To determine which fraction has the least value among [tex]\(\frac{3}{4}\)[/tex], [tex]\(\frac{7}{8}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], and [tex]\(\frac{5}{6}\)[/tex], we should compare the fractions by converting them to decimal form or by finding a common denominator. Let's proceed by comparing their decimal equivalents.
1. [tex]\(\frac{3}{4}\)[/tex]:
- Convert to decimal: [tex]\(\frac{3}{4} = 0.75\)[/tex]
2. [tex]\(\frac{7}{8}\)[/tex]:
- Convert to decimal: [tex]\(\frac{7}{8} = 0.875\)[/tex]
3. [tex]\(\frac{2}{3}\)[/tex]:
- Convert to decimal: [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
4. [tex]\(\frac{5}{6}\)[/tex]:
- Convert to decimal: [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
Now we compare the decimal values:
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{7}{8} = 0.875\)[/tex]
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
Among these values, the smallest decimal is approximately [tex]\(0.6667\)[/tex], which corresponds to the fraction [tex]\(\frac{2}{3}\)[/tex].
Therefore, the fraction with the least value is:
[tex]\[ \boxed{\frac{2}{3}} \][/tex]
