The default meaning of the term divisible means that the result of dividing two integers is an integer.
For example,
- 15 is divisible by 3, because 15 ÷ 3 = 5 (an integer)
- -14 is divisible by 2, because -14 ÷ 2 = -7 (an integer)
- -28 is divisible by -14 because -28 ÷ -14 = 2 (an integer)
- 100 is divisible by -50 because 100 ÷ (-50) = -2 (an integer)
- 9 is not divisible by 2 because 9 ÷ 2 is 4.5 (not an integer)
The term divisible is never used when there is a non-integer involved.
For example,
- 1.5 ÷ 0.5 = 3
- 5 ÷ 2 = 2.5
- -5 ÷ 2.5 = -2
Is 0 divisible by 5?
0 ÷ 5 = 0 (an integer). Hence, 0 is divisible by 5. |
Is 5 divisible by 0?
5 ÷ 0 is undefined. Hence, 5 is not divisible by 0. Anything divided by 0 is undefined. |
Is 0 divisible by 0?
0 ÷ 0 is again undefined. In fact any number divided by 0 is undefined. |
From the last 2 questions, we can deduce that
- whenever you put zero in the denominator, the answer will always be undefined.
- whenever you put zero in the numerator (and a non-zero number in the denominator), the answer will always be zero.
|
The numerator is the top number of a fraction, and the denominator is the bottom number of a fraction. |

If x is divisible by y, then which of the following can be true about x and y?
(A) Since the term divisible is only used in the case of integers, therefore x cannot be equal to 0.5 (non-integer). (B) x is divisible by y means that x ÷ y = integer. Since x ÷ 0 is undefined. Hence, y cannot be equal to zero. (C) Since the term divisible is only used in the case of integers, therefore x can be equal to 0 (integer). (D) We know that divisible means that the result of dividing two integers is an integer. In other words x ÷ y = integer. Hence x ÷ y cannot be a non-integer. (E) x is divisible by y means that x ÷ y = integer. Therefore this is correct. |
Summary:
- Divisible means that the result of dividing two integers is an integer.
- The term divisible is used only when the numerator and the denominator are integers.
- Zero is divisible by all non-zero values.
- No value is divisible by zero