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Tuesday, 28 June 2016

Fractions,Type of Fractions,Divisibility Rules



Fractions






A fraction is known as a rational number and written in the form of p/q where p and q are 
integers and q ≠ 0. The lower number ‘q’ is known as denominator and the upper 
number ‘p’ is known as numerator.





Type of Fractions






Proper Fraction: The fraction in which numerator is less the denominator is called a 
proper fraction.
For Example: number-system-f-18851.pngetc.
Improper fraction: The fraction in which numerator is greater than the denominator is 
called improper fraction.
For Example: number-system-f-18859.png, etc
Mixed fraction: Mixed fraction is a composition of fraction and whole number.
For example: number-system-f-18865.pngetc.
Complex fraction: A complex fraction is that fraction in which numerator or denominator or 
both are fractions.
For Example: number-system-f-18871.png, etc.
Decimal fraction: The fraction whose denominator is 10 or its higher power, is called a 
decimal fraction.
For Example: number-system-f-18877.png
Continued fraction: Fractions which contain addition or subtraction of fractions or a 
series of fractions generally in denominator (sometimes in numerator also) are called 
continued fractions.
It is also defined as a fraction whose numerator is an integer and whose denominator is an 
integer plus a fraction.
For Example: number-system-f-18883.png





Comparison of Fractions






If the denominators of all the given fractions are equal then the fraction of greater 
numerator will be the greater fraction.
For Example: number-system-f-18893.png then, number-system-f-18899.png
If the numerators of all the given fractions are equal then the fraction of smaller 
denominator will be greater fraction.
For Example: number-system-f-18905.png then, number-system-f-18911.png
When numerator is greater than denominator and the differences of numerator and 
denominator are equal, then the fraction of smaller numerator will be the greater faction.
For Example: number-system-f-18917.png then, number-system-f-18923.png





Quicker Method (Cross Multiplication)






This is a short-cut method to compare fractions. Using this method we can compare 
all types of fractions.
number-system-f-18933.png
The fraction whose numerator is in the greater product is greater.

Since 36 is greater than 35, hence, 


Divisibility Rules

Divisibility by 2: 
A number is divisible by 2 if its unit’s digit is even or 0.

Divisibility by 3: 
A number is divisible by 3 if the sum of its digits are divisible by 3.

Divisibility by 4: 
A number is divisible by 4 if the last 2 digits are divisible by 4, or if the last two digits are 0’s.

Divisibility by 5: 
A number is divisible by 5 if its unit’s digit is 5 or 0.

Divisibility by 6: A number is divisible by 6 if it is simultaneously divisible by 2 and 3.

Divisibility by 7: 
A number is divisible by 7 if unit’s place digit is multiplied by 2 and subtracted from the remaining digits and the number obtained is divisible by 7.

Divisibility by 8: 
A number is divisible by 8 if the last 3 digits of the number are divisible by 8, or if the last three digits of a number are zeros.

Divisibility by 9: 
A number is divisible by 9 if the sum of its digits is divisible by 9.

Divisibility by 10: 
A number is divisible by 10 if its unit’s digit is 0.

Divisibility by 11:
 A number is divisible by 11 if the sum of digits at odd and even places are equal or differ by a number divisible by 11.

Divisibility by 12: 
 number is divisible by 12 if the number is divisible by both 4 &3.

Divisibility by 13: 
A number is divisible by 13 if its unit’s place digit is multiplied by 4 and added to the remaining digits and the number obtained is divisible by 13.

Divisibility by 14: 
number is divisible by 14 if the number is divisible by both 2 and 7.

Divisibility by 15: 
Number is divisible by 15 if the number is divisible  both 3 and 5.

Divisibility by 16: 
A number is divisible by 16 if its last 4 digits is divisible by 16 or if the last four digits are zeros.

Divisibility by 17: 
A number is divisible by 17 if its unit’s place digit is multiplied by 5 and subtracted from the remaining digits and the number obtained is divisible by 17.

Divisibility by 18: 
A number is divisible by 18 if the number is divisible by both 2 and 9.

Divisibility by 19: 
A number is divisible by 19 if its unit’s place digit is multiplied by 2 and added to the remaining digits and the number obtained is divisible by 19.



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