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Grade 7 Algebraic Expressions Practice

Combine Like Terms and Build Equivalent Expressions

Terms that match can be added together. You'll combine like terms, use the distributive property, and spot the mistakes people make when simplifying.

Also known as Class 7 maths — the same topics, whether your school calls it grade, class or year.

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Sample questions

A few samples from this topic — try one, then show the answer.

  1. Recognize Like and Unlike Terms

    What does 4n  +  3n  +  4n 4n \;+\; 3n \;+\; 4n\, equal when simplified?
    • 48n
    • 11n
    • 11n211n^{2}
    • 434n
    Show answer
    Answer:
    11n

  2. Build Two-Step Expressions from Situations

    The expression 4s 4s\, gives the perimeter of a square. What does s s\, represent?
    • The side length of the square
    • The perimeter
    • The area
    • The number of sides
    Show answer
    Answer:
    The side length of the square

  3. Use the Distributive Property

    Simplify: 4(c  −  r )(c \; - \; r\,).
    Show answer
    Answer:
    4c - 4r

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A worked example

What does 4n  +  3n  +  4n 4n \;+\; 3n \;+\; 4n\, equal when simplified?
  1. We need to simplify 4n  +  3n  +  4n 4n \;+\; 3n \;+\; 4n\,.
  2. All terms have the variable n n\,, so they are like terms. Combine the coefficients:4  +  3  +  4  =  11→11n\\ 4 \;+\; 3 \;+\; 4 \;=\; 11 \to 11n
  3. The simplified expression is 11n 11n\,.
  4. Checking each option:11n \\ 11n\, ✓48n→\\ 48n \tothis multiplies the coefficients (4×3×4  =  484 \times 3 \times 4 \;=\; 48) instead of adding them ✘11n2→\\ 11n^{2} \toadding like terms does not change the exponent; n n\, stays as n n\,, not n2 n^{2}\, ✘434n→\\ 434n \tothis joins the digits together instead of adding the coefficients ✘

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