[ProtectOurFreedom]

“HOW MANY QUARTERS ARE THERE IN ONE HALF?” — That’s the third grade solution and a very good illustration for that age level. Clever using “quarters.” You can see the answer TWO by inspection.

By ninth grade, you better be able to solve it symbolically / algebraically:

(1/2) / (1/4) =

(1/2) x (4/1) / (1/4) * (4/1) =

(1/2) x (4/1) / 1 =

(1/2) x (4) =

(4/2) =

2

[Lonesome in Massachussets]

By ninth grade, yes. But division by fractions was taught around fifth grade when I was in school, definitely not third. I went to Catholic school, and had 795 in the Math Level II SAT Achievement Test in high school, so I think I was okay in grammar school math. I maintain that teaching it symbolically is absolutely the wrong way to teach it. Teach it intuitively, then show how the symbols can facilitate calculation.

Math instruction in this country is a disgrace. See Richard Feymann's book Mr Feynmann, You Must Be Joking where he was invited to review high school math textbooks by the California Department of Education. Everything he criticized is summed up by your example.