Question

tell whether the ratios form a proportion.

1. \\(\frac{1}{3}, \frac{7}{21}\\) 6. \\(\frac{1}{5}, \frac{6}{30}\\) 7. \\(\frac{3}{4}, \frac{24}{18}\\) 8. \\(\frac{2}{5}, \frac{40}{16}\\)
2. \\(\frac{48}{9}, \frac{16}{3}\\) 10. \\(\frac{18}{27}, \frac{33}{44}\\) 11. \\(\frac{7}{2}, \frac{16}{6}\\) 12. \\(\frac{12}{10}, \frac{14}{12}\\)

tell whether \\(x\\) and \\(y\\) are proportional.

1. \\(\

$$\begin{array}{|c|c|c|c|c|} \\hline x & 1 & 2 & 3 & 4 \\\\ \\hline y & 7 & 8 & 9 & 10 \\\\ \\hline \\end{array}$$

\\) 14. \\(\

$$\begin{array}{|c|c|c|c|c|} \\hline x & 2 & 4 & 6 & 8 \\\\ \\hline y & 5 & 10 & 15 & 20 \\\\ \\hline \\end{array}$$

\\)
tell whether the two rates form a proportion.

1. 7 inches in 9 hours; 42 inches in 54 hours
2. 12 players from 21 teams; 15 players from 24 teams
3. 440 calories in 4 servings; 300 calories in 3 servings
4. 120 units made in 5 days; 88 units made in 4 days
5. 66 wins in 82 games; 99 wins in 123 games
6. 68 hits in 172 at bats; 43 hits in 123 at bats

Explanation:

Step1: Simplify the first ratio

Simplify \(\frac{1}{3}\) (it is already in simplest form) and simplify \(\frac{7}{21}\) by dividing numerator and denominator by 7: \(\frac{7\div7}{21\div7}=\frac{1}{3}\).

Step2: Compare the two simplified ratios

Since \(\frac{1}{3}=\frac{1}{3}\), the two ratios are equal.

Answer:

Yes, the ratios \(\frac{1}{3}\) and \(\frac{7}{21}\) form a proportion.