33 + 33 – 33 x 33 ÷ 0 = infinity free
The correct answer and explanation is:
Correct Answer: The expression 33 + 33 - 33 × 33 ÷ 0 is undefined, not infinity free.
Explanation (300 words):
In mathematics, division by zero is not allowed. The expression given is:
33 + 33 – 33 × 33 ÷ 0
To evaluate this expression, follow the order of operations. The correct order of operations is:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
This is often remembered using the acronym PEMDAS.
There are no parentheses or exponents in this case, so begin with multiplication and division.
Step 1: Multiply 33 × 33 = 1089
Step 2: Divide 1089 ÷ 0
Here is where the issue arises. Division by zero is undefined in mathematics. It does not produce a valid number. This is because dividing any number by zero leads to contradictions. For example, if 1089 ÷ 0 = x, then it would mean 0 × x = 1089. But 0 multiplied by any number is always 0, never 1089. Therefore, the operation has no meaningful solution.
Even though the remaining part of the expression includes valid operations like addition and subtraction, the presence of division by zero invalidates the entire expression. No matter what values are added or subtracted, the undefined division makes the whole expression undefined.
Some people may mistakenly think dividing by zero results in infinity, but in standard arithmetic and algebra, division by zero is not defined at all. It is not considered “infinity free” or equal to infinity. Such ideas only appear in specific areas of mathematics like limits in calculus, and even there, they are handled very carefully and do not justify direct division by zero.
Final conclusion: The expression does not have a valid answer. It is mathematically undefined.