Sure, let's solve the given expression step-by-step:
The given expression is:
[tex]\[
\frac{2}{5} \times \frac{-3}{7} - \frac{1}{14} - \frac{3}{7} \times \frac{3}{5}
\][/tex]
First, let's handle each fraction multiplication individually:
1) Calculate [tex]\(\frac{2}{5} \times \frac{-3}{7}\)[/tex]:
[tex]\[
\frac{2}{5} \times \frac{-3}{7} = \frac{2 \times -3}{5 \times 7} = \frac{-6}{35}
\][/tex]
Since [tex]\(\frac{-6}{35}\)[/tex] is approximately:
[tex]\[
-0.17142857142857143
\][/tex]
2) The second fraction is [tex]\(\frac{1}{14}\)[/tex], which remains the same:
[tex]\[
\frac{1}{14} = 0.07142857142857142
\][/tex]
3) Calculate [tex]\(\frac{3}{7} \times \frac{3}{5}\)[/tex]:
[tex]\[
\frac{3}{7} \times \frac{3}{5} = \frac{3 \times 3}{7 \times 5} = \frac{9}{35}
\][/tex]
Since [tex]\(\frac{9}{35}\)[/tex] is approximately:
[tex]\[
0.2571428571428571
\][/tex]
Now, let's put these values back into the given expression:
[tex]\[
-0.17142857142857143 - 0.07142857142857142 - 0.2571428571428571
\][/tex]
Combine these values by performing the subtraction step-by-step:
[tex]\[
-0.17142857142857143 - 0.07142857142857142 = -0.24285714285714285
\][/tex]
Then,
[tex]\[
-0.24285714285714285 - 0.2571428571428571 = -0.5
\][/tex]
So, the result of the expression is:
[tex]\[
-0.5
\][/tex]
In conclusion, the detailed step-by-step solution shows that:
[tex]\[
\frac{2}{5} \times \frac{-3}{7} - \frac{1}{14} - \frac{3}{7} \times \frac{3}{5} = -0.5
\][/tex]
