Eduki

A fraction can be thought of more than just a part of a whole or a measurement. When we divide a whole number by another whole number, we can also write that fractionally. When 'a' is divided by 'b', we get the quotient a/b. We will look at some questions that will help us understand this better. 

Let us look at this example. How many sandwiches would one person get if 6 sandwiches were divided between 3 people? Since the number of sandwiches is more than the people, it is obvious that each person gets more than 1 sandwich. Keep this in mind when we solve more questions. Each person gets exactly 2 sandwiches each. 

If there were 2 sandwiches and 2 people to share with, it's obvious that each person gets one each. 

How much sandwich would each person get if there were 3 people and 2 sandwiches? If there were more sandwiches than people, each person would get less than 1 sandwich. If we were to write an expression to represent this situation, we get the amount of sandwich each person gets by dividing 2 by 3, that is, 2 ÷ 3. We do not get an exact whole number because they get less than 1 sandwich, meaning, each will get a fraction of a sandwich. 

Now, how can we represent this in a block diagram? Look at the following diagrams, which one do you think correctly represents 2 sandwiches being divided equally among 3 people? 

All images are correct in denoting how two sandwiches can be divided equally among 3 people. Remember that it does not matter how we divide the sandwiches. The only thing that matters is that each of the 3 people should get equal amount of the sandwich.

Let's look at the fraction 1/5. 

The size denoted by 1/5 is equal to the size of one of the equal pieces when a single whole is divided into 5 equal portions. Written numerically, this gives us; 1 / 5 = 1 ÷ 5 Now, let's look at 1/3. 

Here again, 1 / 3 and 1 ÷ 3 denote the size of the shaded portion. We can write 1 / 3 = 1 ÷ 3. Thus, 1 / b = 1 ÷ b.  We know that the expression to show 2 sandwiches being divided among 3 people is 2 ÷ 3. 

What do you think the size of each part will be? We already know that each person will get some amount of sandwich, but it will be less than 1 sandwich. This means that each of the 3 people will get a fraction of a sandwich. But exactly how much is it? Based on what we learnt before, 1 divided by 5 is one object being divided into 5 parts. We related this to being equal to 1/5, since 1/5 means the size of one part when one whole has been divided into 5 parts. 

Applying the same idea, we get 2 divided by 3 (2 ÷ 3) to be equal to 2/3 as well. Meaning the size of each part is 2/3. In all the previous images A, B, C, the amount that each person got was equal to 2/3 as well.