Final answer:
The statement that crossing out all factors in the numerator makes a fraction equal to zero is false. After cancelation, if there is at least one non-zero factor in the denominator, the fraction will assume a simplified form with 1 in the numerator. The process involves reducing the fraction to its simplest form, not making it zero.
Step-by-step explanation:
The statement that 'All of the factors from the numerator have been crossed out which will make the answer zero' is false. When simplifying fractions by canceling out common factors in the numerator and denominator, the goal is to reduce the fraction to its simplest form. If all the factors from the numerator are eliminated, and there is at least one factor remaining in the denominator, the fraction is not zero - instead, it is a fraction that has 1 in the numerator and the remaining product of the factors in the denominator.
For example, if we have a fraction where the numerator is 2×5 and the denominator is 2×5×3, if we cancel out the 2×5 from both the numerator and denominator, we are left with 1/3, not zero. This aligns with the rule that any nonzero number divided by itself is 1, and when this 1 is divided by any other nonzero number, the result is a fraction with 1 in the numerator.
In mathematics, when simplifying expressions, we must always be careful to follow the rules of algebra and understand that canceling factors can reduce a quantity but not necessarily render it zero. This is especially important when dealing with negative exponents, where negative exponents flip the fraction, indicating division rather than multiplication, without making the entire expression zero.