Let's explore how the same fraction can be written in different ways. We'll start by looking at this shape and figuring out what fraction of it is green. This rectangle is divided into six equal parts. The total number of equal parts, six, is our denominator.
Next, let's count how many are shaded green. We can see there are four green squares. So, four sixs of the shape is green.
Here the rectangle is divided into 12 smaller equal parts. The total number of parts is now 12, which becomes our new denominator.
There are eight green parts. So, we can write that the fraction of the shape that's green is 8 12ths.
46ths and 8 12ths represent the same amount of green in the rectangle, which means they are equivalent fractions.
Another fraction that we could use to describe the amount of green has a denominator of three. There are three equal parts here and two of them are green. So both 46 and 8 12ths are also equal to 2/3.
Equivalent fractions all represent the same value. They're just expressed using different numbers. The equation 2/3 = 46 = 8 12th shows this relationship. Let's look at a different problem. What fraction of this new shape is blue? First, let's figure out the total number of equal parts. The easiest way is to see how many small triangles fit into the whole shape. Each square contains two triangles and there are six squares.
So the whole shape is made of 12 equal triangles. That makes 12 our denominator. Now let's count the blue parts. There are four blue triangles. So 4 12ths of the shape is blue. Now let's find a simpler equivalent fraction for 4 12ths. We can simplify 4 12ths by dividing both the numerator and the denominator by their greatest common factor which is 4. 4 / 4 is 1 and 12 / 4 is 3. So 4 12ths equals 1/3.
We can also see this visually. If we rearrange the four blue triangles, they would fill 1/3 of the shape's area. A single amount can be represented by many different but equivalent fractions. The fractions 4 12ths and 1/3 represent the exact same amount of the shape.
