I can help you solve the problems shown in your image. Let's go through each of them step by step:

Problem 27:

$\left(-1 \frac{1}{4}\right) + \left(-3 \frac{1}{2}\right) + 2 \frac{1}{2} + 3 \frac{1}{2}$ First, convert the mixed fractions into improper fractions: $-1 \frac{1}{4} = -\frac{5}{4}, \quad -3 \frac{1}{2} = -\frac{7}{2}, \quad 2 \frac{1}{2} = \frac{5}{2}, \quad 3 \frac{1}{2} = \frac{7}{2}$ Now, express all fractions with a common denominator (LCD = 4): $-\frac{5}{4}, \quad -\frac{7}{2} = -\frac{14}{4}, \quad \frac{5}{2} = \frac{10}{4}, \quad \frac{7}{2} = \frac{14}{4}$ Add them up: $-\frac{5}{4} + -\frac{14}{4} + \frac{10}{4} + \frac{14}{4} = \frac{-5 - 14 + 10 + 14}{4} = \frac{5}{4}$ Thus, the result is: $\frac{5}{4} = 1 \frac{1}{4}$

Problem 28:

$1 - \frac{5}{6} - \left(-\frac{5}{6}\right) + \left(-\frac{5}{6}\right)$ Simplify step by step: $1 - \frac{5}{6} + \frac{5}{6} - \frac{5}{6}$ Notice that the positive and negative $\frac{5}{6}$ cancel out: $1 - \frac{5}{6} = \frac{6}{6} - \frac{5}{6} = \frac{1}{6}$ Thus, the result is: $\frac{1}{6}$

Problem 29:

$(-1.5) + (-4.58) - 4.5 - (-5.9)$ Simplify the terms: $-1.5 - 4.58 - 4.5 + 5.9$ Group the negatives and positives: $(-1.5 - 4.58 - 4.5) + 5.9 = -10.58 + 5.9 = -4.68$ Thus, the result is: $-4.68$

Problem 30:

$(-6) - (-5.4) - (-7) + 1.1$ Simplify the negative signs: $-6 + 5.4 + 7 + 1.1$ Add them: $-6 + 5.4 = -0.6$ $-0.6 + 7 = 6.4$ $6.4 + 1.1 = 7.5$ Thus, the result is: $7.5$

Problem 31:

$(-7) - (-3) - (-0.1) - 6.8$ Simplify the negative signs: $-7 + 3 + 0.1 - 6.8$ Add them step by step: $-7 + 3 = -4$ $-4 + 0.1 = -3.9$ $-3.9 - 6.8 = -10.7$ Thus, the result is: $-10.7$

Problem 32:

$(-3) - 4.27 + 1.1 - (-6.836)$ Simplify the negative sign: $-3 - 4.27 + 1.1 + 6.836$ Add step by step: $-3 - 4.27 = -7.27$ $-7.27 + 1.1 = -6.17$ $-6.17 + 6.836 = 0.666$ Thus, the result is: $0.666$

Let me know if you'd like any further details or explanations on these problems!

Here are 5 questions that expand on these topics:

1. How do you convert a mixed fraction to an improper fraction?
2. What is the significance of finding a common denominator in fractions?
3. Why do positive and negative signs cancel out when they are equal in value?
4. How can you simplify expressions with multiple negative signs?
5. How does adding decimals differ from adding fractions?

Tip: When working with fractions, always ensure that the denominators are the same before adding or subtracting. This simplifies the process and prevents errors.