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# Rates and units

**Gist.** "X per Y" is a rate: quantity = rate × number of units; identical units combine only by addition and subtraction (UnitDep, Roy & Roth 2017).

A comparative before "than" says "more" ("18 inches farther than the grasshopper") unless it is a lesser word ("26 inches lesser than the frog", "4 push-ups less than David").

Money is one quantity whatever it is called: "$ 15", "15 dollars" and "how much money" count the same thing.

**Examples.** "$2 per egg", "60 miles an hour", "3 books each".

**Sources.** Roy & Roth 2017 (AAAI), "Unit Dependency Graph".

```
rate: per each every
total: total altogether together combined sum
money: money dollar cent buck
```

```
rate -> multiply : rate × number of units = total
total -> add : total — the sum of the parts
decrease -> subtract : there is less — subtraction
increase -> add : there is more — addition
```

```
multiply: times product
add: plus sum
subtract: minus difference
```

```
compare: more than fewer less difference
lesser: fewer less lesser shorter smaller younger lighter lower cheaper
```

```
compare -> subtract : "how many more / fewer" — the difference, subtraction (Mitra & Baral 2016: comparison)
```

```
divide: divided quotient
share: equally among split distribute share
```

```
rate -> divide : a rate is found from the whole and the number of units by division (whole ÷ count)
share -> divide : sharing equally among several — division
```

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