5. Your team won 12 out of 15 games. Your friend's team won 15 out of 18 games. Are the ratios proportional?

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UpStudy AI · Accepted Answer

To determine whether the ratios of your team's wins to total games and your friend's team's wins to total games are proportional, follow these steps:

1. **Identify the Ratios:**
   - **Your Team:** Won 12 out of 15 games.  
     Ratio = $$ \frac{12}{15} $$
   - **Friend's Team:** Won 15 out of 18 games.  
     Ratio = $$ \frac{15}{18} $$

2. **Simplify Both Ratios:**
   - **Your Team:**  
     $$ \frac{12}{15} = \frac{4}{5} $$ (divided numerator and denominator by 3)
   - **Friend's Team:**  
     $$ \frac{15}{18} = \frac{5}{6} $$ (divided numerator and denominator by 3)

3. **Compare the Simplified Ratios:**
   - $$ \frac{4}{5} $$ vs. $$ \frac{5}{6} $$

To see if they are equal:
   $$
   \frac{4}{5} \stackrel{?}{=} \frac{5}{6}
   $$
   Cross-multiply to check:
   $$
   4 \times 6 = 24 \quad \text{and} \quad 5 \times 5 = 25
   $$
   Since $$ 24 \neq 25 $$, the ratios are **not** equal.

4. **Conclusion:**
   The ratios $$ \frac{12}{15} $$ and $$ \frac{15}{18} $$ are **not proportional** because they simplify to different values ($$ \frac{4}{5} $$ vs. $$ \frac{5}{6} $$) and their cross-products are unequal.

**Final Answer:**  
No, the ratios are not proportional because 12⁄15 does not equal 15⁄18.
The ratios are not proportional because 12⁄15 does not equal 15⁄18.

Your team won 12 out of 15 games. Your friend’s team won 15 out of 18 games. Are the ratios
proportional?

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Your team won 12 out of 15 games. Your friend’s team won 15 out of 18 games. Are the ratios proportional?