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Proportional relationships worksheet

Grade 7 math, Common Core 7.RP.A.2a. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Proportional relationships

Grade 7 math, Common Core 7.RP.A.2a

Decide if each relationship is proportional, or use the proportion to answer.

  1. 1.
    Is y = 6x a proportional relationship?
  2. 2.
    If 2 pounds of apples cost $16.00, how much do 8 pounds of apples cost?
  3. 3.
    Is y = 4x a proportional relationship?
  4. 4.
    If 4 tickets cost $30.00, how much do 6 tickets cost?
  5. 5.
    Is y proportional to x? Explain.
    x1357
    y4122028
  6. 6.
    If 2 tickets cost $7.00, how much do 12 tickets cost?
  7. 7.
    Is y proportional to x? Explain.
    x1357
    y5152535
  8. 8.
    If 6 pounds of apples cost $48.00, how much do 5 pounds of apples cost?
  9. 9.
    Is y proportional to x? Explain.
    x2468
    y7121722
  10. 10.
    Is y = 5x + 5 a proportional relationship?
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Proportional relationships

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. Yes. It has the form y = kx, with k = 6.

  2. 2. $64.00

    Unit rate: $16.00 ÷ 2 = $8.00 each$8.00 × 8 = $64.00

  3. 3. Yes. It has the form y = kx, with k = 4.

  4. 4. $45.00

    Unit rate: $30.00 ÷ 4 = $7.50 each$7.50 × 6 = $45.00

  5. 5. Yes. y ÷ x is always 4.

  6. 6. $42.00

    Unit rate: $7.00 ÷ 2 = $3.50 each$3.50 × 12 = $42.00

  7. 7. Yes. y ÷ x is always 5.

  8. 8. $40.00

    Unit rate: $48.00 ÷ 6 = $8.00 each$8.00 × 5 = $40.00

  9. 9. No. y ÷ x changes: 7 ÷ 2 = 3.5, but 12 ÷ 4 = 3.

  10. 10. No. The + 5 means the line doesn’t go through (0, 0).

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About proportional relationships

Two amounts are in a proportional relationship when one is always the same number times the other, like 3 dollars for every pound. In a table, y ÷ x is the same for every pair. You can then use the unit rate to find any missing amount.

Worked example 1

If 6 pounds of apples cost $24.00, how much do 11 pounds of apples cost?
  1. Step 1.Unit rate: $24.00 ÷ 6 = $4.00 each
  2. Step 2.$4.00 × 11 = $44.00

Answer: $44.00

Worked example 2

If 2 notebooks cost $7.00, how much do 8 notebooks cost?
  1. Step 1.Unit rate: $7.00 ÷ 2 = $3.50 each
  2. Step 2.$3.50 × 8 = $28.00

Answer: $28.00

Worked example 3

If 4 tickets cost $10.00, how much do 8 tickets cost?
  1. Step 1.Unit rate: $10.00 ÷ 4 = $2.50 each
  2. Step 2.$2.50 × 8 = $20.00

Answer: $20.00

Watch out for

  • Check every pair in the table, not just the first two.
  • A proportional relationship always includes (0, 0): zero pounds cost zero dollars.
  • Find the unit rate first, then multiply.

Practice proportional relationships online

On StudyWiz, your kid can practice proportional relationships with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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