# 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:-

### 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]

## 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….

## 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….