dividend is non-commutative:
8÷2=4 ≠ 2÷8=1/4
8÷2÷2=2 ≠ 2÷8÷2=1/8
divisors are commutative. multipliers are also commutative with divisor
8÷2÷4=1 = 8÷4÷2=1
50÷5x3=30 = 50x3÷5=30
how to explain that?
For the first: $$ a \div b \div c = a \div (b\cdot c) = a \div (c\cdot b) = a \div c \div b $$ This may be easier to see when using fraction notation:
$$ a \div b \div c = a \cdot \frac{1}{b} \cdot \frac{1}{c} = \frac{a}{bc} = \frac{a}{cb} = a \div c \div b $$
On a slightly more technical level, this is a consequence of the fact that when we say $a \div b$ we mean $ab^{-1}$, understood as "$a$ times the multiplicative inverse of $b$." Similarly, $a \div b \div c$ means $ab^{-1}c^{-1}$. But it turns out that $b^{-1}c^{-1} = (cb)^{-1}$, so we get that $a \div b \div c = a \div (c\cdot b)$.