To determine which fractions are greater than [tex]\(\frac{1}{2}\)[/tex], we need to compare each fraction provided to [tex]\(\frac{1}{2}\)[/tex].
Given fractions are:
1. [tex]\(\frac{1}{3}\)[/tex]
2. [tex]\(\frac{3}{4}\)[/tex]
3. [tex]\(\frac{2}{3}\)[/tex]
4. [tex]\(\frac{6}{7}\)[/tex]
5. [tex]\(\frac{1}{4}\)[/tex]
6. [tex]\(\frac{2}{7}\)[/tex]
Let’s compare each fraction to [tex]\(\frac{1}{2}\)[/tex]:
1. [tex]\(\frac{1}{3}\)[/tex]:
- The decimal equivalent of [tex]\(\frac{1}{3}\)[/tex] is approximately 0.3333.
- 0.3333 is less than 0.5, so [tex]\(\frac{1}{3}\)[/tex] is not greater than [tex]\(\frac{1}{2}\)[/tex].
2. [tex]\(\frac{3}{4}\)[/tex]:
- The decimal equivalent of [tex]\(\frac{3}{4}\)[/tex] is 0.75.
- 0.75 is greater than 0.5, so [tex]\(\frac{3}{4}\)[/tex] is greater than [tex]\(\frac{1}{2}\)[/tex].
3. [tex]\(\frac{2}{3}\)[/tex]:
- The decimal equivalent of [tex]\(\frac{2}{3}\)[/tex] is approximately 0.6667.
- 0.6667 is greater than 0.5, so [tex]\(\frac{2}{3}\)[/tex] is greater than [tex]\(\frac{1}{2}\)[/tex].
4. [tex]\(\frac{6}{7}\)[/tex]:
- The decimal equivalent of [tex]\(\frac{6}{7}\)[/tex] is approximately 0.8571.
- 0.8571 is greater than 0.5, so [tex]\(\frac{6}{7}\)[/tex] is greater than [tex]\(\frac{1}{2}\)[/tex].
5. [tex]\(\frac{1}{4}\)[/tex]:
- The decimal equivalent of [tex]\(\frac{1}{4}\)[/tex] is 0.25.
- 0.25 is less than 0.5, so [tex]\(\frac{1}{4}\)[/tex] is not greater than [tex]\(\frac{1}{2}\)[/tex].
6. [tex]\(\frac{2}{7}\)[/tex]:
- The decimal equivalent of [tex]\(\frac{2}{7}\)[/tex] is approximately 0.2857.
- 0.2857 is less than 0.5, so [tex]\(\frac{2}{7}\)[/tex] is not greater than [tex]\(\frac{1}{2}\)[/tex].
Therefore, the fractions that are greater than [tex]\(\frac{1}{2}\)[/tex] are:
- [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(\frac{2}{3}\)[/tex]
- [tex]\(\frac{6}{7}\)[/tex]
