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# Dividing Integers

An integer is a number that has no fractional part or decimal part. Integers include all counting numbers (1, 2, 3, 4, ...), zero (0) and negative of counting numbers (-1, -2, -3, -4, ...).

A set of integers in denoted by $\mathbb{Z}$, such that $\mathbb{Z}$ = {......, -3, -2, -1, 0, 1, 2, 3, ...…}

There are few important points which are to be kept in mind while dividing integers.

Sign Analysis:
If the sign of divisor and dividend are same, then answer will be positive. If the sign of divisor and dividend are opposite, then the answer will come out to be negative.
1. $\frac{\text{Positive}}{\text{Positive}}$ = Positive
2. $\frac{\text{Negative}}{\text{Negative}}$ = Positive
3. $\frac{\text{Positive}}{\text{Negative}}$ = Negative
4. $\frac{\text{Negative}}{\text{Positive}}$ = Negative
• If an integer is divided by 0, then the answer is not defined or indeterminate. For example: $\frac{4}{0}$ = not defined.
• If 0 is divided by integer, then answer will be 0. For example: $\frac{0}{7}$ = 0.
• If an integer is divided by 1, then the answer will be that integer itself. For example: $\frac{22}{1}$ = 22.
• If an integer is divided by itself, then the answer will be 1. For example: $\frac{34}{34}$ = 1.
• When an integer is fully divided by another i.e. it leaves no remainder, the quotient will also be an integer.
• When an integer is not fully divided by another i.e., there is a remainder left, then answer should be written in either fractional or decimal form. This will not be categorized as an integer.

Let us consider few examples to understand this concept

Dividing Integers Examples:

Example 1:

Divide 50 by -5.

Solution:

$\frac{50}{-5}$

Here, the answer will be negative because the numbers have opposite signs.
On dividing 50 by 5, we get 10.

Therefore,
$\frac{50}{-5}$ = -1.

Example 2:

Divide -64 by -3.
Solution:

$\frac{-64}{-3}$

Here, the answer will be positive because both have same signs.
On dividing 64 by 3, we get 21.33

We can write answer in the form of fraction, i.e. $21$$\frac{1}{3}$

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