and then combine their coefficients.

  7. Q7.hard

    Consider the algebraic expression: 5x²y - (3/4)xy² + x²y - 7. Which of the following statements about its terms and coefficients is INCORRECT?
    1. A)The coefficient of x²y is 6.
    2. B)The term with coefficient -3/4 is -(3/4)xy².
    3. C)The expression has 4 terms.
    4. D)The constant term is -7.
    Show answer

    Answer: The coefficient of x²y is 6.

    Hint: First, simplify the expression by combining like terms. Then carefully identify the coefficients for each distinct term.

  8. Q8.hard

    Which of the following pairs of terms are NOT like terms?
    1. A)3mn and -7nm
    2. B)5x²y and 2yx²
    3. C)4pq² and -6p²q
    4. D)x/2 and 3x
    Show answer

    Answer: 4pq² and -6p²q

    Hint: Remember that like terms must have the same variables raised to the same powers, regardless of the order of multiplication or the numerical coefficient.

  9. Q9.hard

    Simplify the expression: 7a - [4b - {3a - (2b - 5a)}]
    1. A)15a - 6b
    2. B)a - 6b
    3. C)15a - 2b
    4. D)a + 2b
    Show answer

    Answer: 15a - 2b

    Hint: Work from the innermost parentheses outwards. Pay close attention to the negative signs before brackets and distribute them carefully.

These are 9 of the 61 questions available for Algebraic Expressions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.