Which of the following tables could you use to compare the ratios 2:5 and 3:4? Responses 2 5 4 10 6 15 8 20 10 25 3 4 6 8 9 12 12 16 15 20 2 5 4 10 6 15 8 20 10 25 3 4 6 8 9 12 12 16 15 20 - no response given 2 5 4 10 3 4 6 8 2 5 4 10 3 4 6 8 - no response given 2 5 3 10 4 15 5 20 6 25 3 4 4 8 5 12 6 16 7 20 2 5 3 10 4 15 5 20 6 25 3 4 4 8 5 12 6 16 7 20 - no response given 2 5 6 15 10 25 3 4 9 12 16 20

1 answer

To compare the ratios 2:5 and 3:4, we can convert these ratios into equivalent fractions and then find common multiples.

The ratio 2:5 can also be expressed as the fraction \( \frac{2}{5} \) and the ratio 3:4 can be expressed as \( \frac{3}{4} \).

To compare these fractions, we can find a common denominator. The least common multiple (LCM) of the denominators 5 and 4 is 20.

Now, convert each fraction:

\[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \]

\[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \]

Thus, in a comparable form, we have:

  • The ratio \( 2:5 \) corresponds to \( 8:20 \)
  • The ratio \( 3:4 \) corresponds to \( 15:20 \)

To compare these ratios based on available data, we look for the pairs that feature these equivalent values.

From your options, we identify the following:

  • The pair \( 2:5 \) and \( 3:4 \) corresponds to \( 8:20 \) and \( 15:20 \).
  • Look through each set of numbers:
  1. Set 1:

    • 2, 5, 4, 10
    • 6, 15, 8, 20
    • 10, 25, 3, 4
    • 6, 8, 9, 12
    • 12, 16, 15, 20
    • No exact matches.
  2. Set 2:

    • 2, 5, 4, 10
    • 3, 4, 6, 8
    • No exact matches.
  3. Set 3:

    • 2, 5, 3, 10
    • 4, 15, 5, 20
    • 6, 25, 3, 4
    • 4, 8, 5, 12
    • 6, 16, 7, 20
    • Contains 2:5 and 3:4.
  4. Set 4:

    • 2, 5, 6, 15
    • 10, 25, 3, 4
    • 9, 12, 16, 20
    • No exact matches.

The table that you could use to compare the ratios 2:5 and 3:4, after consideration, is the third option where you found both ratios present.

So, the answer is the third table.