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🧩 6th grade math · Patterns & Algebra

Equal expressions

Divide each number by the GCF to find what goes inside the parentheses. 56 − 24: the GCF is 8, and 56 ÷ 8 = 7 and 24 ÷ 8 = 3. So 56 − 24 = 8(7 − 3).

Worked example

Write 21 − 14 as a number times a sum: ?(3 − 2). What number goes where the ? is?
Answer: 7
21 = 7 × 3 and 14 = 7 × 2, so 21 − 14 = 7 × 3 − 7 × 2 = 7(3 − 2). Answer: 7.

For grown-ups: Equivalent expressions (distributive property, like terms). Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 6.EE.A.3–4
What this practises, for teachers

Practices equivalent expressions (distributive property, like terms) (6.EE.A.3–4). A printable sheet with its answer key, worked answers on the page, no accounts.

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🖨️ Printable sheet and key

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Try three

  1. Which expression is equal to 15 + 25?
    Show the answer and how
    Answer: 5(3 + 5)
    15 + 25 = 40. The matching expression is 5(3 + 5): work it out to check that it also makes 40.
  2. Which expression is equal to 187 + 68?
    Show the answer and how
    Answer: 17(11 + 4)
    187 + 68 = 255. The matching expression is 17(11 + 4): work it out to check that it also makes 255.
  3. Which expression is equal to 75 + 105?
    Show the answer and how
    Answer: 15(5 + 7)
    75 + 105 = 180. The matching expression is 15(5 + 7): work it out to check that it also makes 180.

Before and after

Learn first: Letters for numbers (6th)

Comes next: One-step equations (6th)

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Equal expressions (6th grade)

  1. 33 + 24 = 3(□ + 8). What number goes in the box?
  2. Which expression is equal to 72 − 12?
  3. 132 + 96 = 12(□ + 8). What number goes in the box?
  4. 33 + 36 = 3(□ + 12). What number goes in the box?
  5. Which expression is equal to 40 + 35?
  6. The GCF of 36 and 198 is 18, so 36 + 198 = 18(□). What number goes in the box, in the parentheses?
  7. Which expression is equal to 84 − 70?
  8. Which expression is equal to 15 + 30?
  9. Which expression is equal to 54 − 18?
  10. 55 + 88 = 11(□ + 8). What number goes in the box?
  11. The GCF of 33 and 121 is 11, so 33 + 121 = 11(□). What number goes in the box, in the parentheses?
  12. Which expression is equal to 180 − 18?

Answer key

  1. 11
  2. 12(6 − 1)
  3. 11
  4. 11
  5. 5(8 + 7)
  6. 13
  7. 14(6 − 5)
  8. 15(1 + 2)
  9. 18(3 − 1)
  10. 5
  11. 14
  12. 18(10 − 1)

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