Compare the ratios from the tables.

Question

2:3 is
5:6
10:12 is
6:9
The ratios in Table 1 are
the ratios in Table 2.

Answer 1

To compare the ratios, we can simplify each ratio and check if they are equivalent.

1. The ratio 2:3 can be compared to 5:6:

   • \( \frac{2}{3} \) and \( \frac{5}{6} \)

   To compare, we can cross-multiply:

   • \( 2 \times 6 = 12 \)
   • \( 3 \times 5 = 15 \)

   Since \( 12 \neq 15 \), the ratios \( 2:3 \) and \( 5:6 \) are not equivalent.

2. The ratio 10:12 can be compared to 6:9:

   • First, simplify 10:12: \( \frac{10}{12} = \frac{5}{6} \) (dividing both by 2)
   • Now compare \( \frac{5}{6} \) with \( \frac{6}{9} \): First, simplify 6:9: \( \frac{6}{9} = \frac{2}{3} \) (dividing both by 3)

   Now we have:

   • \( \frac{5}{6} \) and \( \frac{2}{3} \)

   To compare further, cross-multiply:

   • \( 5 \times 3 = 15 \)
   • \( 6 \times 2 = 12 \)

   Since \( 15 \neq 12 \), the ratios \( 10:12 \) and \( 6:9 \) are also not equivalent.

In conclusion, the ratios in Table 1 (2:3 and 10:12) are not equivalent to the ratios in Table 2 (5:6 and 6:9).