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Grade 7 · unit review

Review: Expression Structure and Equivalent Forms

An expression names a quantity without asserting equality to another quantity. Equivalent expressions give the same output for every allowed input, and their structures can reveal repeated groups, fixed extras, or shared factors.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. Expand 7(x+8).
Need a hint?
  • The distributive property rewrites a product of a factor and a sum as a sum of products.
  • A factor outside parentheses cannot be applied to just the first term.
2. Simplify 7x+8−15x+7.
Need a hint?
  • Like terms have the same variable part and exponent.
  • An x-term and a constant do not combine into one x-term.
3. Factor the greatest common positive integer from 21x+35.
Need a hint?
  • Factoring rewrites a sum as a product.
  • After taking out the common factor, divide every original term by it.
4. A fictional kit needs 7 strips of length x plus one extra strip of length 8. Which expression gives total length?
Need a hint?
  • A context can describe a variable amount repeated several times and a fixed amount added once.
  • Parentheses mean the entire grouped amount is repeated.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. Expand 9(x+10). Candidate answers: (A) 19x (B) 9x+10 (C) 9x+90 (D) x+90. 2. Simplify 9x+10−19x+9. Candidate answers: (A) -10x+1 (B) -10x+19 (C) 28x+19 (D) 9x. 3. Factor the greatest common positive integer from 27x+45. Candidate answers: (A) 9(3x+45) (B) 9(3x+5) (C) 9(3x−5) (D) 9(8x). 4. A fictional kit needs 9 strips of length x plus one extra strip of length 10. Which expression gives total length? Candidate answers: (A) (9+10)x (B) 9(x+10) (C) 9x+10 (D) x+90.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 9x+90. Multiply both terms inside the parentheses by 9: 9·x+9·10=9x+90. 2. -10x+19. Combine like x terms: (9−19)x=-10x. Combine constants separately: 10+9=19. The result is -10x+19. 3. 9(3x+5). The coefficients 27 and 45 share greatest common factor 9. Dividing each by it gives 3 and 5; expanding recovers the original. 4. 9x+10. 9 variable strips contribute 9x; the one fixed extra strip contributes 10. The fixed amount is added once, not once per variable strip.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.