Ratio Notation and Relationships · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The Ratio Is the Fraction Is the Line

Mathematics · Ratio & Proportion · ages 12-14
Name ______________________   Date ____________

  1. A recipe uses 2 cups of red juice for every 5 cups of blue juice. Which fraction compares red cups to blue cups?

    • 2/5
    • 5/2
    • 2/7
    • 5/7

  2. A fruit basket has 2 apples for every 5 oranges. Which one correctly writes this as a ratio?

    • 2:5
    • 5:2
    • 2+5
    • 2-5

  3. For every 2 red beads there are 5 blue beads. Which fraction shows red beads as a part of the blue count?

    red2blue5
    • 2/5
    • 5/2
    • 2/7

  4. In a table where y is always 3 times x, that relationship is multiplicative.

    Circle one:   True   False

  5. For every 3 dogs at the park there are 8 cats. Which ratio notation matches this?

    • 8:3
    • 3/11
    • 3:8

  6. The ratio of red paint to blue paint is 3:5. Using y = (3/5)x, where x is cups of blue paint, how many cups of red paint go with 15 cups of blue paint?

    Answer: ______________

  7. In a table, y is always 3 times x. When x = 4, y = 12. What is y when x = 7?

    Answer: ______________

  8. A table shows x=1, y=5; x=2, y=10; x=3, y=15. What is the ratio of y to x?

    1→52→103→15
    • 5:1
    • 1:5
    • 2:10

  9. For every 2 red beads there are 5 blue beads. If x stands for the number of blue beads, which equation gives the number of red beads y?

    • y = (2/5)x
    • y = (5/2)x
    • y = 2x + 5
    • y = x - 3

  10. Priya says the ratio 2:9 means the line through the origin is y = (9/2)x. What is her mistake?

    • The line does not pass through the origin
    • She flipped the fraction; it should be y = (2/9)x
    • She should have added 2 and 9 first
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Answer key

For grown-ups. Fold this page away before handing over the rest.

The Ratio Is the Fraction Is the Line W1-mt_yK51ZnKA8m-s1

  1. 2/5 · A ratio a:b can always be written as the fraction a/b, so 2:5 becomes 2/5.
  2. 2:5 · The ratio keeps the same order as the words: apples first, then oranges, so it's 2:5.
  3. 2/5 · The ratio 2:5 becomes the fraction 2/5: red compared to blue, not red compared to the total of both.
  4. True · Multiplying x by 3 always gives y, every single time, which is exactly what a multiplicative relationship means.
  5. 3:8 · Ratio notation keeps the order things are described in: dogs first, then cats, so 3:8. Writing 3/11 mixes up part-to-part with part-to-whole.
  6. 9 · Plug x = 15 into y = (3/5)x and simplify.
  7. 21 · Multiply x by the constant 3 to find y.
  8. 5:1 · Every y is 5 times its x, so the ratio y:x is 5:1. Picking one row's raw numbers like 2:10 does not describe the whole pattern.
  9. y = (2/5)x · The ratio red:blue = 2:5 becomes the fraction 2/5, and that fraction is the multiplier in y = (2/5)x.
  10. She flipped the fraction; it should be y = (2/9)x · The first number in the ratio goes on top of the fraction: 2:9 gives 2/9, so the line is y = (2/9)x.
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