To order the fractions [tex]\(\frac{3}{12}\)[/tex], [tex]\(\frac{1}{2}\)[/tex], and [tex]\(\frac{2}{5}\)[/tex] from least to greatest, we need to compare their values. Here are the steps to do so:
1. Convert each fraction to its simplest form, if needed:
- [tex]\[\frac{3}{12}\][/tex] simplifies to [tex]\[\frac{1}{4}\][/tex] because both the numerator and the denominator can be divided by 3.
- [tex]\[\frac{1}{2}\][/tex] is already in its simplest form.
- [tex]\[\frac{2}{5}\][/tex] is already in its simplest form.
2. Compare the simplified fractions:
- We need to compare [tex]\(\frac{1}{4}\)[/tex], [tex]\(\frac{2}{5}\)[/tex], and [tex]\(\frac{1}{2}\)[/tex].
3. To compare these fractions, we can find a common denominator or compare their decimal equivalents:
- [tex]\[\frac{1}{4}\][/tex] is equal to 0.25.
- [tex]\[\frac{2}{5}\][/tex] is equal to 0.4.
- [tex]\[\frac{1}{2}\][/tex] is equal to 0.5.
4. Order the fractions based on their decimal equivalents:
- 0.25 (which is [tex]\(\frac{1}{4}\)[/tex]) is the smallest.
- 0.4 (which is [tex]\(\frac{2}{5}\)[/tex]) is in the middle.
- 0.5 (which is [tex]\(\frac{1}{2}\)[/tex]) is the largest.
Therefore, the order from least to greatest is:
[tex]\[\frac{1}{4}\][/tex] (originally [tex]\[\frac{3}{12}\][/tex]) < [tex]\[\frac{2}{5}\][/tex] < [tex]\[\frac{1}{2}\][/tex].
So, placing these on the number line:
least [tex]\(\quad \frac{3}{12} \quad \frac{2}{5} \quad \frac{1}{2} \quad\)[/tex] greatest
