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.

Use a divisibility test to answer the question.

Problem 1 :

Is 146 divisible by 2?

Solution :

146 is the even number, so it must be divisible by 2

Problem 2 :

Is 153 divisible by 3?

Solution :

By finding the sum of the digits of 153, 

= 1 + 5 + 3

= 9

Since 9 is divisible by 3, the given number 153 is also divisible by 3.

Problem 3 :

Is 378 divisible by 4?

Solution :

The last two digits is 78,

= 78/4

Since the last two digits is not divisible by 4, then 378 is not divisible by 4.

Problem 4 :

Is 1255 divisible by 5?

Solution :

In 1255, the unit digit which is 5, then it is divisible by 5.

Problem 5 :

Is 147 divisible by 6?

Solution :

Since the given number is odd, it is not divisible by 2. 

The sum of the digits = 1 + 4 + 7

= 12

Since the sum is divisible by 3, 147 is divisible by 3. But 147 is not divisible by 6.

Problem 6 :

Is 333 divisible by 6?

Solution :

Since the given number is odd, it is not divisible by 2. 

The sum of the digits = 3 + 3 + 3

= 9

Since the sum is divisible by 3, 333 is divisible by 3. But 333 is not divisible by 6.

Problem 7 :

Is 2769 divisible by 3?

Solution :

The sum of the digits = 2 + 7 + 6 + 9

= 24

24 is divisible by 3, then 2769 is also divisible by 3.

Problem 8 :

Is 5034 divisible by 3?

Solution :

The sum of the digits = 5 + 0 + 3 + 4

= 12

12 is divisible by 3, then 5034 is also divisible by 3.

Problem 9 :

Is 145 divisible by 15?

Solution :

Sum of the digits in 145, 

= 1 + 4 + 5

= 10

It is not divisible by 3. 

Ends with 5, so it is divisible by 5.

Since it is divisible by 3 and not divisible by 5, then it is not divisible by 15.

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