Magic int when dividing by float?

Question

C++ / C#

Hello. C began to study quite recently, and here, as it turned out, there is a lot of "magic" that I do not understand.

#include <stdio.h>
int main()
{
  int a = 13;
  float b = 4.7;
  printf("%d", b/a); //на выходе получаем 660764199 
  printf("%d", b*a); //а здесь - -1207959552
  return 0;
}

When you try to divide/multiply an int by a float (or a float by an int), and then printf printf through the conversion symbol
for integers, that is, %d, the program produces some incomprehensible cosmic numbers.
I realized that you need to use %f and everything will be fine.
But I want to understand where these numbers come from? Since, according to my logic, the answer should have simply discarded the fractional part
and displayed a rounded version. So, let's say, why if int a = 12 is divided by float b = 6, and output through %d it turns out 0, but through %f it comes out 2.0? Or why 13/4.7 is the number mentioned above, and not just 2?

Answer 1

Weird numbers are taken when one type is stored in a memory cell, and printf expects to see another, therefore it incorrectly represents it. Printf will not round or otherwise convert types for you, what they tell him, he will output.

Answer 2

and then in printf output through the conversion character for integers, i.e. %d

It's not a conversion character, nothing is converted: you yourself are telling (fooling) printf about the type of data passed.
The transformation is done like this
printf("%d", (int)(b*a));