Divide the sum of [tex]\(\frac{13}{5}\)[/tex] and [tex]\(\frac{-12}{7}\)[/tex] by the product of [tex]\(\frac{-31}{7}\)[/tex] and [tex]\(\frac{-1}{2}\)[/tex].



Answer :

To solve the problem, we need to proceed step-by-step:

1. Calculate the value of [tex]\( \frac{13}{5} \)[/tex]:
[tex]\[ \frac{13}{5} = 2.6 \][/tex]

2. Calculate the value of [tex]\( -\frac{12}{7} \)[/tex]:
[tex]\[ -\frac{12}{7} \approx -1.7142857142857142 \][/tex]

3. Sum the results of [tex]\( \frac{13}{5} \)[/tex] and [tex]\( -\frac{12}{7} \)[/tex]:
[tex]\[ 2.6 + (-1.7142857142857142) \approx 0.8857142857142859 \][/tex]

4. Calculate the value of [tex]\( -\frac{31}{7} \)[/tex]:
[tex]\[ -\frac{31}{7} \approx -4.428571428571429 \][/tex]

5. Calculate the value of [tex]\( -\frac{1}{2} \)[/tex]:
[tex]\[ -\frac{1}{2} = -0.5 \][/tex]

6. Multiply the results of [tex]\( -\frac{31}{7} \)[/tex] and [tex]\( -\frac{1}{2} \)[/tex]:
[tex]\[ (-4.428571428571429) \times (-0.5) \approx 2.2142857142857144 \][/tex]

7. Divide the sum by the product:
[tex]\[ \frac{0.8857142857142859}{2.2142857142857144} \approx 0.4000000000000001 \][/tex]

Thus, the final result of the division is [tex]\( \boxed{0.4000000000000001} \)[/tex].