Precalculus uses factorials for counting and the binomial theorem, where they show up as quotients like 17! over 4! times 13!. Write the larger factorial down until it reaches the smaller one, cancel, and only then multiply.
Also taught in Algebra 2, at its own level and with its own examples.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
12 - 3 is 9, so write 12! down to 9!: 12 × 11 × 10 × 9!.
Cancel the 9!, leaving 12 × 11 × 10 = 1320 on top.
Divide by 3! = 6: 1320 ÷ 6 = 220.
The answer is 220.
Where students go wrong
Cancelling factorials like ordinary numbers: 8!/4! is not 2!. Expand the top down to 4! and cancel, which leaves 8 × 7 × 6 × 5 = 1680.
Also called simplifying factorials, n factorial or factorial expressions.
Questions about these worksheets
Yes. Every factorials sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the factorials questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Multiplying both factorials out first. 12! is nearly half a billion, and the whole point is that almost all of it cancels before you multiply anything.