The phrase "without giving it much thought" is correct and usable in written English.
It can be used when describing a situation in which someone did something impulsively, without careful consideration or deliberation. For example: "Without giving it much thought, he agreed to take on the extra project."
It would be easy to walk past the New York iSchool without giving it much thought.
Two years ago, without giving it much thought, Mr. Cartwright made the "and Daughters" decision.
There's a couple of people I would attack without giving it much thought".
Without giving it much thought, I offered my grandfather's lard-and-soy-sauce soup.
So, I naturally tossed a dryer sheet into every load, except for towels, without giving it much thought.
You're at your desk and, without giving it much thought, you start reaching over for your water bottle, or your pen.
Emily, a New York University senior who prefers not to use her last name, took on thousands of dollars of student-loan debt without giving it much thought--until now.
A review of those affidavits, which several companies believed would remain secret, showed that gift giving has been part of the state contracting process for years, without companies giving it much thought, a pattern of behavior that led to Gov. John G. Rowland's resignation amid allegations that he had received gifts from employees and state contractors.
I used them during my thesis research and blessed the magical person who put it together without really giving it much thought of how they were created.
For example, without bothering to give it much thought, I had always assumed that if I were drafted into military service I could ride it out in some noncombatant role, along with others as idealistic or cowardly as I am.
She hadn't given it much thought.
