This is part of a series on common misconceptions.
True or False?
is equal to x
Why some people say it's true: You can multiply fractions like this to get the denominator.
Why some people say it's false: The numerator is not
The statement is .
When multiplying the second fraction, we get However, = x a or x or x etc.
Rebuttal: But if it works.
Reply: But it doesn’t work for all values of
Rebuttal: What if stands for a different number each time?
Reply: That would break the rules of algebra.
Rebuttal: What if stands for the square root of anything? can be or and then can be different values.
Reply: is just and can stand for one value only.
Rebuttal: So it never works?
Reply: It works if or
Rebuttal: How can we judge the value if or
Reply: No value could be given to the final fraction, so we can’t do anything, although if and then the statement doesn’t work anyway.