# CLASS-5TYPES OF FRACTION

TYPES OF FRACTION

A fraction is a mathematical expression that represents a part of a whole. It is written as two numbers separated by a horizontal or diagonal line, with the number below the line called the denominator and the number above the line called the numerator.

For example, the fraction 3/4 represents three parts out of a total of four parts.

Fractions can be used to represent parts of a whole, portions of a group, or ratios of two quantities. They can also be used in calculations involving addition, subtraction, multiplication, and division.

A fraction is a mathematical expression that represents a part of a whole. It consists of two numbers separated by a horizontal or diagonal line called a fraction bar or a solidus. The number above the fraction bar is called the numerator, and the number below the fraction bar is called the denominator.

For example, in the fraction 3/5, 3 is the numerator, and 5 is the denominator. This fraction represents three parts out of a total of five parts. Fractions can be proper (where the numerator is less than the denominator), improper (where the numerator is greater than or equal to the denominator), or mixed (where there is a whole number and a fraction combined).

Fractions can be used to represent many things, such as parts of a whole object, portions of a measurement, or ratios between two quantities. They are an essential concept in mathematics and are used in many everyday situations, such as cooking, measuring, and calculating discounts.

In mathematics, a fraction is a numerical quantity that represents a part or a division of a whole. It is represented as two numbers separated by a horizontal line, called a fraction bar or a division bar. The number above the bar is called the numerator, and the number below the bar is called the denominator.

For example, the fraction 3/4 represents three parts out of four equal parts, or three divided by four. The numerator and denominator can be any integers (positive, negative, or zero), but the denominator cannot be zero.

Fractions can be added, subtracted, multiplied, and divided, and they can also be converted into decimal or percentage form. Fractions are commonly used in everyday life, such as in cooking, measurements, and financial calculations.

There are some types of fraction with examples are given below for your better understanding -

Equal parts of a whole are called fractions.

a

In the fraction ------ ‘a’ is the numerator and ‘b’ is the denominator.

b

Different Types Of Fractions -

1) Proper fractions -

a

When a < b, then ------ is a proper fraction.

b

a

and,  ------ is always less than one (1)

b

6        9        13

Examples: ------, ------, ------

7        11       15

2) Improper fractions :-

a

When a > b, then ------ is a Improper fraction.

b

a                  a

Either ------ > 1, or  ------ = 1

b                  b

7        9        12        19

Examples:  -----, ------, ------, -------,etc.

3        4         5        19

1)  Which of the following fractions are proper fractions and which are improper fractions:

13                                  38

a) -------                       e)  -------

16                                   4

17                                 1

c) -------                       h) -------

8                                 7

13

a) ------- is a proper fraction.[since,(numerator 13) < (denominator 16)]

16

17

c) ------ is an improper fraction.[since,(numerator 17) > (denominator 8)]

8

38

e) ------- is an improper fraction.[since,(numerator 38) > (denominator 4)]

4

1

h) ------ is a proper fraction. [since,(numerator 1) < (denominator 7)]

7

3) Like fractions :-

If in all given fraction whose denominators are same, are to be considered as like-fraction.

5        9         6        10

Examples: ------, ------, ------, ------

11       11       11        11

4) Unlike fractions :-

If in all given fraction whose denominators are different, are to be considered as a unlike-fraction.

8        11       18       22

Example: ------, ------, ------, ------

15        9        25       17

5) Mixed number :-

If A Mixed number contains a whole number and a proper fraction.

3            3

6 + ------ = 6 ------

5            5

3

, where 6 is the whole number and ------- is the proper fraction.

5

6) Reciprocal fractions :-

When the product of two fractions is equal to 1, they are called reciprocal fractions.

15/8 is reciprocal of 8/15, so

8          15

------- X ------- = 1

15           8

7) Equivalent fractions :-

Two or more fractions representing the same part of the whole are known as Equivalent fractions.

1st Way -

·  We get equivalent fractions of a given fraction by multiplying both the numerator and the denominator by the same number (except 0).

3          3×2          6

------ = -------- = ------

4          4×2          8

3           3×3           9

------ = --------- = -------

4           4×3          12

3          3×4          12

------ = -------- = -------

4          4×4          16

3          6          9          12

------ = ------ = ------ = ------- = are all equivalent fractions.

4          8         12          16

2nd Way -

· Similarly if we divide the numerator and the denominator by the same number (except 0), we get equivalent fractions.

Example: -

3          3÷3          1

------ = -------- = ------

6          6÷3          2

6          6÷2          1

------ = -------- = ------

12         12÷2         2

1          3          6

------ = ------ = ------ = are all equivalent fractions.

2          6         12