Certainly! Let's solve the given problem step-by-step:
We need to simplify the expression:
[tex]\[
\frac{-3}{7} - \frac{1}{14} - \frac{3}{7}
\][/tex]
### Step 1: Make the Denominators the Same
First, we need to have a common denominator for all the fractions. The denominators we have are 7 and 14. The least common multiple (LCM) of 7 and 14 is 14.
Rewrite each fraction with this common denominator:
[tex]\[
\frac{-3}{7} = \frac{-3 \cdot 2}{7 \cdot 2} = \frac{-6}{14}
\][/tex]
[tex]\[
\frac{3}{7} = \frac{3 \cdot 2}{7 \cdot 2} = \frac{6}{14}
\][/tex]
So, the expression becomes:
[tex]\[
\frac{-6}{14} - \frac{1}{14} - \frac{6}{14}
\][/tex]
### Step 2: Perform the Subtraction
Now, we can subtract the fractions because they all have the same denominator:
[tex]\[
\frac{-6 - 1 - 6}{14}
\][/tex]
Combine the numerators:
[tex]\[
\frac{-6 - 1 - 6}{14} = \frac{-13}{14}
\][/tex]
### Step 3: Simplifying
The fraction [tex]\(\frac{-13}{14}\)[/tex] cannot be simplified further.
### Step 4: Converting to Decimal
Finally, let's convert this fraction to its decimal form:
[tex]\[
\frac{-13}{14} \approx -0.9285714285714286
\][/tex]
### Results for Each Fraction and the Final Answer
- The decimal equivalent of [tex]\(\frac{-3}{7}\)[/tex] is approximately [tex]\(-0.42857142857142855\)[/tex].
- The decimal equivalent of [tex]\(\frac{1}{14}\)[/tex] is approximately [tex]\(0.07142857142857142\)[/tex].
- The decimal equivalent of [tex]\(\frac{3}{7}\)[/tex] is approximately [tex]\(0.42857142857142855\)[/tex].
The final result of the expression [tex]\(\frac{-3}{7} - \frac{1}{14} - \frac{3}{7}\)[/tex] is approximately [tex]\(-0.9285714285714286\)[/tex].
Thus, the detailed step-by-step solution leads us to the final result:
[tex]\[
\frac{-13}{14} \approx -0.9285714285714286
\][/tex]
