The upper row is the basic shape: add the salt and the water to get the whole solution, then divide the salt by that. The lower row adds 100 g of water. The amount of salt does not change and the concentration falls anyway.
How to read this board
"The whole solution" is a card of its own. Buried inside a formula, what you are dividing by stops being visible. 20 ÷ (20+180) hides it; seeing the number 200 appear on a card once makes it much harder to divide by the wrong thing.
The horizontal stacked bar is the split between salt and water. The concentration is exactly the salt's share of that bar, so the number and the picture are saying the same thing.
Where it trips you up
The places that are easy to get wrong, next to how to check each one on the board.
| Where it trips you up | Why that happens | How the board shows it |
|---|---|---|
| Dividing by the water | "Dissolve the salt in the water" points you at the water. You divide by what you have after dissolving it. | 20 g of salt in 180 g of water: divide by the water and you get 11.1%, divide by the solution and you get 10.0%. The board gives the second. |
| Adding water feels like losing salt | The concentration goes down, so it seems as though there is less salt. | The lower row. The salt card stays at 20 g. Only the denominator moves. |
| Evaporating the water off | Adding is easy to picture; taking away stops people. The salt stays put and only the whole solution shrinks. | Put a negative number in "water added later". The denominator falls and the concentration rises. This treats only the water as leaving and no salt as coming out — the same simplification as the undissolved-salt row below. |
| Adding salt moves both parts of the fraction | Unlike water, salt increases the numerator and the denominator. Fixing only one of them gives the wrong answer. | Raise the salt card. The whole-solution card follows it up. |
| Forgetting to turn it back into a percent | Leave off the ×100 and the answer stays at 0.1. | The concentration card carries a % unit. If it reads 0.1, the ×100 is missing. |
| Salt that will not dissolve | There is a limit. Anything beyond it never enters the solution. | The board ignores that limit. Push the salt far enough up and it will report a concentration that could not exist. |
Concentration states what share of the whole the salt is. Try adding water, adding salt and removing water one at a time and you can watch which of the numerator and denominator moved, and which way the percentage went. The shape — a part over a whole — is the same one behind a batting average or a pass rate.
Try this
- Add 100 g of water — 10.0% becomes 6.7%, with the salt still at 20 g. Diluting means the denominator alone grows.
- Double the salt — both parts of the fraction grow, so the concentration does not double. 20 → 40 g takes 10.0% to 18.2%.
- Make the added water negative — that is evaporation. The denominator shrinks and the concentration climbs, which is the direction that gets salt out of seawater.