How to Teach Dividing Fractions With Models | FREE Practice - Free Printable

The image you've shared is a title card for a digital math activity focused on division of fractions using visual models. It doesn't contain a specific problem to solve directly, but rather introduces two fraction division problems and shows two shaded grid models that likely represent those problems visually.

Let’s break down what we see and how to interpret it:

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🔹 Title & Purpose

- "Division of Fractions Models"
- This is a digital learning activity designed to help students understand how to divide fractions using visual models, such as area models or grids.
- The goal is to make abstract fraction division more concrete by showing it through shaded regions.

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🔹 Two Fraction Division Problems Shown

1. $ \frac{4}{8} \div \frac{1}{3} $
2. $ \frac{6}{10} \div \frac{8}{12} $

These are the two problems that the models below are meant to represent.

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🔹 Visual Models (Grids)

There are two 10x10 grids (total of 100 squares), each representing a whole.

#### ✔ Left Grid:
- The leftmost column (10 squares) is shaded in light blue — this represents $ \frac{1}{10} $ of the whole.
- But wait: $ \frac{4}{8} = \frac{1}{2} $. So if the whole is 100 squares, $ \frac{1}{2} $ would be 50 squares.
- However, only 10 squares are shaded in blue. That suggests something different.

Wait — let's re-evaluate.

Actually, looking closely:
- The top row has a striped pattern (brownish), covering 4 squares.
- Then, a vertical column of 10 squares is shaded light blue.
- This may suggest:
- The total rectangle is divided into 8 equal parts horizontally? Or maybe it's a model for $ \frac{4}{8} $?

But the most likely interpretation is that the entire grid represents the whole, and the shading shows how much of the whole is being divided.

Let’s analyze both models carefully.

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## 🔍 Let's Solve the Problems Using Models

We’ll go through each problem step-by-step and explain how the models might represent them.

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🔹 Problem 1: $ \frac{4}{8} \div \frac{1}{3} $

Simplify:
$ \frac{4}{8} = \frac{1}{2} $, so this becomes:
$$
\frac{1}{2} \div \frac{1}{3}
$$

This means: How many $ \frac{1}{3} $'s fit into $ \frac{1}{2} $?

Using the invert and multiply rule:
$$
\frac{1}{2} \div \frac{1}{3} = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2} = 1\frac{1}{2}
$$

So the answer is $ 1\frac{1}{2} $.

Now, how does the left model represent this?

#### 🟦 Left Model Analysis:
- A 10×10 grid = 100 squares.
- The first column (10 squares) is shaded light blue — that's $ \frac{1}{10} $ of the whole.
- But we need to represent $ \frac{1}{2} $ (i.e., 50 squares).
- Wait — perhaps the shaded region is not just one color.

Looking again:
- Top row has 4 shaded squares with diagonal lines (possibly representing $ \frac{4}{8} $ or $ \frac{1}{2} $).
- Then, a vertical strip of 10 squares is shaded blue.

Ah! Maybe this is a double-shaded model.

In fraction division models, especially area models:
- You start with a rectangle representing the dividend ($ \frac{4}{8} $).
- Then you divide it into parts of size $ \frac{1}{3} $, and count how many fit.

Alternatively, think of it this way:

To model $ \frac{4}{8} \div \frac{1}{3} $, you can:
1. Represent $ \frac{4}{8} $ as a portion of a whole.
2. See how many $ \frac{1}{3} $-sized pieces fit into that portion.

But since $ \frac{1}{3} $ is larger than $ \frac{1}{2} $? No — actually, $ \frac{1}{3} \approx 0.33 $, $ \frac{1}{2} = 0.5 $, so $ \frac{1}{3} < \frac{1}{2} $, so one full $ \frac{1}{3} $ fits, and then half of another.

So $ \frac{1}{2} \div \frac{1}{3} = 1.5 $

So the model should show:
- A rectangle split into thirds.
- Half of the rectangle shaded.
- Count how many $ \frac{1}{3} $ sections are inside the shaded half.

That would give 1 full third and half of another → $ 1\frac{1}{2} $

So the left model likely shows:
- A rectangle split vertically into 3 columns (each $ \frac{1}{3} $)
- The shaded area (representing $ \frac{1}{2} $) covers 1 full column and half of the second.
- So 1.5 of the $ \frac{1}{3} $ pieces fit → answer: $ \frac{3}{2} $

But the grid looks like it’s 10×10, so perhaps it's scaled differently.

Alternatively, maybe the blue shading represents $ \frac{4}{8} $, and the diagonal stripes represent $ \frac{1}{3} $, and we’re seeing how many times $ \frac{1}{3} $ fits into $ \frac{4}{8} $.

But without seeing the actual interactive version, we have to infer.

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🔹 Problem 2: $ \frac{6}{10} \div \frac{8}{12} $

Simplify:
- $ \frac{6}{10} = \frac{3}{5} $
- $ \frac{8}{12} = \frac{2}{3} $

So:
$$
\frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2} = \frac{9}{10}
$$

Answer: $ \frac{9}{10} $

Now look at the right model.

#### 🟪 Right Model Analysis:
- A 10×10 grid.
- There are three types of shading:
- Purple diagonal stripes: covers top 6 rows (60 squares) → $ \frac{6}{10} $
- Green horizontal bars: bottom 4 rows, but only 3 columns wide → 12 squares?
- Wait: actually, it looks like:
- The purple striped region covers the top 6 rows → 60 squares = $ \frac{6}{10} $
- The green shaded region covers 3 columns across the bottom 4 rows → 12 squares
- But the other part (not green) is also shaded diagonally?

Wait — perhaps the purple diagonal lines represent $ \frac{6}{10} $, and the green shaded area represents $ \frac{8}{12} $, and we're seeing how many times $ \frac{8}{12} $ fits into $ \frac{6}{10} $.

But $ \frac{8}{12} = \frac{2}{3} \approx 0.666 $, while $ \frac{6}{10} = 0.6 $, so $ \frac{6}{10} < \frac{8}{12} $, so less than one group of $ \frac{8}{12} $ fits into $ \frac{6}{10} $.

And we calculated $ \frac{6}{10} \div \frac{8}{12} = \frac{9}{10} $, which is less than 1, so yes — less than one full piece.

So the model might show:
- A rectangle where $ \frac{6}{10} $ is shaded (say, purple).
- Then, a region of size $ \frac{8}{12} $ is shown (maybe green), and it overlaps partially.
- We see that $ \frac{6}{10} $ is 9/10 of $ \frac{8}{12} $, meaning $ \frac{6}{10} = \frac{9}{10} \times \frac{8}{12} $

So the model is showing how much of the divisor fits into the dividend.

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## ✔ Summary of Solutions

Problem 1: $ \frac{4}{8} \div \frac{1}{3} $

- Simplify: $ \frac{1}{2} \div \frac{1}{3} $
- Multiply: $ \frac{1}{2} \times 3 = \frac{3}{2} = 1\frac{1}{2} $
- Answer: $ \boxed{1\frac{1}{2}} $

Problem 2: $ \frac{6}{10} \div \frac{8}{12} $

- Simplify: $ \frac{3}{5} \div \frac{2}{3} $
- Multiply: $ \frac{3}{5} \times \frac{3}{2} = \frac{9}{10} $
- Answer: $ \boxed{\frac{9}{10}} $

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## 📌 How the Models Help

- Visual models like these help students see:
- How many times a smaller fraction fits into a larger one.
- Why dividing by a fraction gives a larger result (if divisor < 1).
- The relationship between multiplication and division.

For example:
- In $ \frac{1}{2} \div \frac{1}{3} $, even though $ \frac{1}{3} $ is smaller than $ \frac{1}{2} $, it still fits 1.5 times into $ \frac{1}{2} $ — which is counterintuitive unless visualized.

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## ✔ Final Answer

| Problem | Simplified | Solution |
|--------|------------|----------|
| $ \frac{4}{8} \div \frac{1}{3} $ | $ \frac{1}{2} \div \frac{1}{3} $ | $ \boxed{1\frac{1}{2}} $ |
| $ \frac{6}{10} \div \frac{8}{12} $ | $ \frac{3}{5} \div \frac{2}{3} $ | $ \boxed{\frac{9}{10}} $ |

> These models are excellent tools for building conceptual understanding before moving to algorithms.