To determine whether the given fractions are improper, we need to check if the numerator (the top number of the fraction) is greater than the denominator (the bottom number). If the numerator is greater than the denominator, the fraction is classified as an improper fraction.
Let's analyze each fraction:
1. a) [tex]\(\frac{21}{2}\)[/tex]
- Numerator: 21
- Denominator: 2
- Since 21 > 2, [tex]\(\frac{21}{2}\)[/tex] is an improper fraction.
2. b) [tex]\(\frac{4}{5}\)[/tex]
- Numerator: 4
- Denominator: 5
- Since 4 < 5, [tex]\(\frac{4}{5}\)[/tex] is a proper fraction.
3. c) [tex]\(\frac{83}{126}\)[/tex]
- Numerator: 83
- Denominator: 126
- Since 83 < 126, [tex]\(\frac{83}{126}\)[/tex] is a proper fraction.
4. d) [tex]\(\frac{7}{6}\)[/tex]
- Numerator: 7
- Denominator: 6
- Since 7 > 6, [tex]\(\frac{7}{6}\)[/tex] is an improper fraction.
Hence, the improper fractions from the given list are:
- [tex]\(\frac{21}{2}\)[/tex]
- [tex]\(\frac{7}{6}\)[/tex]
The proper fractions are:
- [tex]\(\frac{4}{5}\)[/tex]
- [tex]\(\frac{83}{126}\)[/tex]
In summary, the improper fractions are:
[tex]\[
\boxed{\frac{21}{2}, \frac{7}{6}}
\][/tex]
