Step by step
The question
Question: work out 7 factorial over 5 factorial.
7!5! =
1 Write out top and bottom
We write both factorials out.
7 factorial on top, 5 factorial at the bottom.
7!5! = 7 × 6 × 5 × 4 × 3 × 2 × 15 × 4 × 3 × 2 × 1
2 Cancel
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 7 by 5.
We cancel the numbers that are the same.
Careful: cancel the same numbers
What is left is 7 × 6.
7!5! = 7 × 6
3 Multiply
7 times 6 is 42.
7 × 6 = 42
So it is 42.
7!5! = 42
4 Check
Let's check: 7 factorial is 7 times 6, times 5 factorial.
7! = 7 × 6 × 5!
So dividing by 5 factorial leaves 7 times 6: 42.
So the answer is right!
7! ÷ 5! → 7 × 6 = 42
Let's look back.
First: write out top and bottom.
Then: cancel.
Then: multiply.
Last: check.
Answer
7!5! = 42