To solve the expression [tex]\(\frac{3}{4} - \frac{7}{5} - \frac{3}{10}\)[/tex], we need to carefully execute the subtraction operations of these fractions.
Firstly, recognize the fractions:
[tex]\[
\frac{3}{4}, \quad \frac{7}{5}, \quad \text{and} \quad \frac{3}{10}
\][/tex]
We need to find a common denominator for these fractions to accurately perform the subtraction. The least common multiple (LCM) of the denominators [tex]\(4, 5,\)[/tex] and [tex]\(10\)[/tex] is [tex]\(20\)[/tex].
Convert each fraction to an equivalent fraction with a denominator of [tex]\(20\)[/tex]:
[tex]\[
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\][/tex]
[tex]\[
\frac{7}{5} = \frac{7 \times 4}{5 \times 4} = \frac{28}{20}
\][/tex]
[tex]\[
\frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}
\][/tex]
Now, substitute these values back into the original expression:
[tex]\[
\frac{15}{20} - \frac{28}{20} - \frac{6}{20}
\][/tex]
Perform the subtraction:
[tex]\[
\frac{15 - 28 - 6}{20} = \frac{15 - 34}{20} = \frac{-19}{20}
\][/tex]
Since [tex]\(\frac{-19}{20}\)[/tex] does not match any of the choices given directly, let's consider the closest approximate calculation we have:
[tex]\(\frac{-19}{20}\)[/tex] when converted to a decimal form is approximately [tex]\(-0.95\)[/tex], which is very close to [tex]\(-\frac{19}{20}\)[/tex].
Given the options:
A) [tex]\(+\frac{7}{20}\)[/tex]
B) [tex]\(-\frac{7}{20}\)[/tex]
C) [tex]\(\frac{8}{20}\)[/tex]
D) [tex]\(\frac{5}{20}\)[/tex]
It appears there might have been a slight error in presenting the choices, but among the given options, the negative result should be closely examined.
The closest possible and logical option mathematically corresponding to the derived answer [tex]\((approximately -0.95)\)[/tex] is:
[tex]\[
\boxed{\mathbf{B) -\frac{7}{20}}}
\][/tex]
Note that ideally, [tex]\(\frac{-19}{20}\)[/tex] does not precisely fit with any given options, and choice B appears to be closest in context of verifying the provided result.
