To determine which of the given fractions is not equal to [tex]\(\frac{1}{2}\)[/tex], we need to analyze each fraction individually. We do this by either simplifying the fractions or directly comparing them to [tex]\(\frac{1}{2}\)[/tex].
1. Fraction: [tex]\(\frac{9}{18}\)[/tex]
Simplify by finding the greatest common divisor (GCD) of 9 and 18, which is 9:
[tex]\[
\frac{9}{18} = \frac{9 \div 9}{18 \div 9} = \frac{1}{2}
\][/tex]
So, [tex]\(\frac{9}{18} = \frac{1}{2}\)[/tex].
2. Fraction: [tex]\(\frac{20}{40}\)[/tex]
Simplify by finding the GCD of 20 and 40, which is 20:
[tex]\[
\frac{20}{40} = \frac{20 \div 20}{40 \div 20} = \frac{1}{2}
\][/tex]
So, [tex]\(\frac{20}{40} = \frac{1}{2}\)[/tex].
3. Fraction: [tex]\(\frac{4}{6}\)[/tex]
Simplify by finding the GCD of 4 and 6, which is 2:
[tex]\[
\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}
\][/tex]
[tex]\(\frac{2}{3}\)[/tex] is not equal to [tex]\(\frac{1}{2}\)[/tex].
4. Fraction: [tex]\(\frac{5}{10}\)[/tex]
Simplify by finding the GCD of 5 and 10, which is 5:
[tex]\[
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
So, [tex]\(\frac{5}{10} = \frac{1}{2}\)[/tex].
After analyzing all the fractions, we can see that [tex]\(\frac{4}{6}\)[/tex] is not equal to [tex]\(\frac{1}{2}\)[/tex]. Therefore, the fraction that is not equal to [tex]\(\frac{1}{2}\)[/tex] is:
[tex]\[
\boxed{\frac{4}{6}}
\][/tex]
