Saleem wants to create a table of ratios that are equivalent to 2

Question

3
. He includes the ratios 4
5
and 5
6
.

Are these ratios equivalent to 2
3
? Explain your reasoning.

Answer 1

To determine if the ratios \( \frac{4}{5} \) and \( \frac{5}{6} \) are equivalent to \( \frac{2}{3} \), we can cross-multiply to compare them.

1. For \( \frac{4}{5} \) and \( \frac{2}{3} \):

   • Cross-multiply: \[ 4 \times 3 = 12 \] \[ 2 \times 5 = 10 \] Since \( 12 \neq 10 \), \( \frac{4}{5} \) is not equivalent to \( \frac{2}{3} \).

2. For \( \frac{5}{6} \) and \( \frac{2}{3} \):

   • Cross-multiply: \[ 5 \times 3 = 15 \] \[ 2 \times 6 = 12 \] Since \( 15 \neq 12 \), \( \frac{5}{6} \) is not equivalent to \( \frac{2}{3} \).

Thus, neither \( \frac{4}{5} \) nor \( \frac{5}{6} \) is equivalent to \( \frac{2}{3} \).