To determine which set of fractions is ordered from greatest to least, let's consider the given sets of fractions and compare their values procedurally.
We'll compare the values of each fraction and sort them accordingly.
The fractions provided are:
1. [tex]\(\frac{3}{10}\)[/tex]
2. [tex]\(\frac{1}{4}\)[/tex]
3. [tex]\(\frac{2}{5}\)[/tex]
Let's compare these values by converting them to decimals:
- [tex]\(\frac{3}{10} = 0.3\)[/tex]
- [tex]\(\frac{1}{4} = 0.25\)[/tex]
- [tex]\(\frac{2}{5} = 0.4\)[/tex]
Now let's compare the decimal values to order the fractions from greatest to least:
1. The largest fraction is [tex]\(\frac{2}{5} = 0.4\)[/tex]
2. The next largest fraction is [tex]\(\frac{3}{10} = 0.3\)[/tex]
3. The smallest fraction is [tex]\(\frac{1}{4} = 0.25\)[/tex]
Therefore, in descending order (from greatest to least), the fractions should be:
[tex]\[
\frac{2}{5} \quad (0.4), \quad \frac{3}{10} \quad (0.3), \quad \frac{1}{4} \quad (0.25)
\][/tex]
Now let's verify which given set matches this ordered list:
A. [tex]\( \frac{3}{10}, \frac{1}{4}, \frac{2}{5} \)[/tex]
B. [tex]\( \frac{2}{5}, \frac{3}{10}, \frac{1}{4} \)[/tex]
C. [tex]\( \frac{3}{10}, \frac{2}{5}, \frac{1}{4} \)[/tex]
D. [tex]\( \frac{1}{4}, \frac{3}{10}, \frac{2}{5} \)[/tex]
Upon examining these sets, we see that Set B matches our ordered list [tex]\(\left( \frac{2}{5}, \frac{3}{10}, \frac{1}{4} \right)\)[/tex].
Therefore, the set of fractions that is ordered from greatest to least is:
Set B: [tex]\( \frac{2}{5}, \frac{3}{10}, \frac{1}{4} \)[/tex]
