To determine which of the given proportions is true, let's check each proportion step by step.
1. Proportion: [tex]\(\frac{30}{40} = \frac{24}{36}\)[/tex]
Simplify each fraction:
- [tex]\(\frac{30}{40} = \frac{3}{4}\)[/tex] (dividing numerator and denominator by 10)
- [tex]\(\frac{24}{36} = \frac{2}{3}\)[/tex] (dividing numerator and denominator by 12)
Since [tex]\(\frac{3}{4} \neq \frac{2}{3}\)[/tex], this proportion is not true.
2. Proportion: [tex]\(\frac{10}{15} = \frac{45}{50}\)[/tex]
Simplify each fraction:
- [tex]\(\frac{10}{15} = \frac{2}{3}\)[/tex] (dividing numerator and denominator by 5)
- [tex]\(\frac{45}{50} = \frac{9}{10}\)[/tex] (dividing numerator and denominator by 5)
Since [tex]\(\frac{2}{3} \neq \frac{9}{10}\)[/tex], this proportion is not true.
3. Proportion: [tex]\(\frac{16}{28} = \frac{12}{21}\)[/tex]
Simplify each fraction:
- [tex]\(\frac{16}{28} = \frac{4}{7}\)[/tex] (dividing numerator and denominator by 4)
- [tex]\(\frac{12}{21} = \frac{4}{7}\)[/tex] (dividing numerator and denominator by 3)
Since [tex]\(\frac{4}{7} = \frac{4}{7}\)[/tex], this proportion is true.
4. Proportion: [tex]\(\frac{6}{16} = \frac{4}{14}\)[/tex]
Simplify each fraction:
- [tex]\(\frac{6}{16} = \frac{3}{8}\)[/tex] (dividing numerator and denominator by 2)
- [tex]\(\frac{4}{14} = \frac{2}{7}\)[/tex] (dividing numerator and denominator by 2)
Since [tex]\(\frac{3}{8} \neq \frac{2}{7}\)[/tex], this proportion is not true.
So, the true proportion is:
[tex]\[
\frac{16}{28} = \frac{12}{21}
\][/tex]
Therefore, the correct answer is 3.
