https://file.aiquickdraw.com/mathbot/file/1726249991917b1ok1r8z.jpg

To solve the problem, we need to represent the mixed fraction \( \frac{3\frac{2}{5}}{4} \) using a **linear model** on a number line.

### Step 1: Understanding the Expression
The expression \( \frac{3\frac{2}{5}}{4} \) means we are dividing \( 3\frac{2}{5} \) by 4. Let's first convert the mixed number \( 3\frac{2}{5} \) into an improper fraction.

\[
3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]

Now, dividing \( \frac{17}{5} \) by 4:

\[
\frac{17}{5} \div 4 = \frac{17}{5} \times \frac{1}{4} = \frac{17}{20}
\]

Thus, the expression simplifies to \( \frac{17}{20} \).

### Step 2: Plotting on a Number Line
We now represent \( \frac{17}{20} \) on a number line.

1. First, divide the number line between 0 and 1 into 20 equal parts since the denominator is 20.
2. Each tick mark represents \( \frac{1}{20} \).
3. Count 17 ticks from 0 to reach \( \frac{17}{20} \), which will be just before 1.

The fraction \( \frac{17}{20} \) lies between \( \frac{16}{20} \) and \( \frac{18}{20} \), or equivalently between \( 0.8 \) and \( 0.9 \) on the number line.

### Explanation for the Diagram
- Each tick mark represents an increment of \( \frac{1}{20} \).
- The position of \( \frac{17}{20} \) is shown by counting 17 increments from 0.
- The fraction \( \frac{17}{20} \) is a little less than 1.

Would you like me to create the visual representation of this number line? Let me know if you need more details or further clarification.

### Expanding Questions:
1. How can we convert mixed fractions into improper fractions efficiently?
2. What are the key steps in dividing fractions?
3. How can you represent fractions with larger denominators on a number line?
4. What happens if you divide a fraction by another fraction?
5. Why is it useful to represent fractions on a number line in real-life scenarios?

### Tip:
When dividing fractions, remember that dividing by a number is equivalent to multiplying by its reciprocal!

Represent \( \frac{3\frac{2}{5}}{4} \) using a linear model (i.e., number line). Explain your diagram and label it so that it is clear what each tick mark represents in terms of the problem.

Learn how to represent the fraction \( \frac{3\frac{2}{5}}{4} \) using a linear model on a number line. This problem involves converting mixed numbers to improper fractions and dividing fractions by whole numbers. Suitable for students in Grades 6-8.

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