1What You Have
Cut into twelfths so fourths and thirds can share a grid.
2The Group to Pull Out
One fourth of the same square is a group of 3 cells.
3Count the Groups
2 full groups + 2 of the 3 cells needed
= 2 2/3 groups
8 cells ÷ groups of 3 → 2 groups, then 2 out of 3 of another.
4The Shortcut It Proves
23 ÷ 14 = 23 × 41 = 83
keep · change · flip = 2 2/3 ✓
The flip isn't magic - it's the picture in #3, written as arithmetic.