To determine the order of the fractions [tex]\(\frac{3}{5}\)[/tex] (labeled as A), [tex]\(\frac{1}{2}\)[/tex] (labeled as B), [tex]\(\frac{7}{15}\)[/tex] (labeled as C), and [tex]\(\frac{17}{30}\)[/tex] (labeled as D) from smallest to largest, follow these steps:
1. Identify the fractions:
- Fraction A: [tex]\(\frac{3}{5}\)[/tex]
- Fraction B: [tex]\(\frac{1}{2}\)[/tex]
- Fraction C: [tex]\(\frac{7}{15}\)[/tex]
- Fraction D: [tex]\(\frac{17}{30}\)[/tex]
2. List the fractions with their labels:
- A: [tex]\(\frac{3}{5}\)[/tex]
- B: [tex]\(\frac{1}{2}\)[/tex]
- C: [tex]\(\frac{7}{15}\)[/tex]
- D: [tex]\(\frac{17}{30}\)[/tex]
3. Compare their values to sort them:
By evaluating or using known values of these fractions,
- [tex]\(\frac{7}{15} \approx 0.4666\)[/tex]
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(\frac{17}{30} \approx 0.5666\)[/tex]
- [tex]\(\frac{3}{5} = 0.6\)[/tex]
4. Order these fractions from smallest to largest:
Based on the evaluated decimal values:
- [tex]\(\frac{7}{15}\)[/tex] (label C) is the smallest -> 0.4666
- [tex]\(\frac{1}{2}\)[/tex] (label B) -> 0.5
- [tex]\(\frac{17}{30}\)[/tex] (label D) -> 0.5666
- [tex]\(\frac{3}{5}\)[/tex] (label A) is the largest -> 0.6
Therefore, the order of the fractions from smallest to largest is:
[tex]\[
\boxed{C \quad B \quad D \quad A}
\][/tex]
