Let's analyze and solve this step by step.

We are tasked with pairing mixed numbers and improper fractions that are equivalent to each other. Here’s how to approach it:

Step 1: Start with the Improper Fraction

• The starting improper fraction is $\frac{15}{7}$. We need to find its mixed number form.

Step 2: Convert the Improper Fraction

• To convert $\frac{15}{7}$ to a mixed number, divide 15 by 7:
  • $15 \div 7 = 2$ remainder 1.
  • So, $\frac{15}{7} = 2 \frac{1}{7}$.

Step 3: Identify Equivalent Pair

• We now know that $2 \frac{1}{7}$ is equivalent to $\frac{15}{7}$.

Looking at the tiles in the image, one of them shows $2 \frac{1}{7}$ on the left. The matching pair for this one should be the tile with $\frac{15}{7}$.

Step 4: Analyze Remaining Tiles

Now let’s check the remaining tiles:

1. Mixed Number: $2 \frac{3}{7}$ – Convert to improper fraction: $2 \frac{3}{7} = \frac{2 \times 7 + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7}.$

   • This matches the improper fraction $\frac{17}{7}$ on another tile.

2. Mixed Number: $2 \frac{2}{7}$ – Convert to improper fraction: $2 \frac{2}{7} = \frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7}.$

   • This matches the improper fraction $\frac{16}{7}$ on another tile.

Step 5: Arrange Tiles

Based on the analysis, the proper arrangement would be:

1. Start: $\frac{15}{7} = 2 \frac{1}{7}$
2. $2 \frac{2}{7} = \frac{16}{7}$
3. $2 \frac{3}{7} = \frac{17}{7}$

Would you like further clarification on any of these steps or additional details?

Here are 5 follow-up questions to consider:

1. How do you convert any improper fraction into a mixed number?
2. What is the reverse process of converting a mixed number back into an improper fraction?
3. Why does multiplying the whole number by the denominator work in the conversion?
4. Could this method work for improper fractions with larger numbers?
5. How would you teach this conversion process to a beginner?

Tip: Always divide the numerator by the denominator when converting improper fractions to mixed numbers to determine the whole number part.