This is the whole thing: the seven claims, their ceded amounts stored negative, and the net each one reaches by the single rule
net = gross + ceded. The exercise is this same table with the net column left for you to predict — starting from the naive guess that adding a negative somehow adds.
The trap the exercise sets is the one the sign rule exists to remove. The naive column reads gross + |ceded|: for C4 that is 760 + 100 = 860, as if the cession grew the loss. But ceded is stored negative, so 760 + (−100) = 660 — the cession shrinks it. Adding a negative is the subtraction; you never write a minus sign.
The seven nets
| Claim | Gross | Ceded | Naive gross + \|ceded\| |
Net gross + ceded |
|---|---|---|---|---|
| C1 | 80 | 0 | 80 | 80 |
| C2 | 240 | −40 | 280 | 200 |
| C3 | 420 | −120 | 540 | 300 |
| C4 | 760 | −100 | 860 | 660 |
| C5 | 1,300 | −300 | 1,600 | 1,000 |
| C6 | 90 | −90 | 180 | 0 |
| ATT | 350 | −50 | 400 | 300 |
Only C1 agrees — because ceding nothing (+0) is the one case where sign cannot bite. Every other row moves the opposite way from the naive guess: the book goes from a gross of 3,240 to a net of 2,540, a fall of exactly the −700 ceded. C6 is the sharp one: cede its whole 90 and it nets to 0, not 180.
Live and green
The same seven claims, every prediction now equal to gross + ceded. Press Run — every row ✓.
Fill in the predicted net for each of the seven claims using nothing but net = gross + ceded, with ceded stored negative. Verify every prediction against the computed net in a grid — all rows must come back green — and show the book totals summing to a net of 2,540.
Green all the way down means you have the sign rule in your hands, not just your head: a cession is a negative amount, and net is what you get by summing — never by subtracting. That is the convention every later lesson (and the real engine) leans on.
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