If you're asked to convert a fraction to a percent

…but aren’t told what to make it a percent of.

To clarify:

I have a friend who just started culinary school. She has to take a basic math class as part of it, and having been an art student for a few years before this, and then not taken any high-level math in high-school before that, is a little rusty, so she asked me for some help, being that I have an engineering degree and in theory really know my math.

Well, she said the question is this:

What are the following numbers in percent?

1 1/8
3 1/5

That’s it. It never said as a percent of what. If they were all fractions less than 1, like the second one, I would just assume they meant as a percent of 1. But what about 1 1/8 and 3 1/5? Are they also a percent of 1? Or maybe as a percent of 100? As a percet of the nearest whole number?

I think the most natural interpretation is as a percentage of 1. So 3 1/5 is 320%.

Agreed. I would say

1 1/8 = 112.5%
2/5 = 40%
3 1/5 = 320%

It really isn’t any different than 2/5 representing 40%. 40% of what? Whatever 2/5 was representing. You have 2/5 of something. So whatever that something is, you identically have 40% of it.

If you have 1 1/8 oranges, then you have 112.5% of 1 orange.

If you have 2/5 of a pound, you have 40% of 1 pound.

If you have 3 1/5 squares of chocolate, you have 320% of 1 square.

I don’t see how there is any ambiguity. You are just changing a fraction to be expressed as x/100.

To make the concept easy for her to grasp simply tell her that 1. = 100%

For the fractional amount tell her to divide 100 by the bottom number of the fraction then multilply that result by the top number of the fraction for the percent.

Sometimes a simple question has a simple answer:

per cent [L. per centum] n. per hundred; by the hundred; in, to, or for every hundred.

“Percent” is a shortcut way of saying “per centum”, or a ratio (fraction) with a denominator of 100. So the question was basically asking to convert the given fractions to fractions with 100 as a denominator.

Much of mathematics is manipulating numbers that aren’t associated with anything physical. You don’t question the statement “2 + 2 = 4” by saying, “Two what plus two what equals four what?” Similarly, asking “What is 1/2 in fourths?”, you don’t need to know “half of what.” You can just use the law of proportions to solve by setting the first fraction equal to a second fraction with a variable in the numerator:

1   x
- = -
2   4

Cross-multiplying gives:
2x = 4


which then means two fourths is the equivalent of 1/2.

So for percents, just use the fraction x/100:

 1      x
1- = ---
 8   100

9    x
- = ---
8   100

8x = 900

x = 112.5

which means 112.5 hundredths is equivalent to 1 1/8. Replaceing “hundredths” with “percent” or “%” gives 112.5%

Some of the replies in this thread have overlooked what might be confusing you. 1 1/8 (One and one-eighth) must be converted to 9/8 (8/8 = 1, so 8/8 plus 1/8 = 9/8) before you divide the numerator by the denominator to get the decimal, which is then converted to percent by moving the decimal two places to the right.

Yes, it is possible to have more than 100% of something, at least mathematically. If the fraction is greater than 1, then the percent will be greater than 100 and vice-versa.

2 apples are 200% of 1 apple.

OK, I figured it was something simple like that, Leave it to me to over analyze it and try to add in details that don’t need to be there. :smack:
After doing high level-math with polynomials and such for the last few years, you forget some of the basics. :stuck_out_tongue: But ask me to find some eigen values? Forget about it!