Fractions

Fraction is defined as dividing anything into an equal or non-equal part or parts and every part is known as the fraction which is represented as a form of the number. Fractions are represented with a denominator and a numerator and are always rational numbers. Fractions can be written in both ways by giving slash between the two numbers or by writing one on top and separating the other below by a line such as ½, which is a fraction that can be written by both the ways 1/2 or 12. Here, the denominator is the number that is below or after the slash that is 2 and the numerator that is above or before the slash is 1. And the fraction 1/2 or 12 is read as ‘one by two’.

Types of fractions

There are seven different types of fractions-

• Proper Fractions – 

A fraction is known as a proper fraction when the fraction has a numerator less than the denominator. This is always applicable for recognizing proper fractions. For example, 5/8, 11/23, 9/18, etc. 

• Improper Fractions –

 A fraction is known as an improper fraction when the fraction has a numerator greater than the denominator. Thus is always applicable for recognizing improper fractions.  As in the case of the improper fraction, the denominator can be 1 so a natural number is also an improper fraction. For example, 5/4, 8/2, 11/7, 6/1, etc. An improper fraction is every time greater than 1.

• Mixed Fractions – 

A fraction is known as a mixed fraction or a mixed number when the fraction has a whole number or the natural number followed by a proper fraction. The fraction can be converted into the improper fraction and they are every time greater than 1. For example; {4 x (3/5)}, {8 x (6/8)} etc.

• Like Fractions –

Fractions are called like fractions when the fractions have a similar or equal denominator. It is easy to simplify like fractions, this is because when the denominators are the same addition or subtraction becomes easier as doing L.C.M is not required while calculating. For example, the like fractions are 2/8, 5/8, 3/8, 4/8, 7/8, etc.

While adding these fractions we get a common L.C.M. i.e. 8. So this can be calculated as (2+8+3+4+7)/ 8

= 24/8 = 3

• Unlike Fractions –

 Fractions are called unlike fractions when the fractions have a different or dissimilar denominator. It is not so easy to simplify as compared to like fractions. Here for subtracting or adding the unlike fractions, one is required to calculate the L.C.M of the denominator and simplify accordingly. For example, the, unlike fractions, are 2/4, 6/8, 9/2, etc.

Now, while adding these fractions we need to find the L.C.M.

2/4 + 6/8 + 9/2

Firstly, the L.C.M of 4, 8 and 2 should be calculated

L.C.M = 8

Therefore, by calculating

 (4+ 6+ 36)/8

= 46/8

= 23/4

• Unit fractions –

 A fraction is known as a unit fraction when fraction 1 is the numerator. This is always applicable for recognizing unit fractions. For example; 1/5, 1/9, 1/87, 1/10, etc.

• Equivalent Fractions – 

A pair of fractions is called an equivalent fraction when after simplification the fraction has a similar value. For example; in the case of 11/22 and 1/2, after simplifying these two fractions separately the answer one gets is 0.5 in both cases.

Some problems on fraction 

Problem 1

Simplify –

1. i) 2/3 + 5/3 + 6/3+7/3

1. 10/3
2. 19/3
3. 12/3
4. 20/3
5. 6/3

Solution: (2+5+6+7)/3

= 20/3

1. ii) 4/5 + 5/10 + 6/15

1. 5/3
2. 52/32
3. 7/30
4. 9/11
5. 51/30

Solution: (24 + 15+ 12)/30

=51/30

Problem 2

Shyam learned seven-tenth of the 100 pages of a chapter. There are how many pages to learn for completing the chapter?

1. 20 pages
2. 30 pages
3. 70 pages
4. 100 pages
5. 80 pages

Solution:No. of pages read by Shyam

= 7/10 of 100

= (7/10) X 100

= 70 pages

No. of pages left for learning are

(100-70) pages

= 30 pages

Answer: 30 pages to learn by Shyam for completing the chapter.

Conclusion

It is to conclude that fractions are represented with a denominator and a numerator and are always rational numbers. Fractions can be written in both ways by giving slash between the two numbers or by writing one on top and separating the other below by a line such as ½, which is a fraction that can be written by both the ways 1/2 or 12. There are seven types of fractions; these are proper fractions, improper fractions, mixed fractions, like and like fractions, unit fractions, and equivalent fractions.