ELI5 multiplying fractions and a few other basic rules a 28

[Guest]

Okay so I'm dumb so I thought I would ask you some rally basic questions. I still do not understand how multiply fractions or decimals get smaller. I have a general memory of asking this question in grade school, and after sometime of the teacher trying to explain it to me after class, I just pretended like I understood and left. To be clear I know the rule its not really a question of execution, I just feel silly cuz I just do it not really knowing why. I just didn't understand how if you multiplied two things they could get smaller. Also could you explain how multiply -1*10000 is negative. another weird one for me. Remember I'm dumb so use small words...

[Guest]

"I still do not understand how multiply fractions or decimals get smaller."

Do you understand what a fraction is? "1/3" is itself smaller than 1- it is 1 cut into three equal parts. And if you multiply 1/3 by any thing, that is the same as cutting that "thing" into three equal parts so naturally each part is smaller than the original thing.

(That applies only to "proper fraction", "improper fractions" where the numerator is larger than the denominator, like 7/3, when multiplyed by a number, make it larger.)

As for "-1*10000", do you agree that 1- 1= 1+ (-1)= 0? And the "distributive law" says that a(b+ c)= ab+ ac. So 10000(1+ (-1))= 10000+ (-1)(10000)= 0. That is, (-1)(10000) is the "additive inverse" of 10000, i.e. -10000.

[Angus53]

Understanding fractions involves recognizing that they represent parts of a whole; multiplying fractions or decimals by a number means dividing that number into smaller parts making each part smaller than the original.

For example, "1/3" signifies one part of a whole divided into three equal parts; when multiplied by a number, it subdivides that number, resulting in smaller parts. Similarly, in "-1 * 10000," applying the distributive law demonstrates that it equals the additive inverse of 10000, which is -10000, contributing to the understanding of numerical operations.