Use the given tables to compare the ratios 16:18 and 5:6. Which ratio is greater?

8 9
16 18
24 27
32 36
5 6
10 12
15 18
20 24
(1 point)
Responses

More rows need to be added to the tables to be able to compare the ratios.
More rows need to be added to the tables to be able to compare the ratios.

16:18 is greater.
ratio of 16 to 18 is greater.

The two ratios are equal.
The two ratios are equal.

5:6 is greater.
ratio of 5 to 6 is greater.
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1 answer

To compare the ratios 16:18 and 5:6, we can simplify each ratio:

  1. For 16:18, we can divide both numbers by their greatest common divisor, which is 2: \[ \frac{16}{18} = \frac{16 \div 2}{18 \div 2} = \frac{8}{9} \]

  2. For 5:6, there are no common factors to simplify, so it remains: \[ \frac{5}{6} \]

Next, we can compare the simplified ratios \(\frac{8}{9}\) and \(\frac{5}{6}\) by cross-multiplying:

  • For \(\frac{8}{9}\):

    • Cross-multiply to compare with \(\frac{5}{6}\): \[ 8 \times 6 = 48 \]
  • For \(\frac{5}{6}\):

    • Cross-multiply with \(\frac{8}{9}\): \[ 5 \times 9 = 45 \]

Since \(48 > 45\), we conclude that \(\frac{8}{9} > \frac{5}{6}\).

Therefore, the ratio 16:18 is greater than 5:6.

So, the correct response is: 16:18 is greater.