https://file.aiquickdraw.com/mathbot/file/1725450546485maqie6zr.jpg

The expression in the image is:

\[
3\frac{2}{4} \div \frac{5}{14}
\]

Let's solve this step by step.

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \(3\frac{2}{4}\) can be converted to an improper fraction. 

\[
3\frac{2}{4} = \frac{3 \times 4 + 2}{4} = \frac{12 + 2}{4} = \frac{14}{4}
\]

### Step 2: Simplify the fraction if possible.
\(\frac{14}{4}\) can be simplified by dividing both the numerator and the denominator by 2:

\[
\frac{14}{4} = \frac{7}{2}
\]

### Step 3: Rewrite the division as multiplication.
Dividing by a fraction is the same as multiplying by its reciprocal. So the expression becomes:

\[
\frac{7}{2} \div \frac{5}{14} = \frac{7}{2} \times \frac{14}{5}
\]

### Step 4: Multiply the fractions.
Now, multiply the numerators and denominators:

\[
\frac{7 \times 14}{2 \times 5} = \frac{98}{10}
\]

### Step 5: Simplify the result.
Finally, simplify \(\frac{98}{10}\) by dividing both the numerator and the denominator by 2:

\[
\frac{98}{10} = \frac{49}{5}
\]

So, the final answer is:

\[
\frac{49}{5} \text{ or } 9\frac{4}{5}
\]

Would you like any further details or explanations? Here are some related questions you might find helpful:

1. How do you convert a mixed number to an improper fraction?
2. What is the process for dividing fractions?
3. How do you simplify fractions?
4. What are reciprocal fractions, and how do you use them?
5. How do you convert improper fractions back to mixed numbers?

**Tip:** Always simplify your fractions at each step to make calculations easier!

Learn how to solve the division of the mixed number 3 2/4 by the fraction 5/14. This step-by-step guide covers key fraction operations, including converting mixed numbers to improper fractions, finding reciprocals, and simplifying the result. Suitable for students in Grades 6-8.

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