This is the correct way to teach Math to children, but it makes parents crazy ! 🙂
Why anything multiplying by 0 gives 0 ?
0.x + 0.x = (0 + 0).x [distribution law]
= 0.x [definition of 0]
Subtracting 0.x from both sides,
0.x = 0.x
Parents teach children the intuitive way:
“nothing times anything is nothing”
but this is not rigorous.
Later in life, the children would learn that when doing “zero times” of any thing (eg. bad behaviors: fighting, stealing…) produces “something” (good) 🙂
In the USA and UK, many parents grow up feeling great antipathy towards Math, whereas in Asia like China, Japan, Korea, HK, Singapore, and Europe (eg. France), we grow up fearing Math, probably because of how Math was taught in schools. I remember during schools (and University) Math teachers / professors (men or women) were the fearest teaching staff who threatened to fail you.