@matrix For algebra you snap these smooth pieces over the 1s, 10s, 100s blocks, hiding the individual units that comprise each block & illustrating that their value is currently unknown.
@matrix i hate when people use / or ÷ for division inline, it's fucking ambigious and no one ever used it seriously in any materials in my school or university. It's always over-under notation because that is unambiguous.
@matrix Most of that problem with overly-complex syntax would be quickly solved by simply using Polish or reverse-Polish notation. Every operator takes two operands (the first and second to its right):

Polish:
/ 6 * 2 + 1 2
/ 6 * 2 3
/ 6 6
1

or

* / 6 2 + 1 2
* / 6 2 3
* 3 3
9

Add (((parenthesis))) to make it LISP and thus cooler:
(/ 6 (* 2 (+ 1 2))) and (* (/ 6 2) (+ 1 2))

But I guess will never happen cuz tradition and all of that.
@matrix When I was taught this, it was explained that brackets always have the highest priority during multiplication, so in the 6/2(1+2) example, you'd have 6/2(3) and the 2(3) takes priority over the 6/2 because it's got brackets. Apparently that's not the way it's normally taught? Bracket multiplication taking priority over regular multiplication/division feels more intuitive than treating it the same as regular multiplication. I still got the correct result of 1 using pemdas.
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