TYPES of FRACTIONS, Examples, Addition, Division, Multiplication & Subtraction of fractions


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

  1. Number of girls in a school from all students.
  2. A piece of pizza from whole pizza.
  3. 2/4 part of the whole circle.
  4. 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/.

Example:- (2³/), (5²/).

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) }.