Sure, let's work through the process of arranging the given fractions in descending order step by step for both parts (a) and (b).
### Part (a):
The fractions we need to arrange are:
[tex]\[
\frac{3}{5}, \frac{4}{10}, \frac{2}{3}, \frac{1}{5}, \frac{5}{6}
\][/tex]
First, let's convert all these fractions to their decimal equivalents to easily compare them:
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
[tex]\[
\frac{4}{10} = 0.4
\][/tex]
[tex]\[
\frac{2}{3} \approx 0.6666
\][/tex]
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
[tex]\[
\frac{5}{6} \approx 0.8333
\][/tex]
Now, we arrange these decimals in descending order:
[tex]\[
0.8333, 0.6666, 0.6, 0.4, 0.2
\][/tex]
So, in the form of fractions, we have:
[tex]\[
\frac{5}{6}, \frac{2}{3}, \frac{3}{5}, \frac{4}{10}, \frac{1}{5}
\][/tex]
### Part (b):
The fractions we need to arrange are:
[tex]\[
\frac{1}{3}, \frac{7}{10}, \frac{9}{15}, \frac{2}{5}, \frac{5}{10}
\][/tex]
Similarly, let's convert these fractions to their decimal equivalents:
[tex]\[
\frac{1}{3} \approx 0.3333
\][/tex]
[tex]\[
\frac{7}{10} = 0.7
\][/tex]
[tex]\[
\frac{9}{15} = \frac{3}{5} = 0.6
\][/tex]
[tex]\[
\frac{2}{5} = 0.4
\][/tex]
[tex]\[
\frac{5}{10} = 0.5
\][/tex]
Now, we arrange these decimals in descending order:
[tex]\[
0.7, 0.6, 0.5, 0.4, 0.3333
\][/tex]
So, in the form of fractions, we have:
[tex]\[
\frac{7}{10}, \frac{3}{5}, \frac{5}{10}, \frac{2}{5}, \frac{1}{3}
\][/tex]
To summarize, the fractions arranged in descending order are:
### Part (a):
[tex]\[
\frac{5}{6}, \frac{2}{3}, \frac{3}{5}, \frac{4}{10}, \frac{1}{5}
\][/tex]
### Part (b):
[tex]\[
\frac{7}{10}, \frac{3}{5}, \frac{5}{10}, \frac{2}{5}, \frac{1}{3}
\][/tex]
These are the final answers for the given question.
