Types of Fractions

The three types of fractions are :

Proper Fraction

Improper Fraction

Mixed Fraction


A fraction can be classified in three ways proper fraction, improper fraction and mixed fraction. 

Let us discuss the three types of fractions with the help of an example.

If Sufi has 3 cookies and she wants to give equal share to Rachel, what share both will get? We divide 3 by 2. It is written as fraction \(\frac{3}{2}\).

Fractions

In the above example of sharing 3 cookies among Sufi  and Rachel the fraction \(\frac{3}{2}\) has 3 as numerator and 2 as denominator. When the numerator is greater than the denominator, the fraction is called the improper fraction. Thus an improper fraction represents a quantity greater than one.

We can represent the share of cookies received by Sufi and Rachel in the following way.

Types of Fractions

We can write this as 1 \(\frac{1}{2}\), which is a combination of a whole number and a fraction.

Divisor, Quotient and Remainder

This is called a mixed fraction. Thus, an improper fraction can be expressed as a mixed fraction, where quotient represents the whole number, remainder becomes the numerator and divisor is the denominator. A fraction, where the numerator is less than the denominator is called the proper fraction for example, \(\frac{2}{3}\), \(\frac{5}{7}\), \(\frac{3}{5}\) are proper fractions. A fraction with numerator 1 is called a unit fraction.


Proper Fraction:

Fractions whose numerators are less than the denominators are called proper fractions. (Numerator < denominator)

For examples:

\(\frac{2}{3}\), \(\frac{3}{4}\), \(\frac{4}{5}\), \(\frac{5}{6}\), \(\frac{6}{7}\), \(\frac{2}{9}\) \(\frac{5}{8}\), \(\frac{2}{5}\), etc are proper fractions.

Types of Fractions

Two parts are shaded in the above diagram. Total number of equal parts is 3. Therefore, the shaded part can be represented as \(\frac{2}{3}\) in fraction. The numerator (top number) is less compared to the denominator (bottom number). This type of fraction is called proper fraction.

Similarly,

Proper Fraction

Three parts are shaded in the above diagram. Total number of equal parts is 4. Therefore, the shaded part can be represented as \(\frac{3}{4}\) in fraction. The numerator (top number) is less compared to the denominator (bottom number). This type of fraction is called proper fraction.

Note: The value of a proper fraction is always less than 1.


Improper Fraction:

Fractions with the numerator either equal to or greater than the denominator are called improper fraction. (Numerator = denominator or, Numerator > denominator)

Fractions like \(\frac{5}{4}\), \(\frac{17}{5}\), \(\frac{5}{2}\) etc. are not proper fractions. These are improper fractions. The fraction \(\frac{7}{7}\) is an improper fraction.

The fractions \(\frac{5}{4}\), \(\frac{3}{2}\), \(\frac{8}{3}\), \(\frac{6}{5}\), \(\frac{10}{3}\), \(\frac{13}{10}\), \(\frac{15}{4}\), \(\frac{9}{9}\), \(\frac{20}{13}\), \(\frac{12}{12}\), \(\frac{13}{11}\), \(\frac{14}{11}\), \(\frac{17}{17}\) are the examples of improper fractions. The top number (numerator) is greater than the bottom number (denominator). Such type of fraction is called improper fraction.

Notes:

(i) Every natural number can be written as a fraction in which 1 is it's denominator. For example, 2 = \(\frac{2}{1}\), 25 = \(\frac{25}{1}\), 53 = \(\frac{53}{1}\), etc. So every natural number is an improper fraction.

(ii) The value of an improper fraction is always equal to or greater than 1.


Mixed Fraction:

A combination of a proper fraction and a whole number is called a mixed fraction.

1\(\frac{1}{3}\), 2\(\frac{1}{3}\), 3\(\frac{2}{5}\), 4\(\frac{2}{5}\), 11\(\frac{1}{10}\), 9\(\frac{13}{15}\) and 12\(\frac{3}{5}\) are examples of mixed fraction.

Two \(\frac{1}{2}\), make a whole.

Mixed Numbers

                   \(\frac{1}{2}\)               \(\frac{1}{2}\)

 \(\frac{1}{2}\) + \(\frac{1}{2}\) = \(\frac{2}{2}\) = 1

What will you get if you add one more \(\frac{1}{2}\) to a whole?

Mixed Fraction

 \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\)

= 1 + \(\frac{2}{2}\)

= 1\(\frac{1}{2}\)

Now, you have three half or you can say that you have a whole and a half or \(\frac{1}{2}\).

Number such as 1\(\frac{1}{2}\) is a mixed number.


In other words:

A fraction which contains of two parts: (i) a natural number and (ii) a proper fraction, is called a mixed fraction, e.g., 3\(\frac{2}{5}\), 7\(\frac{3}{4}\), etc.

In 3\(\frac{2}{5}\), 3 is the natural number part and \(\frac{2}{5}\) is the proper fraction part.

In Fact, 3\(\frac{2}{5}\) means 3 + \(\frac{2}{5}\).


Mixed Number (or Mixed Fraction)

Here, a circle is divided into 4 equal parts. All the 4 parts are shaded.

Thus, the shaded part represents \(\frac{4}{4}\) or a whole or 1,

Mixed Fraction

What do we get if we add a quarter more to \(\frac{4}{4}\)?

We get \(\frac{4}{4}\) + \(\frac{1}{4}\) = \(\frac{4 + 1}{4}\) = \(\frac{5}{4}\)

We also have 1 + \(\frac{1}{4}\) = \(\frac{5}{4}\)

We write, 1 + \(\frac{1}{4}\) as 1\(\frac{1}{4}\)

Thus, \(\frac{5}{4}\) = 1\(\frac{1}{4}\) 


When an improper fraction is written as a combination of a whole number and a proper fraction, it is called a mixed number or mixed fraction.


Thus 2\(\frac{1}{5}\), 6\(\frac{1}{7}\), 4\(\frac{2}{3}\), 2\(\frac{1}{5}\), 2\(\frac{3}{4}\), etc. are mixed numbers.


Note: A mixed number is formed with a whole number and a fraction.


Property 1:

A mixed fraction may always be converted into an improper fraction.

Multiply the natural number by the denominator and add to the numerator. This new numerator over the denominator is the required fraction.

3\(\frac{1}{2}\) = \(\frac{3 × 2 + 1}{2}\) = \(\frac{6 + 1}{2}\) = \(\frac{7}{2}\) .

To know more Click Here.



Property 2:

An important fraction can be always be converted into a mixed fraction.

Divide the numerator by the denominator to get the quotient and remainder. Then the quotient is the natural number part and the remainder over the denominator is the proper fraction part of the required mixed fraction.

Example: \(\frac{43}{6}\) can be converted into a mixed fraction as follows:

     7
6 |43
  - 42
      1

Dividing 43 by 6, we get quotient = 7 and remainder = 1.

Therefore, \(\frac{43}{6}\) = 7 \(\frac{1}{6}\)

To know more Click Here.

Note: Proper fraction is between 0 to 1. Improper fraction is 1 or greater than 1. Mixed fraction is grater than 1.


1. Write \(\frac{37}{4}\) as mixed fraction.

Solution:

Divisor, Quotient & Remainder

So, Quotient = 9, Remainder = 1 and Divisor = 4

Mixed fraction = Quotient \(\frac{Remainder}{Divisor}\)

So, \(\frac{37}{4}\) can be expressed as 9\(\frac{1}{4}\) where 9 is a whole number and \(\frac{1}{4}\) is a proper fraction.


2. Classify the following as proper fractions, improper fractions or unit fractions.

\(\frac{8}{12}\), \(\frac{10}{27}\), \(\frac{17}{12}\), \(\frac{2}{5}\), \(\frac{1}{13}\), \(\frac{5}{12}\), \(\frac{6}{15}\), \(\frac{1}{32}\), \(\frac{31}{12}\), \(\frac{27}{4}\)


Proper Fraction

Classify Fractions

Improper Fraction

Classify Fractions

Unit Fraction

Classify Fractions

Solution:


Proper Fraction

Proper Fractions

Improper Fraction

Improper Fractions

Unit Fraction

Unit Fractions


3. Observe the following sets of fractions:

\(\frac{5}{11}\), \(\frac{3}{7}\), \(\frac{1}{9}\), \(\frac{6}{13}\), \(\frac{11}{15}\)    .... (A)          \(\frac{11}{8}\), \(\frac{7}{5}\), \(\frac{23}{11}\), \(\frac{15}{13}\), \(\frac{19}{14}\)    .... (B)

In what respect, are the two sets different?

In the first set, the numerator of each fraction is less than the denominator.

We call such type of fractions as proper fractions.

In the second set, the numerator of each fraction is either greater than or equal to the denominator. We call such type of fractions as improper fractions.

Types of Fractions


Like Fractions:

Fractions with the same denominator are called like fractions.

For example: \(\frac{1}{9}\), \(\frac{2}{9}\), \(\frac{3}{9}\), \(\frac{5}{9}\) and \(\frac{7}{9}\) are like fractions.


Unlike Fractions:

Fractions with the different denominators are called unlike fractions.

For example: \(\frac{4}{7}\), \(\frac{2}{9}\), \(\frac{5}{11}\), \(\frac{2}{5}\) and \(\frac{3}{4}\) are unlike fractions.


Unit Fractions:

Fractions having 1 as numerator are called unit fractions.

For example, \(\frac{1}{6}\), \(\frac{1}{9}\), \(\frac{1}{12}\), \(\frac{1}{17}\) and \(\frac{1}{25}\) are unit fractions.

You might like these

Fraction






Numbers Page

6th Grade Page

From Types of Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

    May 18, 24 02:59 PM

    Rules for Comparison of Numbers
    Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…

    Read More

  2. Numbers | Notation | Numeration | Numeral | Estimation | Examples

    May 12, 24 06:28 PM

    Numbers are used for calculating and counting. These counting numbers 1, 2, 3, 4, 5, .......... are called natural numbers. In order to describe the number of elements in a collection with no objects

    Read More

  3. Face Value and Place Value|Difference Between Place Value & Face Value

    May 12, 24 06:23 PM

    Face Value and Place Value
    What is the difference between face value and place value of digits? Before we proceed to face value and place value let us recall the expanded form of a number. The face value of a digit is the digit…

    Read More

  4. Patterns in Numbers | Patterns in Maths |Math Patterns|Series Patterns

    May 12, 24 06:09 PM

    Complete the Series Patterns
    We see so many patterns around us in our daily life. We know that a pattern is an arrangement of objects, colors, or numbers placed in a certain order. Some patterns neither grow nor reduce but only r…

    Read More

  5. Worksheet on Bar Graphs | Bar Graphs or Column Graphs | Graphing Bar

    May 12, 24 04:59 PM

    Bar Graph Worksheet
    In math worksheet on bar graphs students can practice the questions on how to make and read bar graphs or column graphs. Test your knowledge by practicing this graphing worksheet where we will

    Read More