When an integer is divided by an integer, the result is not always an integer. It is an integer only if the division results in a whole number with no remainder.
Understanding Integer Division
The key to understanding integer division lies in the concept of remainders. An integer division problem can be expressed as:
Dividend (Integer) / Divisor (Integer) = Quotient (Result)
For the quotient to also be an integer, the divisor must divide the dividend evenly.
Examples
Here are some examples to illustrate the concept:
- Integer Result: 10 / 2 = 5 (5 is an integer)
- Non-Integer Result: 10 / 3 = 3.333... (3.333... is not an integer; it's a rational number)
- Integer Result: -12 / 4 = -3 (-3 is an integer)
- Non-Integer Result: 7 / -2 = -3.5 (-3.5 is not an integer; it's a rational number)
Key Conditions for an Integer Result
- The divisor must be a factor of the dividend. In other words, the dividend must be perfectly divisible by the divisor.
- No remainder is produced when the division is performed.
When the Result is Not an Integer
If the divisor is not a factor of the dividend, the result will be a rational number or a decimal number, which is not an integer. This means there is a remainder when the division is carried out.
Division by Zero
Division by zero is undefined in mathematics. It doesn't result in any number, integer or otherwise.
