# Improper Fractions

## What are Improper Fractions?

Fractions in which numerator is greater than denominator are improper fraction.

The fractions is made of two numbers numerator and denominator.

The number in the top is called numerator.

The number in the bottom is called denominator.

In Improper Fraction, Numerator > Denominator.

Examples of Improper fractions.

The above image contain improper fractions.
Note that in all the fractions, the numerator is greater than denominator.

### Values of Improper Fraction

The value of improper fraction is always greater than 1.

The value is calculated by dividing numerator by denominator.

Since in improper fraction, numerator > denominator, we always get value greater than 1 in division.

Example 01
Find the value of fraction 7/5

Solution
7/5 is improper fraction.

Dividing numerator with denominator we get;

Hence, 1.4 is the value of fraction 7/5

Example 02
Find the value of fraction 21/6

Solution
21/6 is an improper fraction since numerator > denominator.

Dividing numerator by denominator we get;

Hence, 3.5 is the value of fraction 21/6.

Conclusion
The value of improper fraction is always greater than 1.

### Improper Fraction – Pictorial Representation

You can easily represent improper fraction in pictorial diagram.

Image representation is very helpful for number understanding. So practicing image representation of improper fraction will help you understand the concepts better.

Follow the below steps for image representation.

(a) Choose any graphical figure ( preferably circle or rectangle)

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

(c) Fill up number of parts equal to numerator value.

Given below are some examples for your understanding.

Example 01
Represent 6/4 in pictorial diagram

Solution
6/4 is a improper fraction since numerator > denominator.

Do the following steps;

(a) Take a circle

(b) Divide the circle into parts equal to denominator value.

Denominator value = 4

Divide the circle into 4 equal parts.

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

Numerator = 6

So we have to fill 6 parts of the circle.

Since, in the above circle we have only 4 parts, we will draw an identical circle besides it.

The above two circles contain total of 8 parts and we have filled 6 parts with colors.

The above figure represents the fraction 6/4.

Note:
Since the value of improper fraction is always greater than 1, we will always need more than one figures to represent the fraction.

Example 02
Represent 7/6 in pictorial diagram

Solution
7/6 is an improper fraction since numerator > denominator.

Follow the below steps for image represntation.

(a) Take a rectangle

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

Denominator value = 6

Divide the rectangle into 6 equal parts.

(c) Fill up number of parts equal to numerator value.

Numerator = 7

We have to fill up 7 parts of rectangle.

Since we have only 6 parts in one rectangle, we will need another identical rectangle for the process.

The above image contains two rectangle with 12 part and we have filled 7 parts of the rectangle.

Hence the image represents the fraction 7/6.

## Solved Questions – Improper Fractions

(01) Check if the below fractions are proper or improper?

(i) 7/10
(ii) 6/5
(iii) 11/7
(iv) 13/15
(v) 1/5

Solution

(i) 7/10
Here Numerator < Denominator.
It is a proper fraction,

(ii) 6/5
Numerator > Denominator.
It is a improper fraction.

(iii) 11/7
Numerator > denominator.
It is improper fraction.

(iv) 13/15
Numerator < Denominator.
It is Proper Fraction.

(v) 1/5
Numerator < Denominator.
It’s a Proper Fraction.

(02) Find the value of below improper fractions.

(i) 6/2
(ii) 5/4
(iii) 7/5
(iv) 12/8
(v) 13/3

Solution

(i) 6/2

Dividing the numerator with denominator.

Hence, 3 is the value of fraction 6/2

(ii) 5/4

Dividing numerator with denominator

Hence, 1.25 is the value of fraction 5/4

(iii) 7/5

Dividing numerator with denominator we get;

Hence, 1.4 is the value of fraction 7/5

(iv) 12/8

Dividing numerator with denominator.

Hence, 1.5 is the value of fraction 12/8

(v) 13/3

4.33 is the value of fraction 13/3