What is the value of 70/0?
The Correct Answer and Explanation is :
The expression 70/0 is undefined.
Why is division by zero undefined?
In mathematics, division is essentially the process of determining how many times one number (the divisor) can fit into another number (the dividend). When we divide by a number other than zero, we are essentially asking, “How many times can this divisor fit into the dividend?”
For example:
- 10 ÷ 2 means “How many times can 2 fit into 10?” The answer is 5.
- 15 ÷ 3 means “How many times can 3 fit into 15?” The answer is 5 again.
But when we attempt to divide by zero, like in the case of 70 ÷ 0, the situation becomes problematic. Here’s why:
- Zero Cannot Divide Into Any Number: Zero represents nothing. So, when we try to divide by zero, we’re asking, “How many times does zero fit into 70?” The problem is, zero cannot be multiplied by any number to produce 70 (or any other number), because multiplying by zero always results in zero.
- Mathematical Inconsistency: Division by zero doesn’t make sense because it leads to contradictions. For example, if we assume 70 ÷ 0 = x, then we are saying that x * 0 = 70. But, as mentioned, x * 0 = 0 for any number x, not 70. This creates an inconsistency in mathematical logic, so division by zero is not allowed.
- Limits and Approaches: If we approach division by smaller and smaller numbers close to zero (such as dividing by 0.0001, 0.00001, etc.), the result increases without bound, growing infinitely large. This is why we say that division by zero doesn’t yield a real number; it is undefined.
In summary, dividing by zero, such as in 70 ÷ 0, doesn’t produce a valid or meaningful result in mathematics, so it is considered undefined.