# Number System: Fraction, Proper, Improper , Mixed and Decimal fraction

**Fraction : **A fraction is a number in the form , where x & y are both integers and y 0. In the form , ‘x’ is called the numerator of the fraction and ‘y’ is called the denominator of the fraction.

We can also describe a fraction as a part of a whole. The denominator denotes how many equal parts the whole is divided into & the numerator denotes how many of the parts we are taking.

**For. eg. ** is a fraction.

5 is the numerator of the fraction & 6 is the denominator of the fraction.

We may also call it as 5 of 6 equal parts.

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We can classify fraction as: **Proper Fraction:** A fraction in which the numerator is smaller than the denominator.

For e.g. ,

**Improper Fraction : **A fraction is which the numerator is greater than the denominator.

For e.g. ,

**Mixed Number or Mixed Fraction :** Mixed number is composed of a whole number and a proper fraction.

For e.g. ,

**Decimal Fraction: **A fraction where the denominator can be expressed as a power of ten (such as 10, 100, 1000, etc).

For e.g. , , …

Decimal fraction can be written as a decimal point and no denominator. In decimal point form, it is easier to make calculations such as addition, subtraction etc.

can be written as 0.8

can be written as 0.11

can be written as 0.009

**Converting Improper fractions to Mixed numbers:**

~ Divide the numerator by the denominator.

~ Use the quotient as the whole number.

~ And the remainder as the numerator of the proper fraction.

~ The denominator will remain the same.

~ If there is no remainder the result is simply a whole number.

**Let’s convert into mixed number.**

= = +

=10+

=10

**Let’s convert into a mixed number.**

= 6 which is a whole number.

**Converting Mixed numbers to Improper fractions.**

~ Multiply the whole number by the denominator.

~ Add the product to the numerator of the proper fraction. The sum total is the numerator of the improper fraction.

~ The denominator will remain the same.

**Let’s convert into an improper fraction.**

= =