Answer :
To order the fractions \(\frac{2}{3}\), \(\frac{3}{5}\), and \(\frac{7}{10}\) from smallest to largest, we can compare their values by converting them to decimals.
1. Convert the fractions to decimal form:
- For \(\frac{2}{3}\):
[tex]\[ \frac{2}{3} \approx 0.6667 \][/tex]
- For \(\frac{3}{5}\):
[tex]\[ \frac{3}{5} = 0.6 \][/tex]
- For \(\frac{7}{10}\):
[tex]\[ \frac{7}{10} = 0.7 \][/tex]
2. Compare the decimal values:
- \(0.6\)
- \(0.6667\)
- \(0.7\)
3. Arrange the decimal values in ascending order:
- \(0.6 < 0.6667 < 0.7\)
4. Match these decimal values back to their corresponding fractions:
- \(0.6\) corresponds to \(\frac{3}{5}\)
- \(0.6667\) corresponds to \(\frac{2}{3}\)
- \(0.7\) corresponds to \(\frac{7}{10}\)
Therefore, the fractions in order from smallest to largest are:
[tex]\[ \frac{3}{5}, \frac{2}{3}, \frac{7}{10} \][/tex]
1. Convert the fractions to decimal form:
- For \(\frac{2}{3}\):
[tex]\[ \frac{2}{3} \approx 0.6667 \][/tex]
- For \(\frac{3}{5}\):
[tex]\[ \frac{3}{5} = 0.6 \][/tex]
- For \(\frac{7}{10}\):
[tex]\[ \frac{7}{10} = 0.7 \][/tex]
2. Compare the decimal values:
- \(0.6\)
- \(0.6667\)
- \(0.7\)
3. Arrange the decimal values in ascending order:
- \(0.6 < 0.6667 < 0.7\)
4. Match these decimal values back to their corresponding fractions:
- \(0.6\) corresponds to \(\frac{3}{5}\)
- \(0.6667\) corresponds to \(\frac{2}{3}\)
- \(0.7\) corresponds to \(\frac{7}{10}\)
Therefore, the fractions in order from smallest to largest are:
[tex]\[ \frac{3}{5}, \frac{2}{3}, \frac{7}{10} \][/tex]
