Let's learn how to simplify fractions.
First, we'll write a different fraction that's equal to 4/8. This square is divided into eight equal triangles and four of them are colored. The colored area covers exactly half of the entire square. This means the fraction 4/8 equals 1/2. The numerator 4 is exactly half of the denominator 8. So, writing 4/8 as 1/2 doesn't change the fraction's value. It just simplifies it.
Let's look at 68. Here a shape is divided into eight triangles and six are colored. We can also see that there are four squares and three of them are shaded. So 6/8 is equivalent to 3/4s.
Dividing the numerator and the denominator by the same number creates an equivalent fraction. The value stays the same. The area covered by six out of eight small triangles is exactly the same as the area covered by three out of four larger squares. Let's practice with a larger fraction. 16 302. The shape is divided into 32 triangles with 16 colored. 16 is half of 32. This means half of the shape is colored. So the fraction 16 32 simplifies to 1/2. To confirm this using division, we can ask what can we divide both 16 and 32 by to get 1/2. To get 1 from 16, we divide by 16. 32 / 16 is 2. Since we can divide both the top and bottom by 16, we've correctly simplified 16 302 to 1/2. Now, let's make a fraction equivalent to 12 30 seconds. We can divide 12 and 32 by 4, which is a common factor. So 12 / 4 is 3. 32 / 4 is 8. So 12 32nd simplifies to the equivalent fraction 3/8.
Simplifying a fraction means finding an equivalent fraction with smaller numbers. We can do this by dividing both the top and bottom by a common factor.
12 32 represents the same portion of the hole as 3/8. It's the same value, just a simpler way to write it.
