Proper fraction

Proper fraction:-

Today in this article i will discuss on the topic proper fraction for school going children.To start my discuss, I will first explain you 

     

**what is fraction?

Answer:- In arithmetic, fraction means the part or parts of a whole body or an object if we equally divide it. 
    

e.g If an whole apple is divided equally one time then we find its two equal parts,each part of of the whole apple is ½  this can be illustrated as follows:
   Number of whole apple = 1
   Number of total equal parts  of the apple=2
  So, 1st part will be = 1÷2 [∵ whole apple is divided in two equal parts]
 Similarly,
2nd part will  also be = ½ 
Now,
        ½ + ½  =2/2 =1 means whole apple
This ½ is called fraction. some examples of fraction are ⅔ ,⅘  6/7, 5/4 ….etc
A fraction has two parts:-
(i) Its lower part is called denominator.
(ii)Its upper part is called numerator.

Let, us take a fraction = ⅘

So,
  It's denominator = 5
and it's numerator = 4

***Types of fractions:-

Fractions are three types:-

(i) Improper fraction

(ii) Mixed fraction

(iii) Proper fraction

*** What is an Improper fraction?Give examples.

Answer:- A fraction whose numerator is greater than denominator is called improper fraction.e.g ; 4/3, 6/5, 8/7…..etc.

Problems on improper fraction:-

(i) write an improper fraction, whose numerator is 5 and denominator 3

Answer:-

Here,
numerator is = 5
and , denominator =3
∴ The improper fraction will be = 5/3 

(ii) Write an improper fraction, whose denominator is 2 and numerator is 3 more than denominator.

Answer:-

   Here, denominator is = 2
∵ numerator is 3 more than denominator
So,
     numerator will be = 2+3 =5
∴ Improper fraction will be = 5/2 

**What is a mixed fraction?Give examples.

Answer:-

A fraction which is consists of a whole number and a proper fraction is termed as a mixed fraction.e.g; 2¹/₂ 3 ⁵/₆…etc
Actually,
 mixed fractions are nothing but another form of improper fractions as mixed fractions can be converted into improper fractions.

**Problems on mixed fraction:-

*Convert the following mixed fractions into improper fractions.

(i) 2¹/₂   (ii) 5¹/₃

Answer:- (i) 2¹/₂
               = 2×2+1/ 2
               =5/2

Rule:-

Whole number(here 2) will be multiplied by denominator(here 2) + numerator will be divided by denominator(here 2)
 

So,ultimate result will be,
      2×2 =4
Now, numerator will be =2×2+1 = 5 which will be divided by denominator 2 
So,fraction will be =5/2, which is an improper fraction.
    

(ii) 5¹/₃

= (5×3+1) /3
     =  15+1/ 3
     = 16/3

*** What is a proper fraction?Give examples

Answet:- The fractions whose denominator is greater than numerator are called proper fractions.
e.g; ⅔ ,8/9, ⅚ ……etc.

**Problems on proper fraction:-

(i) Write the proper fraction,whose denominator is 5 and numerator is 3

Answer:- Here, denominator = 5
                      numerator = 3
    ∴ Proper fraction is = ⅗ 

**Find proper, Improper or mixed fractions from the given following fractions:-

1/3, 5/4, 4¹/₃

Now,let us do some simplify:-

     Simplify:-

     (i)

In the above sum,
the denominators are 3,6 and 3
so,1st we will make these three denominator into a single denominator which will be divisible bt 3,6 and 3; To get this perticular denominator we will find the L.C.M of 3,6 and 3
∴ 3 =  1×3
   6 =  2×3
   3 =  1×3
 ∴ L.C.M = 1×3 ×2 =6 [∵ we know that after finding factors by prime factorisation method, the product of common and uncommon factors become L.C.M of numbers. 
Now
⅔ +⅚ - ⅓ 
=[(6÷3)×2 +(6÷6)×5 -(6÷3)×1]/6 [Rule:-L.C.M will be divided by each individual denominator and result will be multiplied by each individual numerator]
= (2×2 + 1×5 + 2×1)/6
= (4+5+2)/6
  = 11/6
(ii) 3¼  - ⅜  + ½ 
= (3×4+1)/4 - ⅜ +½ 
= 13/4 - ⅜  +½ 
= [(8÷4×13)-(8÷8×3)+(8÷2)×1]/8 [∵ L.C.M of 4,8 and 8 is 8,so denominator will be 8]

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FREQUENTLY ASKED QUESTIONS:-

Give three examples of proper fractions.

Answer:- Three examples of proper fraction are :- 2/3,4/5,7/9......The fractions whose denominator is greater than numerator are called proper fractions.

Give three examples of improper fractions.

Answer:- Three examples of improper fractions are:- 4/3,5/3,7/6 ......,The fractions whose denominator is less than numerator are termed as improper fractions.

What are the differences between proper and improper fractions?

Answer:- The differences between proper and improper fractions are:-(i)In proper fractions,denominator is greater than numerator.e.g;5/6,8/9...where as in improper fractions denominator is less than numerator.e.g; 3/2,5/4,....(ii)In proper fractions the numerator is less than denominator.e.g;8/9,4/7...on the other hand in improper fractions numerator is greater than denominator.e.g; 8/7,6/5...

Give five examples of mixed fractions.

Answer:- The five examples of mixed fractions are :- 2²/₃,5¹/₄,1²/₅,3³/₇,4⁴/₇...The fractions which are made of a whole number and a proper fraction are called mixed fractions.

What will be the sum of a fraction and its conjugate ?

Answer:- The sum of a fraction and its cogugate is always zero.e.g;2/3+(2/3)= 2/3-2/3 =o

What are the six types of fractions?

Answer:- The six different types of fractions are:- (i) Proper fraction:- examples :- ¾,⅚,⅞…… (ii) Improper fractions:- examples:-7/6,9/8,4/3….. (iii) Mixed fractions:- examples:-3³/₄ , 4²/₃ ,1⁵/₆….. (iv) Similar fractions:- examples:- 5/7,4/7,3/7.. (v) Dissimilar fractions:- examples :- ¾, ⅘, 5/7… (vi) Equivalent fractions:- examples:- ½, 2/4, 3/6….

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