Class 5 Exam  >  Class 5 Notes  >  Mathematics for Class 5  >  Chapter Notes: Fractions

Fractions Class 5 Notes Maths

What is a Fraction?

A fraction is a part of a whole. If a whole is divided into equal parts, each part is called a fraction. It is made up of two parts.
Fractions Class 5 Notes Maths

Fractions can be used to

  • name a part of a single thing.
    Fractions Class 5 Notes MathsHere, 1 part out of 4 equal parts is red, we write it as 1 / 4.Fractions Class 5 Notes Maths1 / 4 of the cake has been taken by Neha.
  • name a part of a group of things.
    Fractions Class 5 Notes MathsIn this aquarium, you have 7 fish, out of which 2 are starfish. So, we write 2 / 7 are starfish.

Representation of a Fraction on a Number Line

The fraction 3 / 8 is shown on the number line as:
Fractions Class 5 Notes Maths3 / 8 < 1, so we draw the number line from 0 to 1 and divide it into 8 equal parts. (∵  denominator = 8). The arrow shows the fraction 3 / 8.


Types of Fractions

  1. Proper Fractions
    The fractions in which the numerator is less than the denominator are called proper fractions.
    For example, 0 / 2, 1 / 4, 2 / 5, 3 / 7, 81 / 100, etc., are all proper fractions. All proper fractions are less than 1.
  2. Improper Fractions
    The fractions in which the numerator is greater than or equal to the denominator are called improper fractions.
    For example, 6 / 6, 7 / 4, 21 / 20, 121 / 100, etc., are all improper fractions.
    All improper fractions are greater than or equal to 1.
    Fractions Class 5 Notes Maths(i) Mixed Numbers
    A mixed number has two parts, a whole number part (except 0) and a part with a fraction.
    For example,Fractions Class 5 Notes Mathsare all mixed numbers.Fractions Class 5 Notes Maths
  3. Unit Fractions
    A fraction whose numerator is 1 and the denominator is greater than 1 is called a unit fraction, 
    For example, 1 / 8, 1 / 3, 1 / 5, etc.
  4. Like Fractions
    Fractions that have the same denominator are called like fractions.
    For example, 8 / 12, 7 / 12, 17 / 12, 23 / 12 are all like fractions.
  5. Unlike Fractions
    Fractions whose denominators are different are called unlike fractions.
    For example, 4 / 6, 3 / 8, 12 / 15, 23 / 35 are all unlike fractions.

Edurev Tips: We can write a mixed number as an improper fraction and an improper fraction as a mixed number.


Example 1: Write 7 / 5 as a mixed number.

Method 1: Pictorially, it can be shown as:
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
It can also be represented on the number line as:
Fractions Class 5 Notes MathsJump five-fifths to land on 1. Jump 2 more fifths to land on 7 / 5.
This is same as jumping to 1 and then to another 2 / 5.
∴ 7 / 5 as a mixed number is Fractions Class 5 Notes Maths
Method 2: By Division Method,
Fractions Class 5 Notes MathsFractions Class 5 Notes Maths


Edurev Tips: 

Fractions Class 5 Notes Maths


Example 2: Write Fractions Class 5 Notes Mathsas an improper fraction.

Pictorially, it can be shown as:
Fractions Class 5 Notes MathsFractions Class 5 Notes Maths
Multiply the whole number part by the denominator and add numerator to the product.
Alternatively,
Fractions Class 5 Notes Maths


Equivalent Fractions

Consider the following fraction bars.
Fractions that name the same part of the whole are called equivalent fractions.
Fractions Class 5 Notes Maths
Therefore, 1 / 4, 2 / 8 and 3 / 12 are equivalent fractions and we write 1 / 4 = 2 / 8 = 3 / 12.


Edurev Tips:
Fractions Class 5 Notes Maths

Thus, to find equivalent fractions, we either multiply or divide the numerator and denominator by the same number.


Example 3: Fill in the missing numbers.
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths

Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths


Writing a Fraction in its Simplest Form

A fraction is in its simplest form when its numerator and denominator have no common factors other than 1.

Fractions such as 1 / 2, 3 / 5, 5 / 8 are all fractions in their simplest form. In 1 / 2, there is no common factor of 1 and 2 except 1. Likewise, the only common factor of 3 and 5 in 3 / 5 is 1 and of 5 and 8 in 5 / 8 is 1.
The fraction 10 / 15 is not in its simplest form because 5 is a common factor of 10 and 15.
Similarly, 3 / 21 is not in its simplest form because 3 is a common factor of both 3 and 21.


Example 4: Express the following fractions in their simplest form.
(a) 6 / 8
(b) 15 / 30
(c) 210 / 330

(a) Divide both numerator and denominator by a common factor.
Fractions Class 5 Notes Maths
Dividing 6 and 8 by 2, we have,
Fractions Class 5 Notes Maths
(b) 
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Hence, 15 / 30 in its simplest form = 1 / 2, because 1 and 2 have no common factor except 1.
Alternative Method:
Fractions Class 5 Notes Maths
Method: To reduce a fraction to its simplest form, keep dividing by common factors until the only common factor is 1.
(c)
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths


Comparing Fractions

1. Comparing Fractions with Like Denominators

Example 5: For a singing competition, 6 / 15 of the children are girls and 9 / 15 are boys. Whose number is greater in the competition, of boys or of girls?

To answer this question we have to compare 6 / 15 and 9 / 15. We can use two ways for comparing them and then state a general rule.
Method 1: Comparing Pictorially
Fractions Class 5 Notes MathsOn comparing the shaded parts, you can see that 9 / 15 > 6 / 15.
∴ The number of boys is more.
Method 2: Comparing on Number Line
Fractions Class 5 Notes Maths9 / 15 is to the right of 6 / 15, therefore,  9 / 15 > 6 / 15.


Rule: If two or more fractions have the same denominator, the fraction with the greater numerator is the greater number, e.g., 6 / 7 > 5 / 7 or 5 / 7 < 6 / 7.


2. Comparing Fractions with Unlike Denominators
Example 6: Which is greater: 1 / 3 or 2 / 5?

Pictorially, 1 / 3 and 2 / 5 can be compared as:
Method 1
Fractions Class 5 Notes MathsOn comparing the shaded parts, you can see that 2 / 5 > 1 / 3.
Method 2
Fractions Class 5 Notes MathsComparing fractions on number line, you can see that 2 / 5 is on the right of 1 / 3.
Fractions Class 5 Notes Maths


3. By Finding Equivalent Fractions Using LCM
To compare 1 / 3 and 2 / 5, we convert them into equivalent fractions both having the same denominator.
The common denominator in this case will be taken as the LCM of 3 and 5.
LCM of 3 and 5 = 3 × 5 = 15.
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths


Edurev Tips: This is the most commonly used method for comparing and ordering unlike fractions.


Ordering Fractions

Now that you know how to compare fractions, you can order them in any order— increasing or decreasing.


Example 7: Arrange the fractions 7 / 8, 5 / 12, 15 / 16 in increasing order.

Step 1: Find the LCM of the denominators 8, 12 and 16.
LCM of 8, 12 and 16 = 2 × 2 × 2 × 3 × 2 = 48
Fractions Class 5 Notes Maths
Step 2: Find the equivalent fractions with denominator 48.
Fractions Class 5 Notes Maths
Step 3: Compare the equivalent fractions:
Fractions Class 5 Notes Maths
Arranging the fractions in increasing order,
Fractions Class 5 Notes Maths
You can write the same fractions in decreasing order as
Fractions Class 5 Notes Maths


Ordering Unit Fractions

A unit fraction has 1 as its numerator, but the denominator can vary.
For example, 1 / 2, 1 / 3, 1 / 4, 1 / 5 are unit fractions. What conclusion do you draw from the following diagrams?
Fractions Class 5 Notes MathsIt can be clearly seen that
Fractions Class 5 Notes Maths
Thus, if the numerator is the same, the fraction with the least denominator is the greatest.


Addition and Subtraction of Fractions

1. To Add or Subtract Like Fractions (Fractions with the Same Denominator)

When we add or subtract fractions with the same denominator, we just add or subtract the numerators and keep the denominator same.

Fractions Class 5 Notes Maths

2. To Add or Subtract Unlike Fractions
Example 8: Ravi and Nisha are painting a wall. Ravi painted 1 / 2 of the wall and Nisha painted 1 / 4 of the wall. What part of the wall did they paint altogether?

Wall painted by Ravi = 1 / 2
Wall painted by Nisha = 1 / 4
Total part of the wall painted = 1 / 4 + 1 / 2
To be able to add these, first change one or both of the fractions to fractions having common denominator.
Fractions Class 5 Notes Maths
Therefore, 3 / 4 part of the wall was painted by Ravi and Nisha.


Rule: When we add fractions with different denominators, we change the fractions to fractions having the same denominator. This common denominator is the least common denominator of the given fractions.

What is meant by least common denominator?
Study the two rows of fractions given below:
Fractions Class 5 Notes MathsThe numbers 12, 24 and 36 are some of the common denominators of 1 6 and 34. Of these, 12 is the least common denominator. Also, we can see that 12 is the LCM of 6 and 4. Thus, the least common denominator of two fractions is the same as the least common multiple of their denominators.
To add or subtract unlike fractions, write the given fractions as equivalent fractions with the least common denominator (LCM of the denominators) and then add or subtract like fractions.


Example 9: Add:
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths

Fractions Class 5 Notes Maths
Method 1: LCM of 4 and 5 = 4 × 5 = 20
Fractions Class 5 Notes MathsMethod 2: You may also set your work as under:
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Step 1: LCM of 4 and 5 = 20
Step 2: Divide 20 by the denominator of the first fraction. 20 ÷ 4 = 5
Multiply quotient 5 by numerator 3 and write 3 × 5.
Divide 20 by the denominator of the second fraction. 20 ÷ 5 = 4
Multiply quotient 4 by numerator 2 and write 2 × 4.
Now, complete as shown.
Fractions Class 5 Notes Maths
LCM of 6 and 10 = 30.
Changing 5 / 6 and 1 / 10 to equivalent fractions having the same denominator 30.
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths


Example 10: Subtract:
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths

Fractions Class 5 Notes Maths
Method 1
LCM of 8 and 4 = 8.
Fractions Class 5 Notes Maths
Method 2
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
LCM of 7 and 11 is 7 × 11 = 77.
Fractions Class 5 Notes Maths


Addition of Mixed Fractions

Type I: With Same Denominators

Example 11: When released, a gas balloon first rose by Fractions Class 5 Notes Mathsand then again by

Fractions Class 5 Notes MathsWhat is the total height to which the gas balloon rose?

Pictorially, the problem can be represented as:
Fractions Class 5 Notes MathsThus, we can add mixed numbers by first adding whole numbers and then proper fractions. Therefore, the above work can be set as:
Fractions Class 5 Notes Maths


Example 12: A cow gave Fractions Class 5 Notes Mathslitres of milk in the morning and Fractions Class 5 Notes Maths litres in the evening. Find the total quantity of the milk given by the cow.

Method 1
Fractions Class 5 Notes Maths
Method 2
Total quantity of milk given by the cow
Fractions Class 5 Notes Maths
Convert each mixed number to improper fraction.
Fractions Class 5 Notes Maths
∴ So, the cow gaveFractions Class 5 Notes Mathslitres of milk in all.


Type II: With Different Denominators

Example 13: Add:
Fractions Class 5 Notes Maths

Method 1
Fractions Class 5 Notes Maths
LCM of 2 and 4 = 4.
Fractions Class 5 Notes Maths
Method 2
Fractions Class 5 Notes Maths
By changing into improper fractions
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths


Example 14: Add:
Fractions Class 5 Notes Maths

Method 1
Fractions Class 5 Notes Maths
LCM of 4, 6, 12 = 2 × 2 × 3 = 12.
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Method 2
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths


Edurev Tips: Method 1 is particularly useful when the whole number parts of given fraction are large numbers such as in
Fractions Class 5 Notes Maths


Subtraction of Mixed Fractions

Example 15: Subtract:
Fractions Class 5 Notes Maths

Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths


Example 16: Subtract
Fractions Class 5 Notes Maths

Method 1
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Step 1: Subtract the whole numbers.
Step 2: Change fractions to equivalent fractions, 1 / 4 = 3 / 12.
Step 3: Subtract the fractions.
Method 2
Convert mixed fractions into improper fractions.
Fractions Class 5 Notes Maths


Subtracting from Whole Numbers

Subtracting from 1

Example 17: Mira is preparing a sweet dish. She used 5 / 8 litre of milk from a jug containing 1 litre milk. How much milk is left in the jug?

Quantity of milk remaining in jug
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Or
Fractions Class 5 Notes Maths
Mira still has 3 / 8 litre of milk left in the jug.


Example 18: David lives 3 kilometres away from a town. Paul lives 56 of a kilometre away from the town. How much closer does Paul live to the town than David?

Method 1
Paul lives
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Thus, Paul livesFractions Class 5 Notes Mathskm closer to the town as compared to David.
Method 2
Paul lives
Fractions Class 5 Notes Mathskm closer.
Fractions Class 5 Notes Maths
Thus, Paul livesFractions Class 5 Notes Maths km closer to the town as compared to David.


Edurev Tips: In subtraction sums like Fractions Class 5 Notes Maths where whole number parts are large numbers, it may be easier and more convenient to apply method 1.
Thus,
Fractions Class 5 Notes Maths


Example 19: Subtract:
Fractions Class 5 Notes Maths

Method 1
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Method 2
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
Method 2 is generally preferred.


Properties of Addition of Fractions

  1. Changing the order of two addends does not change the sum.
    Fractions Class 5 Notes Maths
    Pictorially, it can be shown as:Fractions Class 5 Notes MathsFractions Class 5 Notes MathsSimilarly, by actual addition, you can verify that;
    Fractions Class 5 Notes Maths
    Fractions Class 5 Notes Maths
  2. Changing the way in which we group the addends does not change the sum.
    Fractions Class 5 Notes Maths
    Fractions Class 5 Notes Maths
    Fractions Class 5 Notes Maths
    Thus,
    Fractions Class 5 Notes Maths
    Or
    Fractions Class 5 Notes Maths
    Fractions Class 5 Notes Maths
    Fractions Class 5 Notes Maths
    This is called the grouping property of addition of fractions.
  3. Additive property of 0.
    Fractions Class 5 Notes Maths
    Thus, the sum of a fraction and 0 is the fraction itself.

Problems Based on Real Life Situations

Example 20: Deepa used 5 / 9 L of milk to prepare kheer. She added 1 / 2 L more milk to the kheer. How many litres of milk did she use to make the kheer?

Milk used by Deepa = 5 / 9 L
Milk added by her = 1 / 2 L
Total quantity of milk used (in litres)= (5 / 9 + 1 / 2)
Fractions Class 5 Notes Maths
LCM of 9 and 2 is 18.
Fractions Class 5 Notes Maths
∴ Deepa used Fractions Class 5 Notes Maths of milk for the kheer.


Example 21: Pinki had Fractions Class 5 Notes Maths of a ribbon. She used Fractions Class 5 Notes Maths of the ribbon to wrap some gifts. How much ribbon is left with her?

Ribbon with Pinki
Fractions Class 5 Notes Maths
Ribbon used
Fractions Class 5 Notes Maths
Ribbon left (in metres)
Fractions Class 5 Notes Maths
Fractions Class 5 Notes Maths
LCM of 2 and 3 is 6.
Thus, Pinki had Fractions Class 5 Notes Maths of ribbon left with her.

The document Fractions Class 5 Notes Maths is a part of the Class 5 Course Mathematics for Class 5.
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FAQs on Fractions Class 5 Notes Maths

1. What is a fraction?
Ans. A fraction is a mathematical expression that represents a part of a whole or a ratio between two numbers. It consists of a numerator and a denominator, separated by a horizontal line. The numerator represents the number of parts we have, while the denominator represents the total number of equal parts the whole is divided into.
2. How do you find equivalent fractions?
Ans. To find equivalent fractions, you need to multiply or divide both the numerator and the denominator by the same nonzero number. By doing this, you change the representation of the fraction, but its value remains the same. For example, to find equivalent fractions for 2/3, you can multiply both the numerator and the denominator by 2 to get 4/6 or divide them by 3 to get 2/9.
3. How do you write a fraction in its simplest form?
Ans. To write a fraction in its simplest form, you need to find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by that value. The simplest form of a fraction has no common factors other than 1. For example, if the fraction is 8/12, the GCD of 8 and 12 is 4. Dividing both by 4 gives us the simplest form, which is 2/3.
4. How do you compare fractions?
Ans. To compare fractions, you can either find a common denominator and compare the numerators, or you can convert them into decimals and compare the values. If the fractions have the same denominator, you can simply compare the numerators. If the denominators are different, you need to find a common denominator by finding the least common multiple (LCM) of the denominators. Then, convert both fractions to equivalent fractions with the same denominator and compare the numerators.
5. How do you order fractions?
Ans. To order fractions from least to greatest or greatest to least, you can either find a common denominator and compare the numerators, or you can convert them into decimals and compare the values. If the fractions have the same denominator, you can simply compare the numerators. If the denominators are different, you need to find a common denominator by finding the least common multiple (LCM) of the denominators. Then, convert all fractions to equivalent fractions with the same denominator and compare the numerators.
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