If you multiplied by 100% thats the same as saying mulitply by 1
Same goes for division, it would mean divide by 1.
5 x 1 is still 5
5 / 1 is still 5
so you can see that multiplying and dividing by 100% will not change the value of the number. If you were to multiply and divide by 200% thats saying that your multiplier or divisor would be 2:
5 x 2 = 10
5 / 2 = 5/2 or 2.5
so essentially 100% is 100/100 = 1