Certainly! Let's solve the given expression step-by-step.
First, let's list the terms of the expression to get a clear view:
- [tex]\( -5 \)[/tex]
- [tex]\( \frac{7}{10} \)[/tex]
- [tex]\( \frac{3}{7} \)[/tex]
- [tex]\( -3 \)[/tex]
- [tex]\( \frac{5}{14} \)[/tex]
- [tex]\( \frac{-4}{5} \)[/tex]
Now, let's attempt to add these fractions and integers in a more manageable order. We can start by grouping some terms for easier arithmetic operations:
1. First Group: Integers
- Add the integer terms together:
[tex]\[
-5 + (-3) = -8
\][/tex]
2. Second Group: Fractions
- Combine the fractional terms:
[tex]\[
\frac{7}{10}, \frac{3}{7}, \frac{5}{14}, \text{ and } \frac{-4}{5}
\][/tex]
We can add these fractions separately and then combine them with the integer sum. Let's convert all fractions to decimals for simplicity:
- [tex]\( \frac{7}{10} = 0.7 \)[/tex]
- [tex]\( \frac{3}{7} \approx 0.42857142857142855 \)[/tex]
- [tex]\( \frac{5}{14} \approx 0.35714285714285715 \)[/tex]
- [tex]\( \frac{-4}{5} = -0.8 \)[/tex]
Now, add these decimals one by one:
[tex]\[
0.7 + 0.42857142857142855 \approx 1.1285714285714286
\][/tex]
Then add:
[tex]\[
1.1285714285714286 + 0.35714285714285715 \approx 1.4857142857142857
\][/tex]
Finally, add:
[tex]\[
1.4857142857142857 + (-0.8) \approx 0.6857142857142857
\][/tex]
So the sum of the fractions is approximately:
[tex]\[
0.6857142857142857
\][/tex]
Now, combine the sum of the integers with the sum of the fractions:
[tex]\[
-8 + 0.6857142857142857 \approx -7.314285714285715
\][/tex]
Thus, the final result for the sum of the given expression is:
[tex]\[
-7.314285714285715
\][/tex]
