Let's go through the questions and their solutions on this sheet:

Problem 7:

$2 \frac{2}{3} \times (-3 \frac{1}{5})$ First, convert both mixed fractions to improper fractions: $2 \frac{2}{3} = \frac{8}{3}, \quad -3 \frac{1}{5} = -\frac{16}{5}$ Now multiply: $\frac{8}{3} \times -\frac{16}{5} = \frac{8 \times -16}{3 \times 5} = \frac{-128}{15}$ Final answer: $- \frac{128}{15}$

Problem 8:

$- \frac{8}{9} \times \left(-\frac{5}{6}\right)$ Multiply the fractions directly: $-\frac{8}{9} \times -\frac{5}{6} = \frac{8 \times 5}{9 \times 6} = \frac{40}{54}$ Simplify the fraction: $\frac{40}{54} = \frac{20}{27}$ Final answer: $\frac{20}{27}$

Problem 9:

$-2 \frac{3}{4} - 1 \frac{2}{5}$ Convert to improper fractions: $-2 \frac{3}{4} = -\frac{11}{4}, \quad 1 \frac{2}{5} = \frac{7}{5}$ Find a common denominator (LCM of 4 and 5 is 20): $-\frac{11}{4} = -\frac{55}{20}, \quad \frac{7}{5} = \frac{28}{20}$ Now subtract: $-\frac{55}{20} - \frac{28}{20} = -\frac{55 + 28}{20} = -\frac{83}{20}$ Convert to a mixed fraction: $-\frac{83}{20} = -4 \frac{3}{20}$ Final answer: $-4 \frac{3}{20}$

Problem 10:

$-\frac{3}{8} \times \left( \frac{7}{4} \right)$ Multiply the fractions: $-\frac{3}{8} \times \frac{7}{4} = \frac{-3 \times 7}{8 \times 4} = \frac{-21}{32}$ Final answer: $\frac{-21}{32}$

Problem 11:

$3 \frac{1}{4} \times \left(- \frac{5}{8}\right)$ Convert to improper fractions: $3 \frac{1}{4} = \frac{13}{4}$ Now multiply: $\frac{13}{4} \times -\frac{5}{8} = \frac{13 \times -5}{4 \times 8} = \frac{-65}{32}$ Final answer: $-\frac{65}{32}$

Problem 12:

Trisha has 12 $\frac{1}{2}$ cups of sugar and uses 3 $\frac{3}{4}$ cups.

First, convert mixed fractions to improper fractions: $12 \frac{1}{2} = \frac{25}{2}, \quad 3 \frac{3}{4} = \frac{15}{4}$ Find a common denominator (LCM of 2 and 4 is 4): $\frac{25}{2} = \frac{50}{4}$ Now subtract: $\frac{50}{4} - \frac{15}{4} = \frac{50 - 15}{4} = \frac{35}{4}$ Convert to a mixed fraction: $\frac{35}{4} = 8 \frac{3}{4}$ Final answer: $8 \frac{3}{4}$

Would you like more details on any of these solutions?

Here are some related questions:

1. How do you multiply improper fractions?
2. What is the process for converting mixed fractions to improper fractions?
3. How do you find a common denominator for adding or subtracting fractions?
4. What is the method for simplifying fractions?
5. How do you convert improper fractions back to mixed fractions?

Tip: When working with fractions, always simplify your final answer if possible for clarity.