Learn Italian: Faremo ridurre la quantità di zucchero. - We will have the quantity of sugar reduced.

This sentence uses the Italian causative construction. When you arrange for someone else to do an action instead of doing it yourself, Italian uses fare followed directly by an infinitive. So faremo ridurre translates to 'we will have [it] reduced' or 'we will make [someone] reduce [it]'.

Why can't I translate this literally as Avremo la quantità ridotta?

Translating 'to have something done' word-for-word using avere does not work in Italian. You must always use the fare + infinitive structure to express this concept.

If I wanted to apply this lesson's fractions, how would I say 'We will have the quantity of sugar halved'?

You could use the fraction la metà (the half) and say Faremo ridurre la quantità di zucchero alla metà (We will have the quantity of sugar reduced to half). Alternatively, you could use the specific verb dimezzare (to halve) and say Faremo dimezzare la quantità di zucchero.

Why is it di zucchero and not dello zucchero?

When referring to the general material or contents of a measure or quantity, Italian uses a simple di without the definite article. It functions just like saying un chilo di zucchero (a kilo of sugar).