Let's solve the problem by carefully arranging the given fractions in the specified order.
### Part (a)
We have the fractions [tex]\(\frac{1}{5}\)[/tex], [tex]\(\frac{3}{7}\)[/tex], and [tex]\(\frac{7}{10}\)[/tex].
The task is to arrange these fractions in descending order.
1. First, convert each fraction into its decimal form to make comparison easier:
- [tex]\(\frac{1}{5} = 0.2\)[/tex]
- [tex]\(\frac{3}{7} \approx 0.4286\)[/tex]
- [tex]\(\frac{7}{10} = 0.7\)[/tex]
2. Now, we arrange these decimals in descending order:
- [tex]\(0.7\)[/tex]
- [tex]\(0.4286\)[/tex]
- [tex]\(0.2\)[/tex]
3. Converting back to fractions, we have:
- [tex]\(0.7 = \frac{7}{10}\)[/tex]
- [tex]\(0.4286 \approx \frac{3}{7}\)[/tex]
- [tex]\(0.2 = \frac{1}{5}\)[/tex]
Therefore, the fractions in descending order are:
[tex]\[
\frac{7}{10}, \frac{3}{7}, \frac{1}{5}
\][/tex]
### Part (b)
We have the fractions [tex]\(\frac{3}{4}\)[/tex], [tex]\(\frac{5}{6}\)[/tex], and [tex]\(\frac{7}{9}\)[/tex].
The task is to arrange these fractions in ascending order.
1. First, convert each fraction into its decimal form to make comparison easier:
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
- [tex]\(\frac{7}{9} \approx 0.7778\)[/tex]
2. Now, we arrange these decimals in ascending order:
- [tex]\(0.75\)[/tex]
- [tex]\(0.7778\)[/tex]
- [tex]\(0.8333\)[/tex]
3. Converting back to fractions, we have:
- [tex]\(0.75 = \frac{3}{4}\)[/tex]
- [tex]\(0.7778 \approx \frac{7}{9}\)[/tex]
- [tex]\(0.8333 \approx \frac{5}{6}\)[/tex]
Therefore, the fractions in ascending order are:
[tex]\[
\frac{3}{4}, \frac{7}{9}, \frac{5}{6}
\][/tex]
### Final Answer:
- Part (a) in descending order: [tex]\(\frac{7}{10}, \frac{3}{7}, \frac{1}{5}\)[/tex]
- Part (b) in ascending order: [tex]\(\frac{3}{4}, \frac{7}{9}, \frac{5}{6}\)[/tex]
