To arrange the fractions [tex]\(-\frac{1}{3}\)[/tex], [tex]\(-\frac{2}{7}\)[/tex], [tex]\(-\frac{3}{5}\)[/tex], [tex]\(-\frac{4}{9}\)[/tex] in ascending order, we need to compare their values. Here is a step-by-step solution:
1. Identify the approximate decimal values for each fraction:
[tex]\[
-\frac{1}{3} \approx -0.3333
\][/tex]
[tex]\[
-\frac{2}{7} \approx -0.2857
\][/tex]
[tex]\[
-\frac{3}{5} \approx -0.6000
\][/tex]
[tex]\[
-\frac{4}{9} \approx -0.4444
\][/tex]
2. Compare the decimal values for each fraction to determine their order from smallest to largest.
- The decimal value of [tex]\(-0.6000\)[/tex] is the smallest.
- Next, [tex]\(-0.4444\)[/tex] is slightly larger than [tex]\(-0.6000\)[/tex].
- Then, [tex]\(-0.3333\)[/tex] is larger than [tex]\(-0.4444\)[/tex].
- Finally, [tex]\(-0.2857\)[/tex] is the largest fraction among these negatives.
3. Arrange the fractions based on their decimal values in ascending order:
- [tex]\(-0.6000\)[/tex] corresponds to [tex]\(-\frac{3}{5}\)[/tex]
- [tex]\(-0.4444\)[/tex] corresponds to [tex]\(-\frac{4}{9}\)[/tex]
- [tex]\(-0.3333\)[/tex] corresponds to [tex]\(-\frac{1}{3}\)[/tex]
- [tex]\(-0.2857\)[/tex] corresponds to [tex]\(-\frac{2}{7}\)[/tex]
So, the fractions in ascending order are:
[tex]\[
-\frac{3}{5}, -\frac{4}{9}, -\frac{1}{3}, -\frac{2}{7}
\][/tex]
