Fractions - Explanation and Calculation

What is Fractions ?
I know this would be a very silly question. But still, it would be a very useful blog for all the beginners. May be your kids and students will gain some knowledge through it.

Fractions : 

   The whole part divided into several small parts is called as fraction. For example, consider there are four children in a home. Their father bought half kg cake for them. The father told them to share the cake among each other. Now the mother cut the cake into 4 equal parts. Each child is provided with equal part. (i.e.,) Each child has 1 part out of 4. This is expressed as 1 / 4. Here, 1 / 4 is called as fraction.

Fractions consists of two parts : 

1. Numerator
2. Denominator

In the above example 1 is numerator and 4 is denominator.

Types of Fractions : 

    There are three types of fractions :

• Proper Fractions
• Improper Fractions
• Mixed Fractions

Proper Fractions : 

   The fractions with numerator less than the denominator is called as the proper fractions.

Improper Fractions : 

 
   The fractions with numerator equal or greater than the denominator is called as the improper fractions.

Mixed Fractions : 

    A proper fraction combined with the whole number is called as the mixed fraction.

Other than these, when you compare two fractions, there may be two types of fractions.

• Like Fractions 
• Unlike Fractions 

If both fractions have the same denominator , it is called as like fractions. 

If both have different denominators, it is unlike fractions.

These types can be considered when arithmetic operations of fractions are performed.

Operations of Fractions : 

All four arithmetic operations addition, subtraction, multiplication and division can be performed in fractions.

Addition and Subtraction : 

1 /2 + 4/ 2 = ?

Here both denominators are same and hence it is a like fraction. Since, it is a like fraction, only numerators can be added (1 + 4) and the answer can be displayed as 5 / 2. 

The same case holds for subtraction also.

Now consider, 1 / 2 + 1/ 3 .

Now both numerator and denominator are different and hence it is a unlike fraction. So now, we have to take the LCM of both denominators. (LCM of 2,3 is 6) 

Now 

1 x 3 / 2 x 3 = 3 / 6 

1 x 2 / 3 x 2 = 2 / 6

3 / 6 + 2 / 6  = (3+2) / 6 = (5/6)

Hence answer is 5 /6.

Multiplication : 

Multiplication holds the same for both like and unlike fractions.

Example : 2/ 3 * 4 / 5 = ?

Multiply numerators and denominators separately.

(2x3) / (4 x5) = 6 / 20 . Now, this can be reduced to 2 / 10 and again to 1/5.

Division : 

Here also, it is similar to multiplication. 

Example :( 2/ 3 ) / ( 4 / 5 )= ?

Write the first number as it is (2 /3 ).

Instead of division symbol put multiplication symbol. (2 /3 ) * 

Now reciprocal the second number and write it. (2 /3 ) * (5 /4)

Now (2x5) / (3 x 4) = 10 / 12 = 2 / 6.

You can use online fraction arithmetic calculator for more complex and mixed operations.