A fraction is a way to represent a part of a whole.
The whole can be a single object or a group of objects.
Let us understand this concept better.
A fraction means a part of a group or of a region.
When we look at a fraction, it has two important numbers:
Numerator (Top Number):
Denominator (Bottom Number):
Let us understand fractions with the help of an example:
Ethan is celebrating his birthday at home. His mother has baked a cake for his birthday. When his friends came home, he cut the cake.
His mother wants to distribute the cake equally among all his friends.
There are six people (including Ethan’s mother) at the party.
So, his mother cuts the cake into 6 equal parts.
Fractions of a Cake
Can you tell what fraction of the cake Ethan gets?
Total number of slices of cake = 6
Ethan got (onesixth) part of the cake.
So, Ethan ate one part out of six parts of the cake.
Here 1 is the numerator and 6 is the denominator.
So, fractions on the number line are represented by making equal parts of a whole i.e. 0 to 1, and the number of those equal parts would be the same as the number written in the denominator of the fraction. For example, to represent 1/8 on the number line, we have to divide 0 to 1 into 8 equal parts and mark the first part as 1/8.
Examples:
Let us understand the different types of fractions. There are three types of fractions. They are:
1. Proper fractions
2. Improper fractions
3. Mixed fractions
When you locate proper fractions like 1/6, 2/6, 4/6 on a number line, you'll notice a few things:
Example 1: Give the proper fraction whose denominator is 9 and numerator is 5.
Ans: Given numerator is 5 and denominator is 9
We know that Fraction = Part/ Whole
So, Fraction = 5/9
Hence, required fraction is 5/9
Example 2: Fill in the blank using ‘>’, ‘<’, or ‘=’:
Ans:
is half of 1, so it's less than 1.
1. Conversion of improper fraction into mixed fraction
An improper fraction can be expressed as mixed fraction by dividing the numerator by the denominator of the improper fraction to obtain the quotient and the remainder.
Divide the Numerator by the Denominator:
Form the Mixed Fraction:
The quotient becomes the whole number part of the mixed fraction.
The remainder becomes the new numerator of the fraction, and the denominator remains the same.
The mixed fraction is then written as:
Then the mixed fraction will be.
Example:
Improper fraction to Mixed Fraction 2. Conversion of mixed fraction into improper fraction:
Multiply the Whole Number by the Denominator:
Add the Numerator to the Product:
Form the Improper Fraction:
Let us convert this mixed fraction to an improper fraction using the following steps and the explanation given below.
Mixed Fraction to Improper Fraction
These are fractions that represent the same value or part of a whole, even though they have different numerators and denominators.
Equivalent Fractions
Multiplying Both Numerator and Denominator: To find an equivalent fraction, multiply both the numerator (top number) and the denominator (bottom number) by the same number.
Dividing Both Numerator and Denominator: Alternatively, you can divide both the numerator and the denominator by the same number to find equivalent fractions.
Equivalent fractions represent the same part of a whole because they are different ways of expressing the same proportion. When you multiply or divide the numerator and denominator by the same number, you are essentially scaling the fraction but keeping the same overall value.
Example 1: Find any 3 equivalent fractions of .
Ans:
Example 2: Are 1/3 and 4/7 equivalent?
Ans: No, because they do not represent the same part of a whole.
A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.
This means that the fraction cannot be reduced any further.
Find the Highest Common Factor (HCF):
Divide the Numerator and Denominator by the HCF:
Write the Resulting Fraction:
Example 1: Find the simplest form of the fraction 11/33
Example 2: Convert 350/175 into simplest form
Ans: The HCF of 350 and 175 is 175.
So, Divide both the numerator and the denominator by their 175:
So, the simplest form of 350/175 is $\frac{2}{}\backslash frac\{2\}\{1\}$/1, which is equal to 2.
Like fractions and unlike fractions refer to the relationships between the denominators of two or more fractions.
Like and Unlike Fractions
1. Like Fractions
2. Unlike Fractions
If the fractions have the same denominator (bottom number), you can compare them directly by looking at the numerators (top numbers).
In like fractions, the fraction with the greater numerator is greater.
Comparing Like Fractions
Example 1: Among fractions 5/7 and 3/7, 5/7 is greater than 3/7 as 5 is greater than 3.
Example 2: Compare: 5/12 and 17/12.
Comparing Unlike Fractions
Example: Compare: 1/4 and 2/3.
Step 1: First, observe the denominators of the given fractions, i.e., 1/4 and 2/3. Since the denominators are different make them equal by finding the LCM of 4 and 3. LCM(4,3) = 12.
Step 2: Now, let us convert the given fraction in such a way that they have the same denominators. So, multiply the first fraction with 3/3, i.e., 1/4 × 3/3 = 4/12.
Step 3: Similarly, multiply the second fraction with 4/4, i.e., 2/3 × 4/4 = 8/12. Thus, the first fraction becomes 4/12 and the other becomes 8/12.
Step 4: Compare the obtained new fractions, i.e., 4/12 and 8/12. As the denominators are the same, we will compare the numerators. We can observe that 4 < 8.
Step 5: The fraction that has a large numerator is the larger fraction. So, 8/12 > 4/12. So, 1/4 > 2/3.
Addition and subtraction of fractions involve combining or taking away portions of quantities represented by the fractions. Here's a brief overview:
When we add or subtract like fractions, we add or subtract their numerators and the denominator remains the same.
1) +
The two fractions are like fractions, so we add their numerators and keep the denominator the same.
+ = =
2) −
Here, the given fractions are like fractions. So, we subtract their numerators and keep the denominator the same.
− = =
When we add or subtract unlike fractions we follow the following steps:
1) +
The given fractions are unlike fractions, so we first find LCM of their denominators.
LCM of 8 and 24 = 2 × 2 × 2 × 3 = 24
Now, we convert the fractions into like fractions.
(Changing the denominator of fractions to 24)
= and
+ = =
2) −
As the given fractions are unlike fractions, we find the LCM of their denominator.
LCM of 15 and 27 = 3 × 3 × 3 × 5 = 135
Next, we convert the fractions into like fractions
(Fractions with the same denominator)
= and =
 = =
Before applying any operations such as addition, subtraction, multiplication, etc., change the given mixed fractions to improper fractions.
After converting the mixed fractions to improper fractions, one can proceed with the calculations, which are as follows:
Add/Subtract Whole Numbers: Perform the addition or subtraction with the whole numbers separately.
Add/Subtract Fractions: Make sure the fractions have a common denominator before adding or subtracting.
Combine the Results: Add or subtract the results of the whole numbers and fractions to get the final answer.
Example 1:
Ans:
Example 2:
Ans:
Convert Mixed Fractions to Improper Fractions: Multiply the whole number by the denominator of the fraction and add the numerator.
Perform Addition/Subtraction: Use the common denominator to add or subtract the improper fractions.
Convert Back to Mixed Fraction: If needed, convert the resulting improper fraction back to a mixed fraction.
Example 1:
Ans: Convert to Improper Fractions:
Find a Common Denominator:
Example 2:
Ans:
Q1: A rectangular sheet of paper 12 is cm long and 9 cm wide. Find its perimeter.
Length of the rectangular sheet = 12 cm. 12 = = = Breadth of the rectangular sheet = 9 cmPerimeter of a rectangle = 2(l + b)
Perimeter of rectangular sheet of paper
= 2 (+) = 2() = 2 ()
= 44 cm
Q2: Michael finished coloring a picture in hour. Vaibhav finished colouring the same picture in hour. Who worked longer? By what fraction was it longer?
Time taken by Michael to colour the picture = hour
Time taken by Vaibhav to colour the same picture = hour
The two fractions are unlike, so we first convert them to like fractions (fractions having the same denominator). ' LCM of 12 and 4 = 2 × 2 × 3 = 12 and =
On comparing the two fractions we get, >
Therefore, Vaibhav worked longer by  = = = hour.
Q3: Compare the fractions 4/25 and 33/100.
To compare the given fractions, find their decimal values. So, divide 4 by 25 and 33 by 100.
4/25 = 0.16
33/100 = 0.33
From the decimal values, we can conclude that 0.33 > 0.16. So, 33/100 is greater than 4/25.
Therefore, 33/100 is greater than 4/25.
Q4: Mrunal was asked to prove that the given fractions are equal: 30/90 and 25/75. Can you prove the given statement using the LCM method?
Given fractions: 30/90 and 25/75.
The denominators of the given fractions are different. So, find out the LCM of the denominators, i.e., LCM(90, 75) = 450.
Now, multiply 30/90 with 5/5 and 25/75 with 6/6.
30/90 × 5/5 = 150/450
25/75 × 6/6 = 150/450
Compare the numerators now, as the denominators are the same.
So, 150 = 150, i.e., 150/450 = 150/450.
Thus, 30/90 = 25/75, i.e., both the given fractions are equal.
Hence, proved.
Q5: Which of the following fractions is larger: 27/41 or 27/67?
Given fractions: 27/41 and 27/67.
Here, the numerators of both fractions are the same but the denominators are different.
We know that the fraction that has a smaller denominator has a greater value, while the fraction that has a larger denominator has a smaller value.
Here, 41 < 67.
So, 27/41 > 27/67
Therefore, 27/41 is the larger fraction.
94 videos347 docs54 tests

1. What is a proper fraction? 
2. How do you compare fractions with different denominators? 
3. What is the simplest form of a fraction? 
4. How do you add and subtract fractions? 
5. What are equivalent fractions? 

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