Fractions and it’s Types

You buy a cake for a weekend party. You invite two of your friends to the party. You share two portions of the cake with your friends and you eat half the portion of the remaining cake. Did all of you receive the same portion? How can you express the portion of the cake each one received? This type of expressing a portion of a whole can be done using the concept of fractions.

birthday party
Example scenario of fractions: Weekend party

An equal part of a whole is termed as a fraction. When you divide a whole equally, each part or portion is considered a fraction. Let us consider a cake. When you divide a cake into two equal parts, you get two halves. See the below picture to understand the fractions.

fractions of cake
Understanding fractions

Mathematical Representation of Fractions

A representation of fractions has two parts. The number on top of the line is referred to as the numerator; the number on the bottom of the line is referred to as the denominator. For example, one part out of three is represented as pictured.

fractions representation
Fraction notation with numerator and denominator

A part of cake when we divide a whole cake can be represented as pictured. We can divide and represent any whole object.

Representing fractions by dividing a cake

Activity 1: Can you try yourself!

Write a mathematical representation of fractions for the following. One is done for you.
[Hint: Find out how many parts are colored.]

fractions examples
Activity to understand fractions

Types of Fractions

Considering the numerator and denominator of fractions, we can classify fractions into three types of fractions.

1. Proper fractions
2. Improper fractions
3. Mixed fractions

Proper Fractions

A fraction in which the numerator is smaller than the denominator is referred to as a proper fraction.

proper fractions
Proper fraction where numerator is smaller than the denominator

Improper Fractions

A fraction in which the numerator is greater than the denominator is referred to as an improper fraction.

improper fractions
Improper fraction where numerator is greater than the denominator

Mixed Fractions

A fraction that is a combination of both a natural number and a fraction is referred to as a mixed fraction.

mixed fractions
Mixed fraction with a natural number and a fraction

Activity 2: Can you try yourself!
Classify the following fractions into proper, improper, or mixed fractions.


Activity to classify Proper, Improper and Mixed fractions

Equivalent fractions

Fractions that result in the same value upon simplification are referred to as an equivalent fraction.

equivalent fractions
Understanding equivalent fractions with a pizza

Like and Unlike Fractions

Fractions in which the denominator remains the same and numerator varies are called like fractions. For example, fractions like 3/5, 1/5, 7/5, and 4/5 are like fractions as the denominator remains the same, i.e., 5.

Fractions in which both numerator and denominator vary are called unlike fractions. For example, fractions like ¼, 2/5, 3/7, and 4/9 are unlike fractions as both numerators and denominators vary.

Example: Classify like and unlike fractions from the following.
1/8, 3/5, 7/8, 1/6, 2/7, 3/8, and 4/9

Solution: Identify the same denominators. Here, 8 in the denominator are the same for some fractions. The remaining fractions can be considered as unlike fractions.
Like fractions: 1/8, 7/8, 3/8
Unlike fractions: 3/5, 1/6, 2/7, 4/9

Fractions on Number Line

Fraction is always less than 1 except for mixed fractions. Let us learn to represent fractions on the number line by following the given steps below.

Step 1: Draw a number line with equal intervals and mark whole numbers on it.

number line
Number line with whole numbers

Step 2: Decide the denominator of a fraction which you want to show on a number line. For example, consider the denominator to be 5.

Step 3: Mark as many equal points between the whole numbers that you considered as the denominator. Here, it is 5. Write each numerator as 1, 2, 3, … as shown in the image below.

fractions number line
Marking fractions on a number line

Math Facts about Fractions

  • Any fraction with the denominator as 1 is equal to its numerator. For example, 5/1 is 5.
  • Fractions that have the numerator as 1 are called unit fractions. For example, 1/5, 1/8, 1/9.
  • In ancient times, only unit fractions were considered as fractions. These fractions were used especially when they were to split the sack of grains among themselves.

    Real World Applications of Fractions

    Fractions, just like the name suggests, is a part of something bigger or a collection. They are not whole numbers, rather they have two numbers, the part which is known as numerator and the whole known as denominator. Just like whole numbers, fractions too are very useful in day to day life.
    Here are some of the ways fractions will be useful in our lives, sometimes even without realizing it!

    Let us begin with something that everybody is familiar with, that is, eating out with friends. We all love to go out and eat our favorite food items, but what do we do when it comes to splitting the bill at the end? To divide up the bill equally among all the friends, we need to use fractions.

    Ever tried to bake something?
    If we look closely, the recipe usually says ½ teaspoons of salt, ¾ cups sugar and so on.

    We have different cups and spoons to give us an accurate quantity.

    Everybody loves jewelry, but ever wondered if we can use fractions to know the purity of gold? Let’s break it down! 24 karats is pure gold, 22 carat is 22/24 which equals 91.6% of gold and 18 carat is 18/24 which equals 75% gold and so on.

    And who doesn’t love a cheesy pizza! Everytime you feel one whole pizza is too much, always divide and share. Learn math while enjoying your pizza.

    You have just received your latest exam results, but what about your percentage? We need fractions here as well. For example, if you score 55 out of 80 in a test, then we can find percentage by (55/80)*100 which will give us 68.75%

    These are just a few examples of how we use Fractions in our everyday life. There can be ‘n’ number of instances where we use mathematical concepts such as fractions, decimals, percentages everyday. Not to forget that fractions, decimals, percentages and ratios are all connected. They are just different ways of expressing the same value/concept.

    Know more about other concepts of Number Systems on Decimal Numbers, Fibonacci Numbers, Natural Numbers, Prime Numbers and Unit Conversions

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