Let's solve these problems step-by-step:
2) [tex]\(\frac{1}{5} + \frac{1}{2}\)[/tex]
To add these fractions, we first need to find a common denominator. The denominators are 5 and 2. The least common multiple of 5 and 2 is 10.
Now, we convert each fraction to have a denominator of 10:
[tex]\[
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\][/tex]
[tex]\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\][/tex]
Now we can add these fractions:
[tex]\[
\frac{2}{10} + \frac{5}{10} = \frac{2+5}{10} = \frac{7}{10}
\][/tex]
Thus, [tex]\(\frac{1}{5} + \frac{1}{2} = \frac{7}{10} = 0.7\)[/tex].
4) [tex]\(\frac{2}{3} \cdot \frac{1}{5}\)[/tex]
To multiply these fractions, we simply multiply the numerators together and the denominators together:
[tex]\[
\frac{2}{3} \cdot \frac{1}{5} = \frac{2 \cdot 1}{3 \cdot 5} = \frac{2}{15}
\][/tex]
Thus, [tex]\(\frac{2}{3} \cdot \frac{1}{5} = \frac{2}{15} \approx 0.13333333333333333\)[/tex].
So the final results for the problems are:
2) [tex]\(\frac{1}{5} + \frac{1}{2} = 0.7\)[/tex]
4) [tex]\(\frac{2}{3} \cdot \frac{1}{5} = 0.13333333333333333\)[/tex]
