To arrange the fractions [tex]\(\frac{3}{4}\)[/tex], [tex]\(\frac{2}{5}\)[/tex], [tex]\(\frac{7}{15}\)[/tex], and [tex]\(\frac{2}{3}\)[/tex] from smallest to largest, we follow these steps:
1. Calculate the decimal or approximate value of each fraction:
- [tex]\(\frac{3}{4} \approx 0.75\)[/tex]
- [tex]\(\frac{2}{5} \approx 0.4\)[/tex]
- [tex]\(\frac{7}{15} \approx 0.46667\)[/tex]
- [tex]\(\frac{2}{3} \approx 0.66667\)[/tex]
2. Compare the decimal values:
- [tex]\(0.4\)[/tex]
- [tex]\(0.46667\)[/tex]
- [tex]\(0.66667\)[/tex]
- [tex]\(0.75\)[/tex]
Next, we compare these decimal values in ascending order.
3. Arrange the fractions based on the ascending order of their decimal values:
- The smallest fraction is [tex]\(0.4\)[/tex], which corresponds to [tex]\(\frac{2}{5}\)[/tex].
- The next smallest fraction is [tex]\(0.46667\)[/tex], which corresponds to [tex]\(\frac{7}{15}\)[/tex].
- Following that is [tex]\(0.66667\)[/tex], which corresponds to [tex]\(\frac{2}{3}\)[/tex].
- The largest fraction is [tex]\(0.75\)[/tex], which corresponds to [tex]\(\frac{3}{4}\)[/tex].
Thus, the fractions in order from smallest to largest are:
[tex]\[
\frac{2}{5}, \quad \frac{7}{15}, \quad \frac{2}{3}, \quad \frac{3}{4}
\][/tex]
