Percentages

Some of the most common questions I get deal with percentages. These type of questions come in four forms:
1. What is some percentage of some number.
2. What percent is [some fraction].
3. Some number is [what percent] of some number.
4. Some number is some percent of [what number].

Solution to form 1:
Example:
What is 30% of 120. This question is simple for some to see, for others it is not. My first response to this type of question is to ask the question, "Is 30% a number?" The answer to that is a resounding NO! 30% is not a number however .30 is a numerical representation of 30%. We cannot make any mathematical calculations with 30% however we certainly can with .30. So now we know that 30% is .30 in numerical form, we multiply it by 120 to get our answer. Remember, change the percentage in a number that you can make mathematical calculations with.

Solution to form 2:
Example:
What percent is 8/10. The solution to this problem is based on understanding the meaning of the word percent. Percent is a combination of two words, per and cent. Most people recognize the word per: miles per hour, dollars per hour, etc. Cent means 100 such as in the word century which means one hundred years. Therefore the word percent can be thought of as per one hundred. To make a percent out of this, just make the denominator one hundred by either multiplication or division. In this case in order to make 10 into 100 we multiply it by 10. Then we just do the same to the numerator. Any number over one hundred is the same as the percentage. In this case 8/10 turns into 80/100 which is equal to 80%.

Solution to form 3:
Example:
5 is what percent of 10. The solution to this problem lies in understanding the basic equation for the percentage. The equation is [number] * x% = [number]. In our problem the word of is attached to the number ten. The word of gives you a clue as to which number is to be multiplied by the percentage. Therefore the equation is 10x = 5. Now simply solve for x by dividing by 10 on each side. x = 1/2. And as previously mentioned we can convert this to a percentage by multiplying the denominator and numerator by fifty which gives 50/100, or 50%.

Solution to form 4:
Example:
20 is 50% of what? Again this problems requires the understanding of the equation for percentages. The word of gives a clue as to what number is to mulitiplied by the percentage. Unlike example 3, this number is unknown. An additional step of converting the percentage to a number is necessary also. Simply put the percentage in a fraction with 100 as the denominator, 50/100, then divide which gives .5. Now the equation is .5x = 20. Now we solve for x by dividing by .5 giving 40. And yes, 50% of 40 is 20.

I welcome your comments as to how to make my solutions more readable and easy to understand. Also if there are errors please please please correct me. Thank you.