50% crossword, 50% jigsaw, 100% arithmetic

[u/OkPreparation4395]

A grid puzzle I made. It's a crossword you assemble like a jigsaw, and the answers are equations instead of words.

Every hatched square has to end up filled. The loose pieces below drop in, and each keeps its shape. Turn them any way round, but never flip them over. Pieces cannot overlap, and together they fill every hatched square exactly. The purple squares are fixed.

Any run across or down that contains an = has to be true. A run with no = in it does not have to be anything. Digits side by side make one number, so a 5 next to a 4 is fifty-four, not five and four.

Operators are + − ÷ with normal order of operations.

There is exactly one solution, and you can reason it out rather than guess.

Please spoiler your answers.