Sure, let's solve the given mathematical expression step-by-step.
The expression we need to evaluate is:
[tex]\[ \frac{2}{5} \times \frac{-3}{7} - \frac{1}{14} - \frac{3}{7} \times \frac{3}{5} \][/tex]
### Step 1: Simplify each fraction multiplication
#### Fraction 1:
[tex]\[ \frac{2}{5} \times \frac{-3}{7} \][/tex]
Multiply the numerators and denominators:
[tex]\[ \frac{2 \times -3}{5 \times 7} = \frac{-6}{35} \][/tex]
#### Fraction 2:
[tex]\[ \frac{3}{7} \times \frac{3}{5} \][/tex]
Again, multiply the numerators and denominators:
[tex]\[ \frac{3 \times 3}{7 \times 5} = \frac{9}{35} \][/tex]
### Step 2: Convert fractions to decimals
Next, convert these fractions and the standalone fraction into their decimal equivalents for easier subtraction:
- [tex]\( \frac{-6}{35} \approx -0.17142857142857146 \)[/tex]
- [tex]\( \frac{1}{14} \approx 0.07142857142857142 \)[/tex]
- [tex]\( \frac{9}{35} \approx 0.2571428571428571 \)[/tex]
### Step 3: Perform the arithmetic operations
Now, substitute the decimal equivalents into the expression and perform the subtraction step-by-step:
[tex]\[ -0.17142857142857146 - 0.07142857142857142 - 0.2571428571428571 \][/tex]
Subtract the first pair:
[tex]\[ -0.17142857142857146 - 0.07142857142857142 = -0.24285714285714288 \][/tex]
Subtract the result from the third fraction:
[tex]\[ -0.24285714285714288 - 0.2571428571428571 = -0.5 \][/tex]
### Final Answer
So, the final result of the expression is:
[tex]\[ \frac{2}{5} \times \frac{-3}{7} - \frac{1}{14} - \frac{3}{7} \times \frac{3}{5} = -0.5 \][/tex]
