Learn Russian: Мы пишем любую дробь через запятую.

In Russian math and everyday life, decimal fractions are written using a comma (запятая) instead of a decimal point. For example, "three point five" (3.5) is written as 3,5 and read as три целых пять десятых (three whole and five tenths).

Why do we use через (through/across) here to mean "using"?

In Russian typography, через followed by the accusative case is the standard way to describe the punctuation used to format or separate elements. You will often hear phrases like писать через дефис (to write with a hyphen) or писать через запятую (to write with a comma).

Why does запятая change to запятую here?

The preposition через requires the accusative case. Although запятая (comma) functions as a noun, it originated as an adjective and still declines like one. Therefore, its feminine accusative ending is -ую, resulting in запятую.

Is дробь in the accusative case here since it is the direct object?

Yes, it is in the accusative case, which you can see from the modifier любую. Because дробь (fraction) is a feminine noun ending in a soft sign (third declension), its accusative form looks exactly the same as its nominative form.