# Fractions & Types of Fractions and Applications

Found in topics: Fractions

## Definition and example of fraction

A fraction is a number which represents a part of a whole. Fractions in Maths helps us to measure how many parts are there and the size of each part of an object.
Let’s see how to read fractions with examples.

Example

$\frac{5}{11}$
This is read as five – elevenths.

Example

$\frac{3}{8}$ means 3 parts are taken from equally divided 8 parts of whole.

Note

Fractions are always positive, that means numerator and denominator are positive integers.

Note

The Denominator can never be zero in a fraction.

## Which are 10 types of fractions?

There are many types of fractions but the commonly used ten types of fractions are:

1. Unit fraction
2. Like fractions
3. Unlike fractions
4. Simple fraction
5. Complex fraction
6. Decimal fraction
7. Vulgar fraction
8. Proper fraction
9. Improper fraction
10. Mixed fraction

## 1. Unit fraction

A fraction whose numerator is one and denominator can be any positive integer is called a Unit fraction.

Example

$\frac{1}{4}$, $\frac{1}{7}$, $\frac{1}{61}$ etc.
In $\frac{1}{4}$, the numerator is 1 and denominator 4 which is a positive integer.

## 2. Like fractions

The fractions which have the same denominator are called Like fractions.

Example

$\frac{1}{9}$, $\frac{2}{9}$, $\frac{7}{9}$ etc.
So, the above fractions $\frac{1}{9}$, $\frac{2}{9}$ and $\frac{7}{9}$ have the same denominator i.e. 9, so they are like fractions.

## 3. Unlike fractions

The fractions which have different denominators are called Unlike fractions.

Example

$\frac{7}{9}$, $\frac{1}{4}$, $\frac{6}{11}$, $\frac{5}{8}$ etc.
So, the above fractions $\frac{7}{9}$, $\frac{1}{4}$, $\frac{6}{11}$ and $\frac{5}{8}$ have different denominators i.e. 9, 4, 11 and 8 respectively, so they are Unlike fractions.

## 4. Simple fraction

A fraction whose both terms are integers is called a simple fraction.

Example

$\frac{4}{7}$, $\frac{3}{5}$ etc.

## 5. Complex fraction

A fraction whose one or both terms are fractional numbers is called complex fraction

Example

$\frac{2}{\frac{5}{7}}$, $\frac{7}{\frac{5}{\frac{6}{7}}}$ etc.

## 6. Decimal fraction

Fractions whose denominators are 10, 100, 1000 etc. are decimal fractions.

Example

$\frac{3}{10}$, $\frac{11}{1000}$ etc.

## 7. Vulgar fraction

Fractions whose denominators are not 10, 100, 1000 etc. are called vulgar fractions.

Example

$\frac{1}{5}$, $\frac{7}{15}$ etc.

## 8. Proper fraction

A fraction whose numerator is positive and also less than its denominator is called proper fraction.

Example

$\frac{7}{12}$, $\frac{19}{21}$ etc.

## 9. Improper fraction

A fraction whose numerator is greater than its denominator is called improper fraction.

Example

$\frac{11}{5}$, $\frac{85}{21}$ etc.

## 10. Mixed fraction

A fraction which is expressed as a combination of integer and a proper fraction is called mixed fraction.

Example

$2\frac{3}{5}$ here 2 represents integer part and $\frac{3}{5}$ represents proper fraction.

## What is an equivalent fraction?

The two or more than two fractions are said to be equivalent when multiplying the numerator and denominator by a same non zero positive number results in the original fraction.

Example

Let’s take an example of $\frac{1}{3}$ and $\frac{3}{9}$.
Multiply both numerator and denominator by 1:
$\frac{1}{3}×\frac{1}{1}=\frac{1}{3}$
Multiply both numerator and denominator by 2:
$\frac{1}{3}×\frac{2}{2}=\frac{2}{6}$
Multiply both numerator and denominator by 3:
$\frac{1}{3}×\frac{3}{2}=\frac{3}{9}$
Here $\frac{1}{3}$ becomes equal to $\frac{3}{9}$ when multiplied by 3. Hence, $\frac{1}{3}$ and $\frac{3}{9}$ are equivalent fractions.

## How to show fractions with shaded diagram

Fractions can be shown with shaded area in a diagram also. The numerator in a fraction is shown as shaded area and the denominator is the total number of cut pieces in the diagram.

In general, a fraction can be changed into the shaded diagram with the following method.
Fraction = $\frac{\text{numerator}}{\text{denominator}}$ = $\frac{\text{shaded part}}{\text{total number of parts}}$

Let’s see with examples how to shade the area for fractions.

Examples of fractions represented with shaded diagrams

Example 1. Fraction $\frac{1}{2}$
The fraction $\frac{1}{2}$ can be shown like in the next diagram.
The numerator 1 of fraction $\frac{1}{2}$ is represented by the shaded box. The denominator 2 is the total number of equal boxes to be drawn in the diagram.

So, the above diagram refers the 1 part out of 2 equal parts.

Example 2. Fraction $\frac{1}{3}$
The numerator 1 of fraction $\frac{1}{3}$ is represented by the shaded box. The denominator 3 is the total number of equal boxes to be drawn in the diagram.

So, the above diagram refers the 1 part out of 3 equal parts.

Example 3. Fraction $\frac{2}{4}$
Fractions can also be represented with a circle and dividing it into equal sectors, equal to denominator of the fraction and number of shaded sectors equal to the numerator of the fraction.
So, here, total number of sectors in the circle = 4
and number of shaded sectors in the circle = 2

So, the above diagram refers the 2 part out of 4 equal parts.

Example 4. Fraction $\frac{0}{3}$
Total number of boxes = 3
and number of shaded boxes = 0

So, the above diagram refers the 0 part out of 3 equal parts.

Example 5. Fraction $\frac{3}{3}$
Total number of boxes = 3
and number of shaded boxes = 3

So, the above diagram refers the 3 part out of 3 equal parts.

Example 6. Fraction $\frac{4}{10}$
Total number of boxes = 10
and number of shaded boxes = 4

So, the above diagram refers the 4 part out of 10 equal parts.

## Real life example of fractions

A pizza bought from market and sharing with 8 friends equally is a real life example of fractions. The pizza is going to be divided into eight equal pieces assuming that everyone will share one equal piece.

So, a pizza has been cut into total equal pieces of 8 to divide among 8 friends. We can write the one piece of pizza in fractions as $\frac{1}{8}$, where 1 in the numerator denotes one piece and 8 in the denominator denotes the total number of pieces.

In fractions we can say one friend is sharing $\frac{1}{8}\text{th}$ (read as one eighth) part of pizza. As, everybody share equal piece of pizza, so we can also say everyone has shared $\frac{1}{8}$ fraction of pizza.

What we have learnt about fractions from above is that a fraction has a numerator and a denominator. The denominator keeps the value of the total number of parts and numerator holds the value of a part of the whole object.

Hence, we can write in fractions $\frac{1}{8}$ fraction of a whole pizza is shared to each person.

How the fraction is written, if one person is absent out of 8, eventually any one friend will get an opportunity to have 2 pieces of it. So finally we have 7 friends and 8 cut pieces of pizza.

The friend who will get 2 pieces of pizza, in fractions it can be written as $\frac{2}{8}$ piece of pizza. Again, the denominator has a total number of pieces i.e. 8 and the numerator value is 2.
The remaining 6 friends share 1 piece, so their fraction of pizza shared still remains as $\frac{1}{8}$.

## Solved Examples

### 1) Represent $\frac{2}{7}$ on number line.

To represent $\frac{2}{7}$ on number line, we divide 0 to 1 into 7 equal parts.

### 2) Reduce $\frac{12}{52}$ into the lowest term.

$\frac{12}{52}=\frac{12÷4}{52÷4}=\frac{3}{13}$

Here, HCF of 12 and 52 is 4. So, we divide numerator and denominator by 4.

### 3) What is fraction of 9 hours in a day?

One day has 24 hours. Therefore, we can say that total number of parts are 24 and the value of part of an whole object is 9.

∴ This fraction can be written as:

$\frac{9}{24}=\frac{9÷3}{24÷3}=\frac{3}{8}$

### 4) What is fraction of prime numbers from 1 to 20?

Prime numbers from 1 to 20 are 2, 3, 5, 7, 11, 13, 17 and 19, which are total 8 in numbers.

We can write the fraction of prime numbers from 1 to 20 as:

$\frac{8}{20}=\frac{8÷4}{20÷4}=\frac{2}{5}$

### 5) Convert $5\frac{2}{7}$ into improper fraction.

$5\frac{2}{7}=5+\frac{2}{7}=\frac{7 × 5 + 2}{7}$

$=\frac{35 + 2}{7}=\frac{37}{7}$

### 6) Which fraction is greater $\frac{5}{9}$ or $\frac{4}{5}$ ?

$\frac{5 × 5}{9 × 5}=\frac{25}{45}$

$\frac{4}{5}×\frac{9}{9}=\frac{36}{45}$

$\frac{36}{45}$ is greater than $\frac{25}{45}$

i.e. $\frac{4}{5}\text{>}\frac{5}{9}$

## Worksheet 1

### Fill in the blanks.

#### 10) $\frac{25}{20}$ and $\frac{40}{32}$ are ___________ fractions.

Help box
vulgar
proper
like
1
sevenths
greater
$\frac{3}{10}$
equivalent
$\frac{1}{10}$
6

## Worksheet 2

### Match the following.

a) b) Like pair $\frac{1}{6}$ Unit fractions $\frac{3}{8}$, $\frac{7}{8}$ Proper fractions $\frac{3}{9}$, $\frac{4}{7}$ Mixed fraction $8\frac{1}{2}$ Unlike pairs $\frac{4}{12}$

## Worksheet 3

### Multiple choice questions

#### 1) The correct form of fraction for the statement 5 out of 9 is

a) $\frac{9}{5}$

b) $\frac{5}{9}$

c) 95

d) 59

a) 9

b) 18

c) -18

d) -2

#### 3) $\frac{4}{5}$ and $\frac{6}{5}$ fractions are an example of

a) Like fractions

b) Unlike fractions

c) Mixed fractions

d) Equivalent fractions

#### 4) Solve the fraction $2\frac{4}{3}$

a) $\frac{10}{3}$

b) $\frac{14}{3}$

c) $\frac{11}{3}$

d) $\frac{24}{3}$

#### 5) Which fraction is smaller $\frac{2}{3}$ or $\frac{3}{4}$

a) $\frac{2}{3}$

b) $\frac{3}{4}$

c) Both are equal

d) None of these

#### 6) The lowest term of $\frac{35}{42}$ is

a) $\frac{5}{6}$

b) $\frac{5}{42}$

c) $\frac{35}{21}$

d) $\frac{35}{42}$

#### 7) Choose the correct equivalent fraction

a) $\frac{5}{4}=\frac{4}{5}$

b) $\frac{3}{5}=\frac{2}{3}$

c) $\frac{7}{2}=\frac{2}{5}$

d) $\frac{3}{4}=\frac{15}{20}$

#### 8) Arrange $\frac{5}{7}$, $\frac{3}{8}$, $\frac{7}{2}$, $\frac{3}{4}$ in ascending order.

a) $\frac{3}{8}$, $\frac{5}{7}$, $\frac{3}{4}$, $\frac{7}{2}$

b) $\frac{3}{8}$, $\frac{7}{2}$, $\frac{3}{4}$, $\frac{5}{7}$

c) $\frac{3}{4}$, $\frac{3}{8}$, $\frac{5}{7}$, $\frac{7}{2}$

d) $\frac{5}{7}$, $\frac{7}{2}$, $\frac{3}{8}$, $\frac{3}{4}$

a) 4

b) 3

c) 19

d) 5

#### 10) Choose the correct value of x in $\frac{2}{7}=\frac{x}{63}$

a) 2

b) 7

c) 18

d) 63

Last updated on: 27-07-2024