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About Algebraic Expressions — Class 7 IB

Simplify, expand, and factor basic algebraic expressions with one or two variables. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 3). On this page you can practice 50 questions across three difficulty levels — 20 easy, 20 medium, and 10 hard — each with a visual step-by-step solution, plus a timed 25-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Algebraic Expressions

  • Introduction to Algebraic Expressions
  • Like Terms and Simplifying Expressions
  • Expanding Brackets
  • Factoring Expressions
  • Substitution and Writing Expressions from Word Problems

Interactive lesson · about 90 minutes · checkpoint question after every unit

Algebraic Expressions — solved examples for Class 7 IB

Example 1easy

Which pair of terms are considered 'like terms' in algebraic expressions?
  1. A)A. 3x and -5x
  2. B)B. 2y and 2x
  3. C)C. 7 and 7a
  4. D)D. 4ab and 4a

Step-by-step solution

  1. Identify the variables and their powers in each term for all options.
  2. For option A, '3x' and '-5x' both have the variable 'x' raised to the power of 1. These are like terms.
  3. For option B, '2y' has variable 'y' while '2x' has variable 'x', so they are not like terms. Similarly for C and D, the variables or their combinations are different.

Answer: A. 3x and -5x

Example 2medium

Simplify the algebraic expression: 5x + 3y - 2x + 7 - y.
  1. A)3x + 2y + 7
  2. B)7x + 4y + 7
  3. C)3x + 4y + 7
  4. D)7x + 2y + 7

Step-by-step solution

  1. Group the like terms together: (5x - 2x) + (3y - y) + 7.
    (5x−2x)+(3y−y)+7(5x - 2x) + (3y - y) + 7
  2. Combine the 'x' terms: 5x - 2x = 3x.
  3. Combine the 'y' terms: 3y - y = 2y.
  4. Write the simplified expression by combining all parts: 3x + 2y + 7.
    3x+2y+73x + 2y + 7

Answer: 3x + 2y + 7

Example 3hard

Alex was simplifying the expression `5x - (3 - 2x) + 0.5(4x - 6)`. His steps are shown below:
Step 1: `5x - 3 + 2x + 0.5(4x - 6)`
Step 2: `5x - 3 + 2x + 2x - 3`
Step 3: `(5x + 2x + 2x) - (3 + 3)`
Step 4: `9x - 5`
In which step did Alex make the first mistake?
  1. A)Step 1
  2. B)Step 2
  3. C)Step 3
  4. D)Step 4

Step-by-step solution

  1. Original expression: `5x - (3 - 2x) + 0.5(4x - 6)`
  2. Step 1: `5x - 3 + 2x + 0.5(4x - 6)` (Correct: `-(3 - 2x)` becomes `-3 + 2x`)
  3. Step 2: `5x - 3 + 2x + 2x - 3` (Correct: `0.5(4x - 6)` becomes `2x - 3`)
  4. Step 3: `(5x + 2x + 2x) - (3 + 3)` (Correct: This is a correct grouping of terms, which simplifies to `9x - 6`)
  5. Step 4: `9x - 5` (Incorrect: From Step 3, `(5x + 2x + 2x) - (3 + 3)` should simplify to `9x - 6`, not `9x - 5`. The mistake is in the final arithmetic of the constant terms.)

Answer: Step 4

Practice questions on Algebraic Expressions

  1. Q1.easy

    Simplify the expression: 7a + 3b - 2a + 5b.
    1. A)A. 5a + 2b
    2. B)B. 5a + 8b
    3. C)C. 9a + 8b
    4. D)D. 12ab
    Show answer

    Answer: B. 5a + 8b

    Hint: Group the 'a' terms together and the 'b' terms together, then perform the addition or subtraction for each group separately.

  2. Q2.easy

    Expand the expression: 4(2x - 3).
    1. A)A. 8x - 3
    2. B)B. 2x - 12
    3. C)C. 8x - 12
    4. D)D. 4x - 12
    Show answer

    Answer: C. 8x - 12

    Hint: Remember to apply the distributive property by multiplying the term outside the bracket by *each* term inside the bracket.

  3. Q3.easy

    The formula for the cost of renting a bicycle in Amsterdam is C = 5h + 8, where C is the total cost in euros and h is the number of hours. If you rent a bicycle for 3 hours, what is the total cost?
    1. A)A. €13
    2. B)B. €15
    3. C)C. €18
    4. D)D. €23
    Show answer

    Answer: D. €23

    Hint: Substitute the given value for 'h' into the formula and then calculate the result.

  4. Q4.medium

    Expand and simplify the expression: 4(2a - 3b) - 2(a + 5b).
    1. A)6a - 22b
    2. B)6a + 2b
    3. C)10a - 22b
    4. D)10a + 2b
    Show answer

    Answer: 6a - 22b

    Hint: Use the distributive property to multiply the numbers outside the brackets by each term inside. Pay close attention to negative signs when expanding the second bracket.

  5. Q5.medium

    A scientist is tracking the growth of a special plant. The height of the plant, H (in cm), after 'd' days and 'w' weeks is given by the formula H = 5d + 12w + 10. If a plant has grown for 3 days and 2 weeks, what is its height?
    1. A)49 cm
    2. B)59 cm
    3. C)39 cm
    4. D)41 cm
    Show answer

    Answer: 49 cm

    Hint: Substitute the given values for 'd' and 'w' into the formula and then calculate the result. Remember that 'w' represents weeks.

  6. Q6.medium

    A taxi service in Berlin charges a flat fee of €3.50 plus €2.20 per kilometre travelled. If a passenger travels 'k' kilometres, which expression represents the total cost of the ride in euros?
    1. A)3.50k + 2.20
    2. B)2.20k + 3.50
    3. C)(3.50 + 2.20)k
    4. D)3.50 - 2.20k
    Show answer

    Answer: 2.20k + 3.50

    Hint: Identify the variable cost (per kilometre) and the fixed cost (flat fee). The variable cost will be multiplied by the number of kilometres.

  7. Q7.hard

    A farmer is fencing a rectangular enclosure for his animals. The length of the enclosure is `(3x + 5)` metres and the width is `(x - 2)` metres. If he needs to fence 4 such identical enclosures, which expression represents the total length of fencing required?
    1. A)16x + 12
    2. B)32x + 12
    3. C)32x + 24
    4. D)8x + 6
    Show answer

    Answer: 32x + 24

    Hint: First, find the perimeter of one enclosure using the formula P = 2(Length + Width). Then, multiply that expression by the number of enclosures.

  8. Q8.hard

    Which of the following expressions is the fully factored form of `9ab + 15b - 3bc`?
    1. A)3(3ab + 5b - bc)
    2. B)3b(3a + 5 - c)
    3. C)b(9a + 15 - 3c)
    4. D)9b(a + 15 - 3c)
    Show answer

    Answer: 3b(3a + 5 - c)

    Hint: Look for the greatest common factor (GCF) that divides all terms, including both numerical coefficients and variables.

  9. Q9.hard

    If `a = 2x` and `b = 3`, what is the value of the expression `4a - 2(b + a)` when `x = 5`?
    1. A)24
    2. B)10
    3. C)20
    4. D)14
    Show answer

    Answer: 14

    Hint: Substitute the expressions for 'a' and 'b' into the main expression first, simplify it, and then substitute the value of 'x'.

These are 9 of the 50 questions available for Algebraic Expressions. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.