Fraction area models

​When you are working with fractions, it can help to use area models! A fraction area model shows a whole shape split into equal parts.

To figure out what fraction an area model shows, follow these steps:
1. Count the number of equal parts in the whole shape.
2. Write this number as your denominator.
3. Count the number of shaded parts.
4. Write this number as your numerator.
Let's try it!
What fraction does this area model show?

​There are 3 equal parts, so the denominator is 3. Each equal part is 1/3 of the whole.
There are 2 shaded parts. So, the numerator is 2.
This area model shows 2/3 !

​Drawing fraction area models

To draw a fraction area model, follow these steps:
1. Draw a shape, such as a rectangle or circle.
2. Split the shape into the number of equal parts shown by the denominator.
3. Shade the number of parts shown by the numerator.

Let's try it!

Draw an area model to show 4/6 .
First, draw a shape. Let's use a rectangle.

​Then, look at the denominator. The denominator is 6. So, split the rectangle into 6 equal parts. Each part represents 1/6 . The parts must be the same size!

​Now, look at the numerator. The numerator is 4. So, shade 4 parts.

​This area model shows 4/6 !

​Area models and equivalent fractions


Do you notice something about 2/3 and 4/6 ? The same area is shaded on both models!

​The fractions 2/3 and 4/6 are equivalent. They show the same amount.
Remember, to compare fractions with area models, the size of the whole must be the same!

​Area models for mixed numbers

You can use area models to show mixed numbers, too. There will be more than 1 whole shape, but you can use the same steps as before.
Let's try it! What mixed number does this area model show?

​Two rectangles are completely shaded, so the whole number is 2.
Now look at the last rectangle. There are 5 equal parts. So, the denominator of the fraction is 5. Each part represents 1/5 .
There are 3 shaded parts in the last rectangle. So, the numerator of the fraction is 3.

​Area models for improper fractions

You can use area models for improper fractions, too.
Let's try an example. Draw an area model to show 7/2 .
First, draw some rectangles. You can always add more or erase some later if you draw the wrong number.

​Then, look at the denominator. The denominator is 2. So, split each rectangle into 2 equal parts.

​Now, look at the numerator. The numerator is 7. So, shade 7 parts.

​This area model shows 7/2 !