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Fractions

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Fractions  Aptitude basics, practice questions, answers and explanations 
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Simple or Vulgar Fraction

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. Eg:[ 3/4 ]

Decimal Fraction

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. Eg:[ 0.45773 ]

Converting a decimal to vulgar fraction:

Step 1: Calculate the total numbers after decimal point.

Step 2: Remove the decimal point from the number.

Step 3: Put 1 under the denominator and annex it with "0" as many as the total in step a.

Step 4: Reduce the fraction to its lowest terms.
Example: Consider 0.44

Step 1: Total number after decimal point is 2

Step 2 and 3: 44/100 

Step 4: 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:

Step 1: Separate the recurring number from the decimal fraction.

Step 2: Annex denominator with "9" as many times as the length of the recurring number.

Step 3: Reduce the fraction to its lowest terms.

Example: Consider 0.2323232323

Step 1: The recurring number is 23

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

Step 3: Reducing it to lowest terms : 23/99 [it can not be reduced further].

Mixed Recurring to Fractions:

If N= 0.abcbcbc?. Then N = abc - a / 990 = Repeated & non-repeated digits - Non repeated digits / As many 9's as repeated digits followed by as many zero as non - repeated digits

Eg: 0.25757..... = 257 - 2 / 990 = 255 / 990 = 17 / 60.