Step by step
The question
Question: work out 8 factorial over 6 factorial.
8!6! =
1 Write out top and bottom
We write both factorials out.
8 factorial on top, 6 factorial at the bottom.
8!6! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 16 × 5 × 4 × 3 × 2 × 1
2 Cancel
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 8 by 6.
We cancel the numbers that are the same.
Careful: cancel the same numbers
What is left is 8 × 7.
8!6! = 8 × 7
3 Multiply
8 times 7 is 56.
8 × 7 = 56
So it is 56.
8!6! = 56
4 Check
Let's check: 8 factorial is 8 times 7, times 6 factorial.
8! = 8 × 7 × 6!
So dividing by 6 factorial leaves 8 times 7: 56.
So the answer is right!
8! ÷ 6! → 8 × 7 = 56
Let's look back.
First: write out top and bottom.
Then: cancel.
Then: multiply.
Last: check.
Answer
8!6! = 56