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 ]
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.
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.