Certainly! Let's solve the given problem step-by-step:
We start with the expression:
[tex]\[ \left(-3 \frac{6}{7}\right) \left(\frac{1}{81}\right) (2.3) (-0.5) \][/tex]
### Step 1: Convert the mixed fraction to an improper fraction
The mixed number [tex]\( -3 \frac{6}{7} \)[/tex] can be converted to an improper fraction.
[tex]\[ -3 \frac{6}{7} = -3 - \frac{6}{7} = -3 - 0.857142857142857 = -3.857142857142857 \][/tex]
### Step 2: Evaluate the product with the first fraction
Now multiply [tex]\(-3.857142857142857\)[/tex] by [tex]\(\frac{1}{81}\)[/tex]:
[tex]\[ -3.857142857142857 \times \frac{1}{81} = -0.047619047619047616 \][/tex]
### Step 3: Continue with the multiplication by the decimal number [tex]\(2.3\)[/tex]
Next, we multiply [tex]\(-0.047619047619047616\)[/tex] by [tex]\(2.3\)[/tex]:
[tex]\[ -0.047619047619047616 \times 2.3 = -0.10952380952380951 \][/tex]
### Step 4: Finally, include the multiplication by [tex]\(-0.5\)[/tex]
Lastly, we multiply [tex]\(-0.10952380952380951\)[/tex] by [tex]\(-0.5\)[/tex]:
[tex]\[ -0.10952380952380951 \times (-0.5) = 0.054761904761904755 \][/tex]
Hence, the final result of the expression is:
[tex]\[ \left(-3 \frac{6}{7}\right) \left(\frac{1}{81}\right) (2.3) (-0.5) = 0.054761904761904755 \][/tex]
