3 ÷ 1/2 = how many half-rods fit in 3 · keep-change-flip is what division means geometrically · runs locally
3 ÷ 1/2 = how many 1/2-rods fit in 3? = 3 × 2/1 = 6 · keep-change-flip = measurement division · dividing by a/b flips to b/a because you're asking how many fit