Thursday, January 10, 2013

Fraction Chart for Math

Fraction can be defined as part of something bigger than that. Suppose your class has 40 boys and 60 girls thus totaling 100 students. Boys are the part of the class and so are girls. But the class consists both boys and girls and is bigger set. In the class, we say 40 out 100 are boys. We can write this as a Fraction as below

We observe that number 40 is written at the top and then a bar below it and then number 100 below the bar. This is how the fractions are represented.

The boys in the class form a part of the class and they are 40 in number. The class is bigger and has 100 students. So, the part here is the boys and the whole is the class. So, this fraction represents that 40 boys are a part of a class of 100 students. Thus we see, fraction represents the part of a whole.

It must also be noted that there could be fractions where the part can be bigger than the whole.

Fractions Illustration

Let us illustrate how fractions can be formed as a part of the whole. Let us a draw a full circle first as below

Now let us divide the circle into two different parts and shade one part green as shown below

So we have total two parts and one part is green. This is represented as ½.

Now let us divide the original circle into three and shade two parts of it green as below

So we have total three parts and two parts are green. This is represented as `(2)/(3)`

Thus fractions represent a part of the whole.

As we saw a fraction has one number at the top of a bar and one number below it. The top number is called the numerator and the bottom number is called the denominator as shown below.

The chart below shows fractions in pictorial form

Types of Fractions

• If the numerator is less than the denominator, it is called a proper fraction.
All the fractions we saw above like `(1)/(2)` , `(2)/(3)`  etc are proper fractions because the top number or numerator was smaller then the bottom number or denominator
• If the numerator is greater than the denominator, it is called an improper fraction.
Example. `(4)/(3)` , `(7)/(2)`  etc. These fractions represent where the part is greater than the whole. We will illustrate with an example. Suppose your teacher is conducting an examination for you. The examination had 25 questions and the teacher asked you to solve any 20 questions to get the maximum mark of 20. Suppose you managed to solve all the 25 correctly then your score in the test will be `(25)/(20)` . That means that you solved more than the maximum required.
• There are another kind of fractions, which has both a whole number and a proper fraction. These fractions are called mixed fractions.
Example 3 `(1)/(2)` ,4`(2)/(3)`  etc.  Thus these fractions are a mix of whole number and a proper fraction and hence they are called mixed fractions.

Exercises on Fractions

Pro 1: From the figure below, write the region shaded in the circle as a fraction of the whole circle

i)

ii)

iii)

Ans : (i) `(2)/(10)` (ii) `(5)/(6)`       (iii) `(7)/(10)`

Pro 2: Identify the proper, improper and mixed fractions from the following

`(7)/(8)`  ,7 `(1)/(2)`   , `(16)/(2)` , `(1)/(8)` , `(4)/(3)`

Ans: Proper fractions - `(7)/(8)` ,`(1)/(8)`   - Numerator of these fractions are smaller then the denominator

Improper Fraction - `(16)/(2)` , `(4)/(3)`  - - Numerator of these fractions are bigger then the denominator

Mixed Fraction - 7 `(1)/(2)`   - This fraction has  a whole number and a proper fraction