Let's go through the questions in the image and solve them one by one:

10) $-3.127 + (-23.81)$

$-3.127 + (-23.81) = -3.127 - 23.81 = -26.937$ Answer: $-26.937$

11) $\frac{3}{2} - \frac{2}{3} - \frac{1}{4} - \frac{3}{4} - \frac{5}{6} + 10 \frac{2}{3}$

First, convert the mixed number $10 \frac{2}{3}$ to an improper fraction: $10 \frac{2}{3} = \frac{32}{3}$ Now, find a common denominator for all the fractions, which is 12: $\frac{3}{2} = \frac{18}{12}, \quad \frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12}, \quad \frac{3}{4} = \frac{9}{12}, \quad \frac{5}{6} = \frac{10}{12}, \quad \frac{32}{3} = \frac{128}{12}$ Now substitute the values: $\frac{18}{12} - \frac{8}{12} - \frac{3}{12} - \frac{9}{12} - \frac{10}{12} + \frac{128}{12}$ Combine the numerators: $18 - 8 - 3 - 9 - 10 + 128 = 116$ So, the result is: $\frac{116}{12} = \frac{29}{3} = 9 \frac{2}{3}$ Answer: $9 \frac{2}{3}$

12) $93 - (-23)$

$93 - (-23) = 93 + 23 = 116$ Answer: 116

13) $47.168 + 53.62$

$47.168 + 53.62 = 100.788$ Answer: 100.788

14) $- \frac{4}{3} + \frac{3}{15} + - \frac{8}{7} + \frac{7}{10}$

• Find a common denominator and solve the sum of fractions. I'll calculate this next.For question 14, the result of $- \frac{4}{3} + \frac{3}{15} + - \frac{8}{7} + \frac{7}{10}$ is:

$- \frac{331}{210} \approx -1.576$ Answer: $-1 \frac{121}{210}$ or approximately $-1.576$.

15) $-53 - (-19)$

$-53 - (-19) = -53 + 19 = -34$ Answer: $-34$

16) Subtract $-5.44$ from $-7.33$

This is the same as: $-7.33 - (-5.44) = -7.33 + 5.44 = -1.89$ Answer: $-1.89$

17) $105 - 141$

$105 - 141 = -36$ Answer: $-36$

18) $-\frac{1}{2} + \frac{5}{8} + \frac{3}{5} + \frac{5}{6} + \frac{2}{3}$

I'll calculate the sum of these fractions next.For question 18, the result of $-\frac{1}{2} + \frac{5}{8} + \frac{3}{5} + \frac{5}{6} + \frac{2}{3}$ is:

$\frac{89}{40} \approx 2.225$ Answer: $2 \frac{9}{40}$ or approximately $2.225$.

Would you like more details on any of the steps? Here are 5 related questions to deepen your understanding:

1. How do you find the common denominator for fractions?
2. Can you explain the difference between improper fractions and mixed numbers?
3. What is the rule for adding and subtracting negative numbers?
4. How can decimals be added with more precision?
5. How do you convert a mixed number back into an improper fraction?

Tip: Always double-check your fractions by finding the least common denominator to avoid mistakes when adding or subtracting them!