Add Fractions Using Visual Models - Math Worksheets - SplashLearn - Free Printable

Let's solve the fraction addition problems shown in the image step by step.

---

Problem 1:

First Model (Light Blue):
- The rectangle is divided into 5 equal horizontal parts.
- 4 parts are shaded.
- So, the fraction is:
$$
\frac{4}{5}
$$

Second Model (Blue):
- The rectangle is also divided into 5 equal horizontal parts.
- 3 parts are shaded.
- So, the fraction is:
$$
\frac{3}{5}
$$

Now, add them:
$$
\frac{4}{5} + \frac{3}{5} = \frac{7}{5}
$$

This is an improper fraction, which can be written as a mixed number:
$$
\frac{7}{5} = 1 \frac{2}{5}
$$

✔ Sum: $ 1 \frac{2}{5} $

---

Model for the Sum ($1 \frac{2}{5}$):

To draw a model for $1 \frac{2}{5}$, you can:
- Draw one whole rectangle fully shaded.
- Then draw another rectangle divided into 5 parts, with 2 parts shaded.

This represents $1 + \frac{2}{5} = 1 \frac{2}{5}$.

---

Problem 2:

First Model (Orange and White):
- The rectangle is divided into 10 vertical parts (since there are 10 small rectangles).
- 4 parts are shaded orange.
- So, the fraction is:
$$
\frac{4}{10}
$$

Second Model (Purple):
- The rectangle is divided into 10 vertical parts.
- 9 parts are shaded purple.
- So, the fraction is:
$$
\frac{9}{10}
$$

Now, add them:
$$
\frac{4}{10} + \frac{9}{10} = \frac{13}{10}
$$

Convert to a mixed number:
$$
\frac{13}{10} = 1 \frac{3}{10}
$$

✔ Sum: $ 1 \frac{3}{10} $

---

Model for the Sum ($1 \frac{3}{10}$):

- Draw one whole rectangle fully shaded.
- Then draw another rectangle divided into 10 parts, with 3 parts shaded.

---

✔ Final Answers:

#### Top Row:
$$
\frac{4}{5} + \frac{3}{5} = 1 \frac{2}{5}
$$

#### Bottom Row:
$$
\frac{4}{10} + \frac{9}{10} = 1 \frac{3}{10}
$$

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📌 Summary of What to Write in the Boxes:

#### First Problem:
```
4 3 1 2
--- + --- = ------
5 5 5
```

#### Second Problem:
```
4 9 1 3
--- + --- = ------
10 10 10
```

> Note: In the second problem, the fractions are already in simplest form? Actually, $\frac{4}{10}$ can be simplified to $\frac{2}{5}$, but since the model shows 10 parts, it's acceptable to keep it as $\frac{4}{10}$ unless simplification is required. But here, since we're adding like denominators, keeping it as $\frac{4}{10}$ is fine.

But if the instructions want simplified forms, then:
- $\frac{4}{10} = \frac{2}{5}$, but the model shows 10 parts, so likely they want what the model shows — so leave as $\frac{4}{10}$.

---

✔ Final Answer to Fill In:

#### Top:
$$
\frac{4}{5} + \frac{3}{5} = 1 \frac{2}{5}
$$

#### Bottom:
$$
\frac{4}{10} + \frac{9}{10} = 1 \frac{3}{10}
$$

And draw models accordingly.

Let me know if you'd like me to generate the drawings!