## 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: etc.

**Improper fraction:**The fraction in which numerator is greater than the denominator is

called improper fraction.

For Example: , etc

**Mixed fraction:**Mixed fraction is a composition of fraction and whole number.

For example: etc.

**Complex fraction:**A complex fraction is that fraction in which numerator or denominator or

both are fractions.

For Example: , etc.

**Decimal fraction:**The fraction whose denominator is 10 or its higher power, is called a

decimal fraction.

For Example:

**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:

### Comparison of Fractions

If the denominators of all the given fractions are equal then the fraction of greater

numerator will be the greater fraction.

numerator will be the greater fraction.

For Example: then,

If the numerators of all the given fractions are equal then the fraction of smaller

denominator will be greater fraction.

denominator will be greater fraction.

For Example: then,

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.

denominator are equal, then the fraction of smaller numerator will be the greater faction.

For Example: then,

### Quicker Method (Cross Multiplication)

This is a short-cut method to compare fractions. Using this method we can compare

all types of fractions.

all types of fractions.

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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