Use fraction bars or a number line to create a model for 1 3/8 divided by 1/3

To model the division of \( 1 \frac{3}{8} \div \frac{1}{3} \) using a fraction bar, we need to follow these steps:

### Step 1: Convert the Mixed Number to an Improper Fraction
First, convert \( 1 \frac{3}{8} \) to an improper fraction:
\[
1 \frac{3}{8} = \frac{8 \times 1 + 3}{8} = \frac{11}{8}
\]

So, we now have \( \frac{11}{8} \div \frac{1}{3} \).

### Step 2: Rewrite Division as Multiplication
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
\[
\frac{11}{8} \div \frac{1}{3} = \frac{11}{8} \times \frac{3}{1} = \frac{11 \times 3}{8 \times 1} = \frac{33}{8}
\]

### Step 3: Visualize Using a Fraction Bar
We can visualize this division with fraction bars:

1. Draw a fraction bar representing \( 1 \frac{3}{8} \). It will be one full bar (for the "1") and another bar divided into 8 equal parts, with 3 of those parts shaded in.
   
2. Next, think about how many \( \frac{1}{3} \) pieces fit into \( 1 \frac{3}{8} \). Since we converted the problem into multiplication by \( \frac{3}{1} \), the result \( \frac{33}{8} \) tells us how many pieces of size \( \frac{1}{3} \) fit.

### Step 4: Convert \( \frac{33}{8} \) Back to a Mixed Number
\[
\frac{33}{8} = 4 \frac{1}{8}
\]
This means \( 1 \frac{3}{8} \div \frac{1}{3} = 4 \frac{1}{8} \), or 4 full pieces of \( \frac{1}{3} \) and an additional \( \frac{1}{8} \) of a \( \frac{1}{3} \)-sized piece.

### Visualization Summary
- A fraction bar for \( 1 \frac{3}{8} \) would be 1 full bar and 3/8 of a bar.
- Then, calculate how many times \( 1/3 \) fits into that, which turns out to be \( 4 \frac{1}{8} \).

Would you like a detailed breakdown of any part? Here are 5 related questions to explore further:

1. How do you multiply improper fractions step by step?
2. Why is dividing by a fraction equivalent to multiplying by the reciprocal?
3. How can you represent \( 4 \frac{1}{8} \) using fraction bars or a number line?
4. How would you perform this division on a number line instead of using fraction bars?
5. What is the difference between mixed numbers and improper fractions in division problems?

**Tip:** Always convert mixed numbers into improper fractions before performing operations like multiplication or division.

Learn how to model the division of 1 3/8 by 1/3 using fraction bars. This step-by-step guide walks you through converting mixed numbers to improper fractions, multiplying by the reciprocal, and visualizing the solution with fraction bars. Suitable for Grades 5-7.

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