TYPES OF FRACTIONS

In this section, you will learn different types of fractions. Within the world of fractions, we do have several types and ways of writing them. Let's discuss these now.

Proper Fraction :

In a proper fraction, the numerator will always be smaller than the denominator. 

Examples : 

2/5,  3/11

Improper Fraction :

In an improper fraction, the numerator will be equal to or larger than the denominator. 

Examples : 

7/5,  3/2, 1/1

Mixed Fraction :

A fraction consisting of a natural number and a proper fraction is called a mixed fractions.

Examples :

2¾, 1⅜, 5½

Like Fractions:

In two or more fractions, the denominators (bottom numbers) are same, they are called as like fractions.

Example : 

3/5 , 6/5, 2/5, 7/5

In the above fractions, all the denominators are same. That is 5.

Unlike Fractions :

In two or more fractions, the denominators (bottom numbers) are different, they are called as unlike fractions.

Example : 

3/5 , 6/7, 2/9, 7/2

In the above fractions, all the denominators are different. They are 5, 7, 9 and 2.

Equivalent Fractions :

Take 1/2 and you can see that the denominator is twice the numerator. So, any fraction where the denominator is twice the numerator is equivalent (the same as) a half. So

are all equivalent fractions that mean 1/2.

When a half is written as 1 over 2 rather than 2 over 4, or 5 over 10, or any other version, it is said to be in its lowest term or simplest form. This is because no number, except 1, will divide into both the top number and the bottom number. So to put a fraction in its lowest form, you divide by any factors common to both the top number and the bottom number.

Equivalent fractions can be found for any fraction by multiplying the top number and the bottom number by the same number. For example, if you have 3/4, then multiplying by 2 gives

or by 3 gives

Multiplying by 10 gives

and all of these fractions are exactly the same as 3/4.

Difference between Proper Fraction and Improper Fraction

The picture shown below clearly illustrates this. 

Mixed Fractions

Mixed fraction is a quantity which is expressed as a whole number and a proper fraction.

Always its value will be greater than or equal to 1. 

The picture given below clearly illustrates this. 

Conversions

1. An improper fraction can be converted into a mixed numeral and vice versa. 

2. A proper fraction can never be converted into a mixed numeral. 

3. When we convert a mixed numeral into a fraction, always, we will get an improper fraction. 

Converting an Improper Fraction to a Mixed Numeral

The picture given below illustrates, how to convert an improper fraction into mixed number. 

Converting a Mixed Numeral to an Improper Fraction

The picture shown below illustrates how to write a mixed number as an improper fraction.

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