# Simple and Decimal Fractions

## Simple and Decimal Fractions

##### Simple or Vulgar Fraction e.g:[ 3/4 ]

A number expressed with numerator and denominator. Say I have 3 of 10 apples then I will express it as 3/10. The total is written below a horizontal or diagonal line, and the number of parts comprising the fraction (numerator) is written above. Such fractions are called vulgar fractions or simple fractions.

##### Decimal Fraction e.g:[ 0.45773 ]

Expressing the fraction in decimal values (denominator a power of 10) is called decimal fraction. 1/2 is expressed as 0.5 in decimal fraction.

##### Converting a decimal to vulgar fraction :
###### Method:

a) Calculate the total numbers after decimal point. b) Remove the decimal point from the number. c) Put 1 under the denominator and annex it with '0' as many as the total in step a. d) Reduce the fraction to its lowest terms.

##### Example: Consider 0.44
###### Step a:

Total number after decimal point is 2

44/100

###### Step d:

Reducing it to lowest terms : 44/100 = 22/50 = 11/25

Converting a recurring decimal to vulgar fraction A decimal with recurring value is called recurring decimal. E.g: 2/9 will give 0.22222222...... where 2 is recurring number.

###### Method:

a) Separate the recurring number from the decimal fraction. b) Annex denominator with '9' as many times as the length of the recurring number. c) Reduce the fraction to its lowest terms.

##### Example: Consider 0.2323232323
###### Step a:

The recurring number is 23

###### Step b:

23/99 [the number 23 is of length 2 so we have added two nines]

###### Step c:

Reducing it to lowest terms : 23/99 [it can not be reduced further].

How to Convert a mixed-recurring decimal to vulgar fraction ? A decimal with both recurring and non-recurring value is called mixed recurring decimal. E.g: 28/25 will give 1.1199999999...... where 11 is non-recurring number and 9 is recurring number.

###### Method:

a) Separate the recurring number, non recurring number from the decimal fraction. b) Round the decimal after point to the first recurring value. c) Result of step b - non recurring number. d) Annex as many '0' as non-recurring number length and as many '9' as recurring number length. e) Step c / Step d f) Add the fraction with the number before decimal point.

##### Example: Consider 1.11999999...
###### Step a:

The recurring number is 11, non-recurring number is 9

###### Step b and c:

119-11 [rounded value of number after decimal point - non recurring value]

900

108/900 [c/d]

###### Step f:

1+108/900 [adding with number before decimal point ] Reducing it to lowest terms : 900+108 / 900 = 1008/900 = 28/25.