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Which table shows equivalent ratios?

A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 4, 5, 6. Column 2 is labeled Inches with entries 36, 48, 60, 72.
A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 3, 4, 6. Column 2 is labeled Inches with entries 22, 39, 48, 72.
A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 5, 6, 7. Column 2 is labeled Inches with entries 24, 60, 72, 84.
A 2-column table with 4 rows. Column 1 is labeled Feet with entries 2, 3, 4, 6. Column 2 is labeled Inches with entries 28, 36, 48, 72.

1 answer

To determine which table shows equivalent ratios, we need to check if the ratios of Feet to Inches in each table are consistent.

We'll calculate the ratio of Feet to Inches for each entry in the tables.

  1. First Table

    • 2 Feet = 36 Inches → Ratio = 2/36 = 1/18
    • 4 Feet = 48 Inches → Ratio = 4/48 = 1/12
    • 5 Feet = 60 Inches → Ratio = 5/60 = 1/12
    • 6 Feet = 72 Inches → Ratio = 6/72 = 1/12

    (The ratios are not equivalent.)

  2. Second Table

    • 2 Feet = 22 Inches → Ratio = 2/22 = 1/11
    • 3 Feet = 39 Inches → Ratio = 3/39 = 1/13
    • 4 Feet = 48 Inches → Ratio = 4/48 = 1/12
    • 6 Feet = 72 Inches → Ratio = 6/72 = 1/12

    (The ratios are not equivalent.)

  3. Third Table

    • 2 Feet = 24 Inches → Ratio = 2/24 = 1/12
    • 5 Feet = 60 Inches → Ratio = 5/60 = 1/12
    • 6 Feet = 72 Inches → Ratio = 6/72 = 1/12
    • 7 Feet = 84 Inches → Ratio = 7/84 = 1/12

    (All are equivalent to 1/12.)

  4. Fourth Table

    • 2 Feet = 28 Inches → Ratio = 2/28 = 1/14
    • 3 Feet = 36 Inches → Ratio = 3/36 = 1/12
    • 4 Feet = 48 Inches → Ratio = 4/48 = 1/12
    • 6 Feet = 72 Inches → Ratio = 6/72 = 1/12

    (The first ratio is different.)

Based on this evaluation, the third table shows equivalent ratios, as they all equal 1/12.