Question

he had been playing fast and _______with the department's budget​

Answer 1

He had been playing fast and loose with the department's budget.

Detailed answer

The fast and loose is an idiom. The sentence is now a proper sentence.

• The sentence now conveys that the person is illegally, and without any idea using the budget of the department which he/she is not meant to use.
• The word "loose" creates a grammatically appropriate sentence that has a proper meaning.
• No other word can be used at this moment as this is an idiom and cannot be changed.