https://file.aiquickdraw.com/mathbot/file/17298790896108u3agnz2.jpg

The given expression is:

\[
2 \frac{4}{5} \div \frac{4}{7}
\]

### Step-by-step solution:

1. **Convert the mixed number** \( 2 \frac{4}{5} \) into an improper fraction:
   \[
   2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5}
   \]

2. **Rewrite the division as multiplication by the reciprocal**:
   \[
   \frac{14}{5} \div \frac{4}{7} = \frac{14}{5} \times \frac{7}{4}
   \]

3. **Multiply the fractions**:
   \[
   \frac{14}{5} \times \frac{7}{4} = \frac{14 \times 7}{5 \times 4} = \frac{98}{20}
   \]

4. **Simplify the result**:
   \[
   \frac{98}{20} = \frac{49}{10}
   \]

   This is the simplified form of the result.

### Final Answer:
\[
2 \frac{4}{5} \div \frac{4}{7} = \frac{49}{10} \quad \text{or as a mixed number:} \quad 4 \frac{9}{10}
\]

Would you like further details on any step or more questions related to this?

Here are 5 related questions:
1. How do you convert a mixed number into an improper fraction?
2. What is the process for dividing fractions?
3. How do you simplify fractions?
4. Can this division problem be solved using decimal conversions?
5. How does multiplying by the reciprocal work in fraction division?

**Tip:** Always simplify the fractions as much as possible to make calculations easier.

Learn how to divide the mixed number 2 4/5 by the fraction 4/7 with a clear, detailed solution. This example covers conversion to improper fractions, multiplication by reciprocals, and simplifying fractions. Suitable for 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