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.

My Background

Some of you might like to know who the author of this blog is. My name is Pete Berardi. You can find a biography page and resume on my website http://www.peteberardi.com/. I have been a math tutor at San Diego City College for over a year. Fall of 2008 was my third semester and I love tutoring mathematics. I have declared myself as a math major and have taken Trigonometry, Precalculus, and Caluculus I,II, and III at San Diego City College. In the Spring 2009 I will be taking classes at City College and at SDSU. After completely mastering college level Algebra, I feel fully qualified to post solutions to common problems. In addition, as a tutor, students come to me with the hardest problems, therefore I can anticipate what some students will struggle with. Please feel free to leave comments of my solutions. I am always looking for ways to explain problems to students in a way that they understand and retain the information. Also if you have questions that you would like answered, feel free to post them or email them to me. Teaching mathematics, in my opinion, is fun and highly enjoyable.

Title of the Blog (mathiskras)

In addition to studying mathematics I am also studying the Russian language. I originally wanted this blog to be called mathisbeautiful, however that name was taken. Since the word beautiful in Russian is krasivaya, short for it being kras, I thought this would be a great substitution. As a Math tutor, teaching most Algebra I, Algebra II, Trigonometry, and Precalculus, I know the problems that most students have. The problems I am asked about seem to have a recurring theme. This site will be a listing of the tough problems that students face and need help on. The blog will state the problem and give a solution in a way such that a teacher would give it full credit on an exam.