Step by step
The question
Question: work out 9 factorial over 7 factorial.
9!7! =
1 Write out top and bottom
We write both factorials out.
9 factorial on top, 7 factorial at the bottom.
9!7! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 17 × 6 × 5 × 4 × 3 × 2 × 1
2 Cancel
7 times 6 times 5 times 4 times 3 times 2 times 1 is on top and at the bottom.
A top and a bottom divided by the same number: they cancel.
Careful!
We never divide 9 by 7.
We cancel the numbers that are the same.
Careful: cancel the same numbers
What is left is 9 × 8.
9!7! = 9 × 8
3 Multiply
9 times 8 is 72.
9 × 8 = 72
So it is 72.
9!7! = 72
4 Check
Let's check: 9 factorial is 9 times 8, times 7 factorial.
9! = 9 × 8 × 7!
So dividing by 7 factorial leaves 9 times 8: 72.
So the answer is right!
9! ÷ 7! → 9 × 8 = 72
Let's look back.
First: write out top and bottom.
Then: cancel.
Then: multiply.
Last: check.
Answer
9!7! = 72