Question

Saleem wants to create a table of ratios that are equivalent to 2
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 \( \frac{2}{3} \).