Conversion of Fractions:

1. Improper Fractions into Mixed Fractions:

To convert any improper fraction into a mixed fraction, numerator is divided with the denominator.
For ex: Converting 7/3 into a Mixed Fraction.

7 will be divided by 3, the quotient will be 2 and the remainder will be 1.

After dividing, the divisor (which is 3) will become the denominator, the quotient (which is 2) will be the whole number and the remainder (which is 1) will become the numerator.

2. Mixed Fractions Into Improper Fractions:

To convert mixed fraction into an improper fraction:

For Numerator: Multiply the denominator of mixed fraction with the whole number and then add the numerator of mixed fraction. The result obtained will be the numerator of improper fraction.

For Denominator: The denominator of the improper fraction will be same as the denominator of mixed fraction.

Thus in this way, Mixed Fraction is converted to Improper Fraction.

TYPES OF FRACTIONS 2

Fractions can also be divided into another category on the basis of Numerator and Denominator:
1. PROPER FRACTIONS
2. IMPROPER FRACTIONS
3. MIXED FRACTIONS

1. PROPER FRACTIONS:

The fractions in which the numerator is smaller than the denominator than such fractions are called proper fractions.

Such fractions are less than 1.

In all the fractions given above in the picture, numerator is smaller than denominator. Hence all the above fractions are proper fractions.

2. IMPROPER FRACTIONS:

The fractions in which the numerator is equal to denominator or greater than the denominator, such fractions are known as improper fractions.

These fractions are greater than 1.

In all the fractions given above in the picture, numerator is equal or greater than the denominator. Hence all the above fractions are improper fractions.

3. MIXED FRACTIONS:

Mixed fractions are the fractions which include a whole number and a proper fraction in it.

Mixed fraction is an another way of writing the improper fraction.

Here in the above image 8/3 which is an improper fraction, is changed into mixed fraction where 2 is the whole number and 2/3 is a proper fraction.

Thus Mixed Fractions are the combination of Whole Number and Proper Fractions.

TYPES OF FRACTIONS (1)

There are two different categories of types of fractions:

1. LIKE AND UNLIKE FRACTIONS
2. PROPER , IMPROPER AND MIXED

LIKE FRACTIONS:

When the pair of fraction have same denominator, then they are said to be like fractions.

Ex: 3/4 and 2/4

UNLIKE FRACTIONS:

When the pair of fraction have different denominator, then they are said to be unlike fractions.

Ex: 1/4 and 1/2
  

Concept of Fractions

Fractions simply means the part of a whole.

Thus, whenever there  are various parts of a whole quantity the concept of fraction is used.

For Ex: A piece of a pizza is divided into 8 equal parts, So to denote the value of each piece of pizza fractions are used.

How to Write the Fractions?

Fractions consist of two parts (i) Numerator (ii) Denominator and fractions are mostly in p/q form, where p (upper portion) is Numerator and q (lower portion) is Denominator.
Thus Fraction = Numerator/Denominator.

What does Numerator and Denominator show in a Fraction?

Numerator (upper portion) shows the required parts out of total parts while Denominator shows the total parts.

For Ex: A cake is divided into eight equal pieces. Shyam eats 2 pieces of cake , Ram eats 3 pieces of cake and the remaining pieces are eaten by Mukesh.

Here when we want to know what part of cake is eaten by Shyam , Ram and Mukesh, we use fractions:

Part of cake eaten by Shyam: Parts eaten = 2 ,Total Parts = 8.
So the fraction of cake eaten by Shyam = 2/8 = 1/4.
Thus Shyam ate 1/4th part of cake.

Part of cake eaten by Ram: Parts eaten = 3 ,Total Parts = 8.
So the fraction of cake eaten by Ram = 3/8
Thus Shyam ate 3/8th part of cake.

Part of cake eaten by Mukesh: Remaining parts = (8 - 2 - 3) = 3 parts ,Total Parts = 8.
So the fraction of cake eaten by Mukesh = 3/8

Thus Shyam ate 3/8th part of cake.

Cake divided into 8 equal pieces.

In this figure, Red Region shows part eaten by Shyam.

Green Region shows part eaten by Ram and

Violet Region shows parts eaten by Mukesh.

Perimeter of Rectangle

What is Perimeter?

Perimeter means the total boundary which is covered by the closed shape.

Perimeter can be thus obtained by adding all the sides of the given shape.Thus, According to this,                                         

   Perimeter = sum of various sides.

Formula for finding perimeter of Rectangle:

When for a given shape there are sides of equal length, we can make a formula to find the perimeter.

Thus the formula for perimeter can be obtained as follows:

In a rectangle the pair of the opposite sides are equal.

 Considering one of the side of rectangle as 'L' and other side as 'B'.According to concept of perimeter: 

Perimeter of rectangle should be = L + B + L + B.

 On rearranging the terms            = L + L + B + B

 As both 'L' and 'B' are added twice we can write the above formula as                                                = 2 * ( L + B).

Thus formula for perimeter of Rectangle becomes 2 * (L + B).      

Perimeter of Square

Perimeter means the total boundary which is covered by the close shape.

Perimeter can be thus obtained by adding all the given sides of the shape.

Formula for finding perimeter of Square:
When for a given shape there are sides of equal length, we can make a formula to find the perimeter.

Thus the formula for perimeter and area can be obtained as follows:

In a square all the sides are equal. 

Considering the length of sides to be 'S'.
According to concept of perimeter: 
Perimeter of square should be = S + S + S + S.
                                                 = 4 * S.
Thus formula for perimeter becomes 4 * S.      

CONCEPT OF MULTIPLICATION

MULTIPLICATION simply means addition of the same number with itself for given number of times.For Ex. 5*5 means             Addition of 5 five times i.e. 5+5+5+5+5=25.

• Multiplication is a  technique to know the result where the same numbers are added.

• It is also useful for making addition less time consuming.For Ex. 2+2+2+2+2+2+2+2+6+6+8         

   This can be solved as 2*+8*2+6*2+8*1                                                                             = 16+12+8                                                                                 = 16+20                                               =36 

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