What does Divisibility mean?

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 =…

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?
  • Yes
  • No

0 ÷ 5 = 0 (an integer). Hence, 0 is divisible by 5.

 

Is 5 divisible by 0?
  • Yes
  • No

5 ÷ 0 is undefined. Hence, 5 is not divisible by 0.

Anything divided by 0 is undefined.

 

Is 0 divisible by 0?
  • Yes
  • No

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.


I forgot, what is the numerator and the denominator?

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?
  1. x can be equal to 0.5
  2. y can be equal to 0
  3. x can be equal to 0
  4. x ÷ y can be a non-integer
  5. x ÷ y is an integer

(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

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