# Order of evaluating an a fraction's components - 0/0

• Square1
In summary: Yes, division by 0 is a unique case where it is not possible to evaluate the expression. It is not allowed in algebraic operations.
Square1
Just wondering if I've forgotten a rule here, or there is some new terminology I can learn.

We know 0/x when x > 0, is equal to 0. x/0 is undefined..since we "blow up" dividing any value by a value that is more than infinitely small...by zero.

We say that 0/0 is also undefined. We choose to consider the denominator 0 here first to say, "dividing by zero...can't be defined", instead of first considering the numerator and saying maybe, "zero is going to be divided. It's going to be equal to zero no matter what since we started with nothing".

Question: Is there an algebraic rule, or convention, that generally states you should start to evaluate the denominators first? Or is x/0 simply its own case where we can begin and end evaluating the parts that make up an expression?

Square1 said:
Just wondering if I've forgotten a rule here, or there is some new terminology I can learn.

We know 0/x when x > 0, is equal to 0. x/0 is undefined..since we "blow up" dividing any value by a value that is more than infinitely small...by zero.
The basic rule is that division by 0 is not allowed.
Square1 said:
We say that 0/0 is also undefined.
0/0 is called an indeterminate form. It shows up in limits where both the numerator and denominator are approaching zero. This is indeterminate, because some quotients with this form actually have a limit, which can be literally any number or even ##\infty## or ##-\infty##.
Square1 said:
We choose to consider the denominator 0 here first to say, "dividing by zero...can't be defined", instead of first considering the numerator and saying maybe, "zero is going to be divided. It's going to be equal to zero no matter what since we started with nothing".

Question: Is there an algebraic rule, or convention, that generally states you should start to evaluate the denominators first?
No. The rule is that division by zero is not allowed.
Square1 said:
Or is x/0 simply its own case where we can begin and end evaluating the parts that make up an expression?

Ssnow

## 1. What does it mean when the numerator and denominator of a fraction are both 0?

When both the numerator and denominator of a fraction are 0, the value of the fraction is considered undefined. This means that the fraction cannot be evaluated and does not have a numerical value.

## 2. Can a fraction's components be evaluated in any order?

No, the order of evaluating a fraction's components follows the same rules as the order of operations in mathematics. The numerator and denominator should be evaluated in order, from left to right.

## 3. Is it possible for a fraction's components to be evaluated differently depending on the order?

Yes, the value of a fraction can change depending on the order in which its components are evaluated. This is why it is important to follow the correct order of operations when evaluating fractions.

## 4. What is the result of dividing 0 by 0?

Dividing 0 by 0 is considered an indeterminate form, meaning that the result cannot be determined. It is not equal to any specific number and is considered undefined.

## 5. Can simplifying a fraction with a 0 in the numerator or denominator change its value?

Yes, simplifying a fraction with a 0 in the numerator or denominator can change its value. This is because simplification involves dividing both the numerator and denominator by their greatest common factor, which can result in a different value for the fraction.

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