Definition of Fraction
A fraction is a part of the whole. Such as a piece of cake from a whole cake.
(1/2) is a fraction where 1 = numerator & 2 = denominator
1. Examples of fractions
- Number of girls in a school from all students.
- A piece of pizza from whole pizza.
- 2/4 part of the whole circle.
- A piece of an Apple from the whole apple.
2. Types of fractions
There are different types of fractions which we use in mathematics as well as in our daily life-
1.) Proper fraction
The fraction in which numerator is less than its denominator.
Example:- (1/4), (5/8), (2/5), etc.
In the above examples, all the numerator is less than from denominator.
2.) Improper fraction
The fraction in which numerator is more than its denominator.
Example:- (12/5), (13/2), (47/3), etc.
In the above examples, all the numerator is more than from denominator.
3.) Mixed fraction
The fraction in which we show quotient, remainder & divisor as 2³/₄.
Example:- (2³/₄), (5²/₈).
In the above examples, colours show the position of quotient, remainder & divisor.
3. Equivalent fraction
The fraction which is equal to the other fractions then they are known as equivalent fractions.
Examples:- (1/2) & (2/4) are equivalent to each other. But why they are equivalent. Let's discuss-
If we reduce (2/4) in the lowest form (2/4)÷(2/2) = (1/2)
Here we get (1/2) & it is equal to (1/2). So both fractions (1/2) & (2/4) are equivalent to each other.
4. Addition of fractions
We add different whole numbers & integers. Here we are discussing how to add the fractions.
Add the fractions (1/2) & (2/4).
We can add fractions in different ways-
1.) By Equivalent fraction-
Solve-
= (1/2) + (2/4)
{In equivalent fraction we will make both fractions equal by multiply (1/2) from 4 & multiply (2/4) from 2 as below}
= (1/2)×(4/4) + (2/4)×(2/2)
= (1×4)/(2×4) + (2×2)/(4×2)
=(4/8) + (4/8)
{ Here both fractions making equal, now we will add both the fractions }
= (4 + 4)/8
= 8/8
=1
{ Here we get our answer 1}
2.) By L.C.M.
Solve-
= (1/2) + (2/4)
{ In L.C.M. we will take L.C.M. of both denominator}
= L.C.M. of both denominator 2 & 4 will be 4.
= {(1×2) + (2×1)}÷4
= {2 + 2} ÷ 4
= 4 ÷ 4
= 1
{ Here we get our answer 1}
5. Multiplication of fractions
Multiply the fractions (3/5) & (4/7)
We can multiply both fractions as below-
Solve-
= (3/5) × (4/7)
{ Multiply both numerator 3 & 4 to each other & multiply both denominator 5 & 7 to each other}
= (3×4) / (5×7)
= 12/35
{ Here we get our answer (12/35) }
6. Division of fractions
Divide the fractions (4/5) & (7/2)
We can divide both fractions as below-
Solve-
= (4/5) ÷ (7/2)
{ Now we will do reciprocal of (7/2) as (2/7) & change the sign of ÷ to × }
= (4/5) × (2/7)
{ Multiply both numerator 4 & 2 to each other & multiply both denominator 5 & 7 to each other}
= (4×2) / (5×7)
= 8/35
{ Here we get our answer (8/35).
7. Subtraction of fractions
Subtract the fraction (4/5) & (3/5)
We may subtract the fraction (4/5) & (3/5) with the help of L.C.M. & equivalent method.
But we are solving it directly because here both denominators are the same.
Solve-
= (4/5) - (3/5)
= (4 - 3) / 5
= 1/5
{ Here we get our answer (1/5) }.