INTEGER MULTIPLICATION AND DIVISION RULES

Integer Multiplication Rules

Rule 1 : 

Positive x Positive = Positive

Example :

3 x 5 = 15

Rule 2 : 

Negative x Negative = Positive

Example :

(-3) x (-5) = 15

Rule 2 : 

Positive x Negative = Negative

Example :

3 x (-5) = -15

Rule 2 : 

Negative x Positive = Negative

Example :

-3 x 5 = -15

Integer Division Rules

Rule 1 : 

Positive ÷ Positive = Positive

Example :

20 ÷ 4 = 5

Rule 2 : 

Negative ÷ Negative = Positive

Example :

(-20) ÷ (-4) = 5

Rule 2 : 

Positive ÷ Negative = Negative

Example :

20 ÷ (-4) = -5

Rule 2 : 

Negative ÷ Positive = Negative

Example :

-20 ÷ 4 = -5

Divisibility Rules for Integers

Divisibility Rule for 2 :

All even integers are divisible by 2.

The integers which have the digits 0, 2, 4, 6 or 8 in one's place are known as even integers.

If the given integer has one of the above digits in one's place, then the integer is divisible by 2.

Divisibility Rule for 3 :

To check whether an integer is divisible by 3, we have to add all the digits in the integer.

If the sum of the digits is a multiple of 3, then the integer is divisible by 3.

Divisibility Rule for 4 :

If the last two digits of an integer are zeros or the integer formed by the last 2 digits is divisible by 4, then the integer is divisible by 4.

Divisibility Rule for 5 :

If an integer has 0 or 5 in one's place, then it is divisible by 5.

Divisibility Rule for 6 :

If an integer is divisible by both 2 and 3, then it is divisible by 6.

We already know that all even integers are divisible 2.

Hence, all the even integers which are divisible by 3 are divisible by 6.

Divisibility Rule for 7 :

An integer is divisible by 7, when the difference between twice the digit in one's place and the integer formed by other digits is either zero or a multiple of 7.

Divisibility Rule for 8 :

In an integer, if the last three digits are zeros or the integer formed by the last 3 digits is divisible by 8, then the integer is divisible by 8.

Divisibility Rule for 9 :

To check whether an integer is divisible by 9, we have to add all the digits in the given integer.

If the sum of the digits is a multiple of 9, then the integer is divisible by 9.

Divisibility Rule for 10 :

If an integer has 0 in one's place, then it is divisible by 10.

Divisibility Rule for 11 :

In an integer, if the sum of the digits in odd places and sum of the digits in even places are equal or they differ by an integer divisible by 11, then the integer is divisible by 11.

Divisibility Rule for 12 :

If an integer is divisible by both 3 and 4, then it is divisible by 12.

Divisibility Rule for 15 :

If an integer is divisible by both 3 and 5, then it is divisible by 15.

Divisibility Rule for 18 :

If an integer is divisible by both 2 and 9, then it is divisible by 18.

Divisibility Rule for 25 :

In a integer, if the last two digits are zeroes or the integer formed by the last two digits is a multiple of 25, then the integer is divisible by 25.

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