Division of integers is the opposite operation of multiplying integers It is the process by which one is trying to determine how many times a number is contained into another.

Say for instance you do 42 ÷ 6

You are trying to find out how many times 6 is contained into 42

Since 6 × 7 = 42, 6 is contained into 42 seven times

Thus, 42 ÷ 6 = 7

Notice that

quotient × divisor = dividend

dividend ÷ divisor = quotient

dividend ÷ quotient = divisor

In other words, the product of 4 × 5 = 20

Then, dividing the product, which is 20 by 4 gives you back 5

However, dividing the product(20) by 5 gives you back 4

We can use this fact to find the rule for dividing integers

2 × 6 = 12

12 ÷ 6 = 2

12, 6, and 2 are positive, so

Positive ÷ Positive = Positive

2 × -6 = -12

-12 ÷ -6 = 2

12 and 6 are negative, but 2 is positive, so

Negative ÷ Negative = Positive

In the previous example, notice that -12 ÷ 2 = -6

12 is negative, 2 is positive, but 6 is negative, so

Negative ÷ Positive = Negative

Finally, consider:

-2 × - 6 = 12

12 ÷ -2 = -6

12 is positive, 2 is negative, and 6 is negative, so

Positive ÷ Negative = Negative

Notice also that the rule for division of integers is the same for multiplying integers.Therefore, if you remember the rule for multiplying integers, you already know it for division.**The division of two integers with the same signs is positive****The division of two integers with different signs is Negative**