https://file.aiquickdraw.com/mathbot/file/1727397483982m0er3f90.jpg

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.

Solve a variety of fraction multiplication and subtraction problems, including mixed and improper fractions.

This lesson covers solving problems involving the multiplication and subtraction of mixed and improper fractions. Learn how to convert mixed numbers to improper fractions, find common denominators, and simplify your answers. Suitable for middle school students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation