Working With Percentages

     Typical percentage problems ask for a percent increase, decrease, or percentage of an initial amount. Others ask how a certain amount relates to a second amount. In doing these problems the old fashioned way, you change the percentage to a decimal and multiply. In same case, you will change a decimal back to a percentage for the final answer. And sometimes you need to change fractions to decimals and back again. First, we will talk about percentages in general just to get a comfortable feel as to what they are and a little manipulating.
     Percentage means "per hundred." Anything out of a hundred can easily be expressed as a percent. 76 out of 100 is 76%, 34 out of 100 is 34%, etc. You can relate this to money. one dollar is a whole, and the cents are the "percents." Now you now why a penny is called a cent. One penny is 1% of a dollar. This is helpful to remember when changing decimals to percents and percents to decimals. But we need to think like a math person. So, we need to relate "per hundred" to other easy totals.
     Half of something is always obviously 50%. It should be easy for you to cut things in half in your head. This is sometimes helpful for getting a starting point. 2 out 4, 3 out of 6, 12 out of 24 are all 50%. If you cut the first number in half in the previous examples, you will have half of 50%, or 25%. 1 out of 4, 1.5 out of 6, 6 out of 24 are all 25%. You could carry this further by cutting those new numbers in half and come up with 12.5%.
     Let's look at more relationships. 36 out of 100 is the same as 18 out of 50. Just cut each number in half. Do it again and you have 9 out of 25, 4.5 out of 12.5, etc. This is helpful when given totals close to 50 or 25. For instance, 17 out of 50 is 34%. (Do the reverse as before and double them.) 27 out of 50 is 54%, 45 out of 50 is 95%, etc. Each "fiftieth" represents 2%.
     For 25's, multiply by four. (There are 4 quarters in a dollar.) 7 out of 25 is 28% (4 x 7 = 28), 10 out of 25 if 40%, etc. Each "twenty-fifth" represents 4%.
     It is similar for 20's. There are five 20's in a dollar, so multiply by 5. 13 out of 20 is 65%. (5 x 13 = 65.) 15 out of 20 is 75%, etc. Each "twentieth" represents 5%.
     Anything out of 10 can be readily made into a percentage as well. There are 10 dimes in a dollar, so multiply by ten. 6 out of 10 is 60%, 4 out of 10 is 40%, etc. Each "tenth" represents 10%.
     How about greater than 100? 34 out of 200 is 17%. We have 34 out of "two" hundreds, so we split the 34 in half. 17 per each hundred. 48 out of 300 is 16%. We have 48 for "three" hundreds, so divide 48 by 3.
     In closing this first part, try thinking of some ways on our own to relate percentages easily.

Finding a Percent

     Let's go the other way as the previous section by looking at a percentage of a certain number. If you have had trouble with percentages or just want an easy way, take notes. It is VERY easy to find 10% of any number. Just move the decimal point one place to the left. If there is no decimal point, it is a given that it is on the very end to the right. Example find 10% of 67. The decimal point is to the right of the 7. Moving it one place to the left will make it 6.7. That is 10% of 67. That's just too easy. How about 10% of  37.93 ? Moving the decimal one place left gives 3.793. Try a few of these on your own.
     How about 1% ? It is just as easy to find 1% as it is to find 10%. If you noticed, the numbers for 10% are the same as the original numbers. That's what makes 1% and 10% easy-just move the decimal. To find 1%, move the decimal one more place to the left after you find 10%. Or, you could just move it 2 places right away. For example, find 1% of 78. The decimal is to the right of 78. (Remember 78 is the same as 78.0, 78.00, etc.) Moving it one place left gives 10% or 7.8. Moving it one more gives .78 or if you like writing, 0.78. The 0 is just a place holder, does not affect the value. If there are no numbers after moving the decimal, add zeroes. Example. 1% of 8. To move it 2 places left, we need to add a zero in front. 1% of 8 is .08 or 0.08. 1% of 59 is .59, etc. try some on your own.
     Perhaps you now realize how easy it is to find 5%. Just find 10% and cut it in half. Example: Find 5% of 34. 10% of 34 is 3.4, half of 3.4 is 1.7, so 5% of 34 is 1.7. Yes, you do need to practice cutting things in half.
     Most of you probably figured out how to rapidly find 2%, 4%, etc. For 2%, just add 1% + 1%. For 4%, add 1% + 1% + 1% +1%. Or, for 2% you could multiply 1% by 2 and 1% by 4 to get 4%. 9% could be gotten by subtracting 1% from 10%. 20% could be gotten by adding 10% + 10%. 45% could be gotten by adding 10% +
     What makes this useful? Some people do not like multiplying without a calculator. Especially decimals. For a problem like:
     Find 12% of 75
For some of you, that may have panicked you without a calculator. But now, instead of doing .12 x 75, just find 10% and 1%. Because as you now know, 10% + 1% + 1% = 12%. So, 12% of 75 = 7.5 + .75 + .75. And that is a piece of cake!
     The combinations are endless. 17% = 10% + 5% + 2%, 35% = 10% + 10% +10% + 5%, etc. Finding a percentage of a number should now be almost a no-brainer!

 
 
Changing a Decimal to a Percent and Percent to Decimal

     To change a percent to a decimal, move the decimal 2 places to the left and drop the percent sign. Some people have trouble remembering this. Again, relate it to money. one cent is 1%. Written as a decimal and dollar sign, we all know 1 cent is $.01. So for 1%, the decimal is to the right of the 1 and we move it 2 places left. We need to add a zero as a place holder. But again, some people do have trouble remembering where the decimal goes. Many want to write 9% as .9 and 5% as .5. But think of dollars and cents. 9% is 9 cents or $.09. 5% is the same as 5 cents or $.05. 50 cents is 50% or $.50 or just .5. For 90%, we would write .9 or .90.
     In going from a decimal to a percent, again it helps to think of money. But the easiest way is to move the decimal 2 places to the right (the opposite as before) and add a percent sign. .9 is how we write 90 cents or 90%. Move the decimal in .9 2 places right, a zero as a place holder, and add a percent sign. How about .05 ? Move it to the right of 5, add a percent sign, and get 5%. But you did remember that .05 is 5 cents and that is 5%, right?
     This leads us to the old fashioned way of finding a percentage. You change the percentage to a decimal and multiply. For some, this is easier because it is the way they are most comfortable doing it. If it is, I urge you to keep on doing it that way. Don't fix something that isn't broke. For finding something like 47% of 80, simply multiply .47 x 80.