https://file.aiquickdraw.com/mathbot/file/17265397721257rqbq9up.jpg

Let's solve each of the mixed fraction problems step by step.

### (c) \( 2 \frac{2}{5} \times 1 \frac{7}{8} \)

1. **Convert the mixed fractions to improper fractions:**
   - \( 2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5} \)
   - \( 1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{15}{8} \)

2. **Multiply the improper fractions:**
   \[
   \frac{12}{5} \times \frac{15}{8} = \frac{12 \times 15}{5 \times 8} = \frac{180}{40}
   \]

3. **Simplify the result:**
   \[
   \frac{180}{40} = \frac{9}{2}
   \]
   This can also be written as:
   \[
   4 \frac{1}{2}
   \]

### (d) \( 2 \frac{1}{5} \div 1 \frac{1}{2} \)

1. **Convert the mixed fractions to improper fractions:**
   - \( 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5} \)
   - \( 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} \)

2. **Divide the improper fractions by multiplying with the reciprocal of the divisor:**
   \[
   \frac{11}{5} \div \frac{3}{2} = \frac{11}{5} \times \frac{2}{3} = \frac{11 \times 2}{5 \times 3} = \frac{22}{15}
   \]

3. **Simplify or convert to a mixed fraction:**
   \[
   \frac{22}{15} = 1 \frac{7}{15}
   \]

### Final answers:
- (c) \( 4 \frac{1}{2} \)
- (d) \( 1 \frac{7}{15} \)

Would you like further details on any step, or have any questions?

### Related Questions:
1. How do you convert improper fractions back to mixed fractions?
2. What is the general method for multiplying two fractions?
3. How do you simplify a fraction after multiplication?
4. Why do we multiply by the reciprocal when dividing fractions?
5. Can mixed fractions be directly divided without converting to improper fractions?

### Tip:
Always simplify the fractions before performing operations to make calculations easier.

Solve the mixed fraction operations: (c) 2 2/5 × 1 7/8, (d) 2 1/5 ÷ 1 1/2.

Learn how to solve mixed fraction problems step by step. This example covers multiplication and division of fractions, converting mixed fractions to improper fractions, and simplifying results. Suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation