https://file.aiquickdraw.com/mathbot/file/17296123159745hg2edsd.jpg

Let's solve the problems in the image step by step. 

### Part A: Perform the indicated operations

1. \( 3 \frac{2}{5} + 4 \frac{1}{5} \)
   - Convert the mixed fractions to improper fractions:
     - \( 3 \frac{2}{5} = \frac{17}{5} \)
     - \( 4 \frac{1}{5} = \frac{21}{5} \)
   - Now add them:
     - \( \frac{17}{5} + \frac{21}{5} = \frac{38}{5} = 7 \frac{3}{5} \)

2. \( \frac{8}{20} + \frac{11}{20} \)
   - Since the denominators are the same, add the numerators:
     - \( \frac{8 + 11}{20} = \frac{19}{20} \)

3. \( 9 \frac{2}{4} - 5 \frac{1}{4} \)
   - Convert the mixed fractions to improper fractions:
     - \( 9 \frac{2}{4} = 9 \frac{1}{2} = \frac{19}{2} \)
     - \( 5 \frac{1}{4} = \frac{21}{4} \)
   - Find a common denominator (which is 4):
     - \( \frac{19}{2} = \frac{38}{4} \)
     - Now subtract: \( \frac{38}{4} - \frac{21}{4} = \frac{17}{4} = 4 \frac{1}{4} \)

---

### Part B: Find the product of the following

1. \( \frac{1}{2} \times \frac{2}{3} \)
   - Multiply the numerators and denominators:
     - \( \frac{1 \times 2}{2 \times 3} = \frac{2}{6} = \frac{1}{3} \)

2. \( \frac{2}{5} \times \frac{6}{9} \)
   - Simplify \( \frac{6}{9} \) to \( \frac{2}{3} \), then multiply:
     - \( \frac{2}{5} \times \frac{2}{3} = \frac{4}{15} \)

3. \( \frac{1}{7} \times \frac{3}{10} \)
   - Multiply the numerators and denominators:
     - \( \frac{1 \times 3}{7 \times 10} = \frac{3}{70} \)

4. \( \frac{3}{6} \times \frac{2}{8} \)
   - Simplify \( \frac{3}{6} = \frac{1}{2} \) and \( \frac{2}{8} = \frac{1}{4} \), then multiply:
     - \( \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \)

5. \( \frac{5}{8} \times \frac{1}{3} \)
   - Multiply the numerators and denominators:
     - \( \frac{5 \times 1}{8 \times 3} = \frac{5}{24} \)

6. \( 3 \times \frac{3}{10} \)
   - Convert 3 to \( \frac{3}{1} \), then multiply:
     - \( \frac{3}{1} \times \frac{3}{10} = \frac{9}{10} \)

7. \( 25 \times \frac{2}{5} = n \)
   - Multiply:
     - \( 25 \times \frac{2}{5} = \frac{50}{5} = 10 \)
     - So, \( n = 10 \)

8. \( 2 \times 40 = n \)
   - Multiply:
     - \( 2 \times 40 = 80 \)
     - So, \( n = 80 \)

9. \( 60 \times \frac{3}{4} = n \)
   - Multiply:
     - \( 60 \times \frac{3}{4} = \frac{180}{4} = 45 \)
     - So, \( n = 45 \)

10. \( \frac{1}{8} \times 54 \)
    - Convert 54 to \( \frac{54}{1} \), then multiply:
      - \( \frac{1}{8} \times \frac{54}{1} = \frac{54}{8} = 6 \frac{6}{8} = 6 \frac{3}{4} \)

11. \( 2 \times \frac{1}{4} \)
    - Multiply:
      - \( 2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \)

---

Would you like further details on any of the steps? 

Here are 5 questions that expand on these topics:
1. How do you convert mixed fractions to improper fractions?
2. Why is finding a common denominator important when adding or subtracting fractions?
3. What is the rule for multiplying two fractions?
4. How can simplifying fractions before multiplying make calculations easier?
5. Can you explain why multiplying by a fraction less than 1 always results in a smaller product?

**Tip:** When multiplying fractions, always check if the fractions can be simplified before multiplying. This saves time and makes the arithmetic easier!

Perform operations and find the product of fractions as shown in the uploaded image.

Learn how to perform addition, subtraction, and multiplication of fractions and mixed numbers with step-by-step solutions. This guide covers converting mixed numbers to improper fractions, finding common denominators, and multiplying fractions efficiently. Perfect for Grades 5-7 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation