To solve the expression [tex]\(\frac{3}{5} - 1 + \frac{2}{3}\)[/tex], let's break it down step by step.
1. Express all numbers in decimal form:
- [tex]\(\frac{3}{5} = 0.6\)[/tex]
- [tex]\(1 = 1.0\)[/tex]
- [tex]\(\frac{2}{3} \approx 0.6666666666666666\)[/tex]
2. Perform the subtraction and addition:
- First, subtract 1 from [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
0.6 - 1 = -0.4
\][/tex]
- Next, add [tex]\(\frac{2}{3}\)[/tex] to the result:
[tex]\[
-0.4 + 0.6666666666666666 \approx 0.2666666666666666
\][/tex]
3. Simplify the result:
- In this case, the resulting number is already simplified:
[tex]\[
0.2666666666666666
\][/tex]
Therefore, the solution for the expression [tex]\(\frac{3}{5} - 1 + \frac{2}{3}\)[/tex] is approximately [tex]\(0.2666666666666666\)[/tex].
Comparing this value to the options provided:
- [tex]\(\frac{1}{2} = 0.5\)[/tex]
- [tex]\(-\frac{2}{5} = -0.4\)[/tex]
- [tex]\(\frac{2}{15} \approx 0.1333\)[/tex]
- [tex]\(\frac{4}{15} \approx 0.2667\)[/tex]
The approximate value of 0.2666666666666666 is closest to [tex]\(\frac{4}{15}\)[/tex].
Thus, the correct answer is [tex]\(\frac{4}{15}\)[/tex].
