Fractions as part of a set
A fraction is a part of a whole. If you do not fully understand what a fraction is click here. Often we deal with fractions as part of one whole item, such as one square, one pizza or one cake. However sometimes we need to find a fraction of a set or group of items. For example if your mother gives you ten mangoes and asks you to give half of them to your brother, what will you do?
It’s very simple. Since a half is one out of two equal parts all you have to do is divide the ten mangoes into two equal groups as shown below.
You have divided the mangoes into two equal groups so each of these groups contains half of your mangoes. Each group has five mangoes so we can say half of ten mangoes is five mangoes. You can find half of any set of items by dividing the items into two equal groups.
What if you had six sweets that you wanted to share equally among three of your friends? Each friend would get one out of three equal parts or one third. What is one third of six sweets? You would have to divide the sweets into three equal groups as shown in the picture below.
You have divided the sweets into three equal parts or thirds. Each group has two sweets. One third of six sweets is two sweets. You can find one third of a set of items by dividing the items into three equal groups.
Now imagine you had nine apples. You want to give two thirds of your apples to your best friend. That is two out of three equal parts of your apples. What is two thirds of nine apples? Start by dividing your apples into three equal groups or thirds as you can see below.
Each group has three apples. One third of nine apples is three apples. You want to give your best friend two thirds of the apples so you must give him two of these groups. When you add these two groups together you get six apples. Two thirds of nine apples is six apples. This is shown in the diagram below.
Helpful hint: The denominator tells us how many equal groups to divide the items into. The numerator tells us how many of these groups we need.
Let us go back to our first example. Your mother gave you ten mangoes to share with your brother. You decided to give your brother three fifths (
)of the mangoes, How many mangoes should you give him? What is three fifths of ten mangoes?
The denominator (5) tells you to divide the mangoes into five equal groups as shown below.
The numerator (3) tells us that you should give your brother three of these groups. See the diagram below.
Therefore, three fifths of ten mangoes is six mangoes.
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