There are different models that can be used to add fractions, but one common model is the area model, which represents fractions as parts of a whole.
To use the area model to add fractions, you can follow these steps:
1. Draw a rectangle to represent the whole. The size of the rectangle can be arbitrary, but it should be divided into equal parts to match the denominators of the fractions you are adding.
2. Divide the rectangle into the appropriate number of equal parts to represent the denominators of the fractions. For example, if you are adding 1/3 and 1/4, divide the rectangle into 12 equal parts (3 x 4 = 12).
3. Shade the appropriate number of parts in each fraction. For example, shade 4 out of 12 parts for 1/3 and 3 out of 12 parts for 1/4.
4. Count the total number of shaded parts in the rectangle. This represents the numerator of the sum of the fractions.
5. Write the sum of the fractions as the total number of shaded parts over the total number of parts in the rectangle.
For example, to add 1/3 and 1/4 using the area model:
1. Draw a rectangle to represent the whole.
```
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
```
2. Divide the rectangle into 12 equal parts.
```
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
| | | | |
+---+---+---+---+
1 2 3 4
```
3. Shade 4 out of 12 parts for 1/3 and 3 out of 12 parts for 1/4.
```
+---+---+---+---+
|###|###|###| |
+---+---+---+---+
|###|###|###| |
+---+---+---+---+
|###|###| | |
+---+---+---+---+