Is the statement “any number divided by itself is 1” a true statement? If not, for what number or numbers is the statement not true?
The Correct Answer and Explanation is:
The statement “any number divided by itself is 1” is mostly true but not always true. The exception is when the number is zero.
Correct Answer:
The statement is not true for zero.
0 ÷ 0 is undefined, not 1.
Detailed Explanation (Around 300 Words):
Division is the process of determining how many times one number fits into another. When you divide a number by itself, you’re essentially asking: “How many times does this number fit into itself?” For any number other than zero, the answer is 1. For example:
- 5 ÷ 5 = 1
- −3 ÷ −3 = 1
- 100 ÷ 100 = 1
This works because any nonzero number times 1 gives the original number back. Mathematically, a ÷ a = 1 for any a ≠ 0.
However, things change when the number involved is zero. Let’s consider the division 0 ÷ 0. This seems to ask, “How many times does 0 fit into 0?” This question has no clear answer, because:
- 0 × 1 = 0
- 0 × 2 = 0
- 0 × 100 = 0
- 0 × any number = 0
So any number multiplied by 0 gives 0, which means 0 ÷ 0 could be anything. This leads to an infinite number of possible answers, which is not allowed in standard arithmetic. Therefore, 0 ÷ 0 is considered undefined, because it does not have one single, clear value.
On the other hand, 0 ÷ any nonzero number is equal to 0, because zero divided into groups of something still gives zero groups. For example:
- 0 ÷ 5 = 0
- 0 ÷ −8 = 0
Final Conclusion:
The statement “any number divided by itself is 1” is false for zero. For all nonzero numbers, it is true. The exception is 0 ÷ 0, which is undefined.
