Math rules (Fractions) ?

I would like you to go deeper into the question but, okay so a fraction a part of a whole number okay? Also fractions can always be written as a decimal. Fractions have to forms improper and proper. Proper means it is like: 1 3/4.

But improper is: 7/4. That's all for now.

Fractions

A. Special Fractions1. simplifies to b. 2. does not simplify any further. 3. simplifies to 0.4. is undefined. Examples does not simplify. is undefined. So is. Special note: Why is it OK to have 0 on top (in the numerator) and not on the bottom (in the denominator) ? Consider for a moment what division means. The reason that is because 2·5 = 10. The fraction because 2·0 = 0. The fraction can't equal anything. There is no number you can multiply by 0 and get 10 as your answer. The fraction is undefined. What about? It's undefined, too, but for a slightly different reason. If you multiply the 0 in the denominator by any number at all you get the 0 in the numerator. It seems that can equal any number. As a result we say is indeterminate, which is a special kind of undefined expression. B. Negative Fractions 1. is the same as and 2. simplifies to 3. is NOT the same as Examples C. Cancellation (a ≠ 0, b ≠ 0, c ≠ 0) 1. cancels to 12. cancels to 3. cancels to 4. cancels to 5. cancels to b6. cancels to b Examples D. Addition1. 2. 3. Examples E. Subtraction1. 2. 3. 4. Examples F. Multiplication1. 2. 3. Examples Careful!1. 2. Mixed numbers are shorthand for addition and not multiplication. For example, means and NOT. G. Division1. 2. 3. Examples