Let's solve the problem of adding the fractions step by step.
We need to find the sum of the following fractions:
[tex]\[
\frac{3}{4} + \frac{-4}{13} + \frac{-7}{16} + \frac{5}{26}
\][/tex]
To solve this, let's consider each fraction:
1. The value of [tex]\(\frac{3}{4}\)[/tex] is approximately [tex]\(0.75\)[/tex].
2. The value of [tex]\(\frac{-4}{13}\)[/tex] is approximately [tex]\(-0.3077\)[/tex].
3. The value of [tex]\(\frac{-7}{16}\)[/tex] is approximately [tex]\(-0.4375\)[/tex].
4. The value of [tex]\(\frac{5}{26}\)[/tex] is approximately [tex]\(0.1923\)[/tex].
Now, we need to sum these values:
[tex]\[
0.75 + (-0.3077) + (-0.4375) + 0.1923
\][/tex]
Let's add them step by step:
1. Adding [tex]\(0.75\)[/tex] and [tex]\(-0.3077\)[/tex]:
[tex]\[
0.75 - 0.3077 \approx 0.4423
\][/tex]
2. Adding the result to [tex]\(-0.4375\)[/tex]:
[tex]\[
0.4423 - 0.4375 \approx 0.0048
\][/tex]
3. Finally, adding [tex]\(0.0048\)[/tex] to [tex]\(0.1923\)[/tex]:
[tex]\[
0.0048 + 0.1923 \approx 0.1971
\][/tex]
Thus, the sum of the fractions is approximately:
[tex]\[
0.1971
\][/tex]
So, the detailed step-by-step solution gives us the sum:
[tex]\[
\frac{3}{4} + \frac{-4}{13} + \frac{-7}{16} + \frac{5}{26} \approx 0.1971
\][/tex]
