Problem - A student multiplied a number by 5/6 instead of 6/5. What is the percentage error in the?

Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it's 7/8" thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8" is going to be 7/16". If you write that out you have 1/2 x 7/8 = 7/16. And you notice that 1/2 is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.

Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn't it? Practice this a bit and people will think you went to wizard school.

Percent is simply a ruler with 100 marks. The only confusion is trying to keep track of what the marks represent, since that changes from time to time.

You are given that the correct value is 6/5 and the wrong value is 5/6. The error is:

e = 6/5 - 5/6

The first thing we need to do is to get these numbers on the same ruler. The easy way to do that is called "cross multiply.

e = 6/5 x 6/6 - 5/6 x 5/5 = 36/30 - 25/30

It's called cross multiply because it looks like you went "6 x 5 and 5 x 6".

e = 11/30

Now you want to know the percent of 11/30 relative to 6/5, remembering that we can use 6/5 = 36/30. IOW we want 11 as a percent of 36. So we have a simple formula for that:

11/30 x 100% = 36.67%

Big difference!