# Proper Fractions

## What are Proper Fraction?

A fraction in which numerator is less than denominator is called proper fraction.

We know that fraction is made of two components, numerator and denominator.

The top number of fraction is called numerator.

The bottom number of numerator is called denominator.

In proper fraction, Numerator < Denominator.

When you divide the numerator and denominator, you will find that the value of proper fraction is always less than 1.

Examples of Proper Fraction

In the above image, all the three fractions are examples of proper fraction since their numerator is less than denominator.

### Values of Proper Fraction

As stated earlier, the value of proper fraction is always less than 1.

We can find the value of Proper fraction by dividing numerator with denominator.

Example 01
Find value of fraction 3/5

Solution
The fraction 3/5 is a proper fraction since numerator < denominator.

Dividing numerator and denominator for fraction value.

Hence, the value of fraction 3/5 is 0.6

Example 02
Find the value of fraction 6/8

Solution
The given number is proper fraction since numerator < denominator.

Dividing numerator and denominator

Hence, 0.75 is the value of the fraction.

Conclusion
The value of Proper Fraction is always less than 1

### Proper Fraction – Pictorial Representation

Here we will understand how the proper fractions can be represented in different figure.

Proper fraction can be easily represented in figure using following steps:

(a) Take any figure ( circle or rectangle) for any fraction.

(b) Divide the figure into parts equal to the denominator.

(c) Fill up as many empty parts as numerator value.

Let us understand the process with example.

Example 01
Represent fraction 3/5 in pictorial diagram.

Solution
Note that the fraction 3/5 is a proper fraction.

To represent fraction in the picture, do the following steps.

(a) Take a circle

(b) Divide the circle in parts same as number of denominator.

Denominator = 5

Divide the circle into 5 equal parts

(c) Fill up the part equal to numerator value.

Numerator = 3

So fill up three parts of numerator.

Hence fraction 3/5 is represented above.

It means that out of total 5 parts, 3 parts are filled.

Note
Instead of circle, you could take any other figure. But dividing the figure into equal parts is challenging for any other irregular diagram.

So i will suggest to draw rectangle or circle for your drawing convenience.

Example 02
Represent fraction 3/8 in pictorial diagram

Solution
Fraction 3/8 is a proper fraction.

(a) Take a rectangle.

(b) Divide the rectangle into parts equal to number of denominator.

Denominator value = 8

So divide the rectangle into 8 equal parts.

(c) Fill up the rectangular part equal to numerator value.

Numerator value = 3

Fill up three parts of rectangle

Hence the above image represents the fraction 3/8.

It tells that out of total 8 parts, 3 parts are filled.

In order to add proper fraction we have to make sure that their denominator is same.

So first we have to make denominators equal and then do the addition.

(a) Take LCM of denominators

(b) Multiply fractions to make denominators equal to LCM.

(c) Now simply add the numerator and retain the same denominator.

Let’ see some solved examples of proper fraction addition.

Example 01
Add the fractions; \mathtt{\frac{2}{11} \ +\ \ \frac{5}{6}}

Solution
Both the fraction 2/11 and 5/6 are the like fraction.

(a) Take LCM of the denominators

LCM ( 11, 6 ) = 66

(b) Multiply the fractions to make denominator 66

Fraction 2/11
Multiply numerator and denominator by 6

\mathtt{\Longrightarrow \ \frac{2\times 6}{11\times 6} \ =\ \frac{12}{66}}

Fraction 5/6
Multiply numerator and denominator by 11

\mathtt{\Longrightarrow \ \frac{5\times 11}{6\times 11} \ =\ \frac{55}{66}}

Now both the fractions 12/66 and 55/66 have same denominator.

(c) Add the numerators and keep the denominator as it is.

Hence, 67/66 is the solution.

Example 02
Add the fractions; \mathtt{\frac{4}{9} \ +\ \ \frac{3}{5} \ }

Solution
(a) Take LCM of denominator.
LCM ( 9 , 5) = 45

(b) Multiply the fraction to make denominator 45

Fraction 4/9
Multiply numerator and denominator by 5.

\mathtt{\Longrightarrow \ \frac{4\times 5}{9\times 5} \ =\ \frac{20}{45}}

Fraction 3/5
Multiply numerator and denominator by 9

\mathtt{\Longrightarrow \ \frac{3\times 9}{5\times 9} \ =\ \frac{27}{45}}

Both the fractions 20/45 and 27/45 have same denominator.

(c) Simply add the numerator and retain denominator.

hence, 47/45 is the solution.

## Proper Fractions – Solved Problems

(01) Which of the following fractions are proper fraction

(i) 1/3
(ii) 9/6
(iii) 5/7
(iv) 10/13
(v) 15/7

Solution

(i) 1/3
Is a proper fraction since numerator < denominator.

(ii) 9/6
Not a proper fraction since numerator > denominator

(iii) 5/7
It is a proper fraction.

(iv) 10/13
Not a proper fraction.

(v) 15/7
It is a proper fraction.

(02) Find the value of below proper fractions.

(i) 2/5
(ii) 7/10
(iii) 9/12

Solution

In order to find the value of fraction we have to divide numerator with denominator.

(i) 2 / 5

0.4 is the value of fraction 2/5

(ii) 7/10

Dividing numerator with denominator.

0.7 is the value of fraction 7/10

(iii) 9/12

0.75 is the value of fraction 9/12