No, an integer divided by an integer is not always an integer.
When you divide two integers, the result is not always an integer; it can also be a rational number (a fraction). It's crucial to understand the conditions under which the result will be an integer.
Understanding Integer Division
- Integers: Whole numbers (positive, negative, and zero). Examples: -3, -2, -1, 0, 1, 2, 3.
- Division: The process of splitting a number into equal parts.
- The Question: If we take any two integers and divide them, will the result always be another integer?
When Division Results in an Integer
The division of two integers results in an integer only when the numerator (the number being divided) is a multiple of the denominator (the number dividing). In other words, the denominator must divide evenly into the numerator.
Examples:
- 6 / 3 = 2 (Integer) - Because 6 is a multiple of 3.
- -10 / 2 = -5 (Integer) - Because -10 is a multiple of 2.
- 0 / 5 = 0 (Integer) - Zero divided by any non-zero integer is always zero.
When Division Does NOT Result in an Integer
If the numerator is not a multiple of the denominator, the result will be a fraction or a decimal, which is not an integer.
Examples:
- 5 / 2 = 2.5 (Not an Integer)
- 7 / 3 = 2.333... (Not an Integer)
- -4 / 3 = -1.333... (Not an Integer)
Summary
To summarize: integer division results in an integer only if the numerator is perfectly divisible by the denominator (without any remainder). Otherwise, the result is a rational number (fraction or decimal) and not an integer.
