To solve the problem of subtracting the fractions [tex]\(\frac{2}{15} - \frac{3}{10}\)[/tex], we need to follow these steps:
1. Find a common denominator:
The denominators of our fractions are 15 and 10. The lowest common multiple (LCM) of these denominators is 30. This will be our common denominator.
2. Convert the fractions to have the common denominator:
- For [tex]\(\frac{2}{15}\)[/tex], we need to convert it so its denominator is 30:
[tex]\[
\frac{2}{15} = \frac{2 \times 2}{15 \times 2} = \frac{4}{30}
\][/tex]
- For [tex]\(\frac{3}{10}\)[/tex], we also need to convert it so its denominator is 30:
[tex]\[
\frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30}
\][/tex]
3. Perform the subtraction:
Now we subtract the two fractions with the common denominator:
[tex]\[
\frac{4}{30} - \frac{9}{30} = \frac{4 - 9}{30} = \frac{-5}{30}
\][/tex]
4. Simplify the result:
The fraction [tex]\(\frac{-5}{30}\)[/tex] can be simplified. We find the greatest common divisor (GCD) of 5 and 30, which is 5:
[tex]\[
\frac{-5 \div 5}{30 \div 5} = \frac{-1}{6}
\][/tex]
So, the simplified result of [tex]\(\frac{2}{15} - \frac{3}{10}\)[/tex] is [tex]\(\frac{-1}{6}\)[/tex].
Given the multiple-choice options:
[tex]\[
\begin{align*}
\text{1.} & \quad \frac{1}{6}\\
\text{2.} & \quad -\frac{1}{150}\\
\text{3.} & \quad -\frac{1}{5}\\
\text{4.} & \quad -\frac{1}{6}
\end{align*}
\][/tex]
The correct choice that matches our result [tex]\(\frac{-1}{6}\)[/tex] is option 4. Therefore, the answer is:
[tex]\[
\boxed{4}
\][/tex]
