Table of contents  
What are Fractions?  
Types of Fractions  
Multiplication of Fractions  
Division of Fractions  
Some Solved Questions 
The term fraction comes from the Latin word "Fractus," which means broken. It signifies a portion of an entire, made up of several equal parts from the whole.
For instance, pizza slice.
Fractions of a Pizza Slice
A fraction is represented by 2 numbers on top of each other, separated by a line. The top number is called the numerator, and the bottom number is the denominator. For example, 3/4, which means 3 parts out of 4 equal parts.
A fraction number line, as the name suggests, represents fractions on a number line.
Fractions on number line
(i) Proper Fraction: It is a fraction whose denominator is greater than the numerator, such as
Example: 1/4, 7/9, 50/51. Proper fractions are greater than 0 and less than 1.
Suppose we have to mark 5⁄6 on the number line.
It shows as:
Proper Fraction
(ii) Improper Fractions: These Fractions have a numerator that is greater than or equal to the denominator. Examples: 7/5,19/6,101/45, etc. Improper fractions are greater than 1 or equal to 1.
To represent an improper fraction on a number line, we can always convert it to a mixed fraction Suppose, we have to plot 5/2 on the number line.
Improper Fraction
(iii) Mixed fractions: In this fractions, are a combination of a whole number and a proper fraction. Example: 43/5.
The mixed numbers or the mixed fractions are always greater than 1 since their numerator is greater than the denominator.
Let’s understand how to represent a mixed fraction on a number line. Suppose, we have to mark 334 on the number line.
(iv) Like Fraction: In this type, there are fractions with the same denominator.
Example: 1/4, 2/4, 3/4.
Like Fraction(v) Unlike Fraction: In this fraction, there are fractions with different denominators.
Unlike Fraction
(vi) Equivalent Fraction: Equivalent fractions are fractions that have different numerators and denominators, but they still represent the same value.
For example: Let us mark 1/2 and 2/4.
Multiplication of Fractions
Multiplication of a fraction with a whole number
Example: To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number, and keep the denominator the same.
2/3 * 4 = 8/3
Therefore, when you multiply the fraction 2/3 by the whole number 4, the result is 8/3.
Multiplication of mixed fraction
(i) Fraction as an Operator ‘Of’
The ‘of’ operator basically implies multiplication.
Example: 1/5 of 2 = (1/5)×2= 2/5
or, 1/2 of 11 = (1/2) × 11 = 11/2
(ii) Multiplication of Fraction by a Fraction
To multiply two fractions, just multiply the numerators to get the numerator of the product, and multiply the denominators to get the denominator of the product.
Multiplication of Fraction by a Fraction
Example: To multiply fractions, multiply the numerators together and the denominators together.
1/2 * 3/4 = 3/8
Therefore, when you multiply the fraction 1/2 by the fraction 3/4, the result is 3/8.
(iii) Value of the Products
We know that the product of two whole numbers is bigger than each of the two whole numbers.
For example, 2× 4 = 8 and 8 > 4, 8 > 3.
when two proper fractions are multiplied, the product is less than each of the fractions. Or, we say the value of the product of two proper fractions is smaller than each of the two fractions.
The product of two improper fractions is greater than each of the two fractions.
Here are two examples of dividing fractions using the reciprocal method for a Class 7 Student:
Example 1:
Let's divide the fraction 2/3 by the fraction 3/4.
Therefore, when you divide the fraction 2/3 by the fraction 3/4, the result is 8/9.
Example 2:
Let's divide the fraction 5/6 by the fraction 2/5.
Therefore, when you divide the fraction 5/6 by the fraction 2/5, the result is 25/12.
Q.1. Multiply 21/5 and 15/4
Multiplying 21/5 × 15/4 =
we get 51/4
Q.2. Shyama bought around 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala then bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?
From the above question, it is given that,
Fruits bought by Shyama is = 5 kg 300 g
= 5 kg + (300/1000) kg
= 5 kg + 0.3 kg
= 5.3 kg
Fruits bought by Sarala is = 4 kg 800 g + 4 kg 150 g
= (4 + (800/1000)) + (4 + (150/1000))
= (4 + 0.8) kg + (4 + .150) kg
= 4.8 kg + 4.150kg
= 8.950 kg
So, Sarala bought more fruits.
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HOTS Question: Fractions and Decimals Doc  5 pages 
Long Question Answer: Fractions and Decimals Doc  1 pages 
Infographics: Ways to Represent Fraction Doc  1 pages 
1. What are fractions? 
2. What are the types of fractions? 
3. How do you multiply fractions? 
4. How do you divide fractions? 
5. Can you provide some solved questions related to fractions and decimals? 
HOTS Question: Fractions and Decimals Doc  5 pages 
Long Question Answer: Fractions and Decimals Doc  1 pages 
Infographics: Ways to Represent Fraction Doc  1 pages 

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