The denominator of an integer is 1.
Integers are whole numbers (positive, negative, or zero), and they can all be expressed as a fraction with a denominator of 1. This is because any number divided by 1 equals itself.
Understanding Integers as Fractions
An integer can be represented as a fraction in the form a/b, where a is the numerator and b is the denominator. When the denominator is 1, the fraction simplifies to the integer itself.
For example:
- 5 can be written as 5/1
- -3 can be written as -3/1
- 0 can be written as 0/1
Why the Denominator is 1
The reason integers have a denominator of 1 is rooted in the definition of rational numbers. A rational number is any number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Since every integer can be expressed with a denominator of 1, all integers are considered rational numbers. This makes 1 the implicit denominator of any integer.
Examples
| Integer | Fractional Representation | Denominator |
|---|---|---|
| 10 | 10/1 | 1 |
| -7 | -7/1 | 1 |
| 256 | 256/1 | 1 |
| 0 | 0/1 | 1 |
Conclusion
Therefore, the denominator of any integer is always 1, allowing it to be expressed as a fraction and classified as a rational number.
