# Division of Integers

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

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