When it does not come out even

You already cut a floor into whole shares. Now there are 12 tiles and 5 people. A whole tile each will not land. The leftover is still a share (bråk).

Origins

Egypt
c. 1850–1650 BCE

Scribes already split loaves and fields that would not come out even. The leftover was named as a part of one, not thrown away.

Same floors,
cut smaller

Sharing gave you whole tiles first. This page is what you do with the tiles that will not make another full round.

Honesty: nobody invented leftover parts. People cut food and land long before a name for the cut.

12 tiles. 5 people. Watch the leftover.

First give whole tiles, equal. What will not make another full round sits aside. Then cut those leftover tiles into as many parts as people — one extra piece each.

Drag people or tiles. Grey tiles are leftover. Striped bits are the leftover, cut.

12 tiles · 5 people · 2 each · leftover 2 · each leftover part 2/5

Tiles 12 People 5

Whole round first. Then cut the leftover.

A cut question, then a job

Write 12 ÷ 5 as a mixed number.

Nothing is at stake. Nobody is waiting for a tile.

Five people, twelve floor tiles. You cannot give three whole tiles each — that would need fifteen. Give two each. Two tiles left. Cut those two into five equal strips. Each person takes two strips: two fifths extra.

Each person gets 2 and 2/5 tiles. That is a job.

Jobs — estimate first

Cover the answer. Say a range. Then open.

1. Loaf. 3 loaves, 4 people. Whole loaves each? What leftover part?

Estimate: less than one loaf each, more than half?

Answer

0 whole each. Leftover 3. Cut 3 into 4: each gets 3/4 of a loaf.

2. Same 12, more people. 12 tiles, 8 people. Whole each, leftover?

A bit more than one each?

Answer

1 each (8 tiles), leftover 4. Four tiles among 8 people: 4/8 = 1/2 extra. Each gets 1 and 1/2.

3. Why not smash. Why sit leftover aside first, instead of cutting every tile at once?

So you still see the whole share.

Answer

Whole tiles are still tiles. The leftover is the only cut you need. A names that leftover part, not a new kind of number.

Gate — four, all required

Each right gate item is 20 points. Hands-on is 20. Wrong is 0 until you retry and get it. Next unlocks only at 100 — and only if that page exists.

1. What is this tool doing?

2. 12 tiles, 5 people. Whole each, leftover?

3. Those 2 leftover tiles, 5 people. Each extra part?

4. Which is a real question?