How to work out percentages
90In order to find x percent of any number the general way of doing that is to multiply the number by the percentage. Since percentage means hundredths of any number, percentages are written with the decimal point moved two places toward the left-hand side. With whole numbers the decimal point does not show, and since moving the decimal point over one place would indicate tenths, examples of how percentages should be written before multiplying are: .05 (five percent) or .20 (20 percent). An example is find 40% of 80: Multiply 80 (since its a whole number you don't see the decimal point) by 0.40 (which is how percentages can be written, although the 0 before the decimal point isn't really necessary). The answer is 32.
Multiplying any number by any percentage (and remembering to include the decimal points in the answer) will give the percentage.
Quick tricks for finding percentages can be used. For example, if one wants to find 30% of a number s/he can start with the original number, mentally move the decimal point over one place (in order to find 10% really quickly) and then mulitply that 10% by 3 (because 10 x 3 =30). Any time the percentage involved is divisible by 10 this trick can be used.
Another quick trick for finding 5 percent is to move the decimal point over one place (again, to find 10 percent easily) and divide that result in half (because half of 10 is 5).
Finding percentages that are multiples of 5 (for example, 25) can be done in three steps: Move the decimal point over one place to get 10%, divide that figure in half to get 5%, and then mulitply that figure by 5 (because 5 x 5 = 25).
Also, knowing that 10% equals 1/10th of any number means that finding 10% can also be done by dividing by 10.
Most people are familiar with the fact that a quarter (25 cents) is 1/4th of 100 and that 50 cents is 1/2 of 100. Keeping those basics in mind, one can easy remember that finding 25% of any number means dividing it by 4 and that finding 50% of any number means dividing it by 2.
In the case of something like 75% figuring that out could be done either by using the above divisible-by-5 method or, if its easier, finding 25% and multiplying that by 3 (because 3 x 25 = 75).
A trick for finding 40% might be moving the decimal point over one to get 10% and either remembering that figure or writing it down. Then divide the number for which you're trying to find 40% of by 2. Once you have half of the number subtract that 10% you first figured out - and you've got your 40%.
The finding-10% trick/aid can also be turned into a finding=1% trick/aid. If you move the decimal point over two places you have found 1% of any number. You can easily multiply that 1% to get any other percentage simply by asking "how many 1's are in this percentage?". For example, to find 20 percent you can first find 1% and then multiply that 1% by the 20 (because there are 20 1's in 20). This will also let you find, for example, the 20%.
Finally, there is the issue of figuring out a tip in a restaurant. Again, the quick way (for 15%) is to move the decimal over one place to get the 10%, divide the 10% to figure out what 5% is, and then add together the 10% and 5%. A 20% tip is easier - just get the 10% and multiply it by 2.
Comments
I like your maths,
Thanks for very good lesson
Good tips, I always forget and have to call my husband...
i still dont get it
Oh noo..... don't tell me that. :) Let's see: One percent equals one one-hundredth of any whole. If you cut up a giant pie into one hundred pieces each of those pieces would equal one percent. Ten of those pieces would equal ten percent.
To find the percent of any number write a decimal point followed by the percent you want to find. For example, to write 40% as .40. What that means is 40 one-hundredths of the whole. To find something like 40% of any number multiply that number by the .40 (40% written in a way that lets you multiply). You'll get a number that shows that 40% of the whole is.
The trick for finding 40% quick is to remember that 40 is 4 times 10. Finding 10% is easy because to do that you just move the decimal point on place. (For example, 10% of 80 is 8. Finding 40% is just a matter of finding that 10% and multiply by 4 (because 4 x 10 equals 40).
So what is the percentage of 6% in 580 ?
Well, it is the 580 multiplied by .06 (the .06 represents 6 1/100ths). The answer is 34.80.
Another way to do it is to quickly realize that 10% of 580 can be found by moving the decimal point over one place, and getting 58.00. 1% of 580 can be found by moving the decimal point over yet one more place (5.80).
You can then find 6% by multiplying the 5.80 by 6 (because 6 equals 6 1's). Again, of course, you will get 34.80.
How would you figure out 6.25% of 300? Like a grocery bill of $300.00 and the sales tax, which will be 6.25%?
Ordinarily, if you had paper or a calculator, you'd multiply $300.00 by 6.25, remembering, of course, to count over 4 places for the decimal point in the answer.
If you're in a store and can't do that, I think the way I'd do it is this. I could easily know in my head that 1% of $300 is $3. (Since 1% of $100 is $1, one-one hundredth of a hundred, 1% of $300 is $3. Instead of having one imaginary "pie" with 100 pieces you have 3 imaginary pies with 100 pieces.)
So, since I would know that 1% of $300 is $3 I would then do two things:
First, because I know that 6 is 6 x 1, I would multiply $3 (the 1%) by 6 (which would tell me what 6% is). I'd, of course, get $18.00. I'd tuck that number in my head (or you could write it somewhere), while I figured out "Part II" of the process.
Part II is knowing that .25 is not a whole percent. It's just a quarter of a percent. Since you've already figured out that 1% of $300 is $3, figure out what one-fourth or 1/4 of that is to figure out how much the .25 is. You probably know what one-fourth of $3 is in your head, but if you didn't you could divide the $3 by 4 to get .75.
For the person who needs a a trick to figure out what 1/4 (or .25) of $3.00 is, think of this: It's simple to know that one-quarter of $1 is 25 cents. Since you're dealng with $3.00, not $1.00, multiply that 25 cents by 3. You now have that .25 of $3.00. Now that you have the .75, which is one quarter of one percent of $300.00, you can add that to the $18.00 you got (as 6% of $300).
6.25 percent of $300 is $18.25.
In other words, to find something like 6.25 percent of anything, if you separate it into two little problems (what is 6 percent? what is one quarter of a percent?), and then add the two results, you get the answer.
What you're doing is keeping in mind that a whole percent (what's on one side of the decimal point) is one thing, and a fraction of a percent (what's on the other side of the decimal point) is another thing. You figure out those two easy things, add them together, and there you have it (most of the time - busy stores are known to make us confused sometimes :)).
wow thank i got a A on my test
Excellent, 7th Grade Kid. :)
thank you your page realy help out a old timer like myself going back to school is a hard thing to do after you,v been out of it for so long.Thank again
Lisa, you naughty woman,,, 6.25% of 300 = 18.75 (not 18.25) I realise its just a typo on your part but thanks to you, i was clueless about percentages until i arrived here, thank you for getting me going again. Top tip excercise!!, if you buy something that includes vat at 17.5% try working out the vat content before you get back to the car!! the theory is the same.. and the receipt will give you the answer!!
Thanks for pointing out the typo. That is typical of the kind of thing I do - dumb typos/mistakes on the stuff that matters, rather than mistakes/typos on stuff that doesn't matter as much. :)
thanks this helps i knew tis b4 but forgot it i havent used presentages in a while
Could you tell me how to work out what the % difference is between £16 & £17. Many Thanks
Great hub!!
Very detailed explanations..
There's this equation that says, 55% of 72 = ? But the thing is that I came up to the Ans: 95.4 and I'm confused because the answer is even larger than the real estate number set which is (72). Can someone PLEASE help we with this with sugar and ice-cream on top!!!??
Sincerely,
A 6th Grader :)
Lisa Hw your rea;ling smart at phsical and mental mathematics. If only you were here to help me with the thery But your not But reading all the Comments you posted can help me a little, WHY does mathematics have to be so HARD I'm only in grade 6 for crying out loud. Only 6 more years in school :(. Some one please help me!!!!!
Sincerely,
A confused 6th Grader That needs alot of help
Hope someone answers!!!
6th Grader: Sorry I took a while to see this, but here's my response:
55% of 72 is 39.6The regular way to find 55 percent of 72 would be to multiply the 72 by .55 (the decimal point shows 55/100ths, in other words, percent). If you had a dollar's worth of pennies, and separated out 55 of the 100 pennies you'd be looking at 55% of that dollar's worth of pennies.Another way to work it out would be:Look at easy tricks to figuring out .55%. Notice that you already know that there are 5 10's in 50.So decide to figure out 10% by moving the decimal over. Write that number down down.10% of 72 is 7.20.Now, though, you still need to figure out what the additional 5% is, but that's easy too:5 is half of 10, so 5% of 72 is 3.60 (because 10% is 7.20 you just divide it by two to find the 5%/half). Write down that 3.60 (the 5%).Since you've already figured out that 50% is half of 100% (of 72) you know that 50% equals 36.(You can either find that 50% by dividing the 72.00 by 2 or else multiply the 7.20 (10%) by 5 (because there are 5 10's in 50).You now that know have the 50% of 72. That is 36. You still have to add the 5% to it, though, because you're looking, of course, for 55% - not 50%.If you add that additional 5% (the 3.60 you wrote down before) to the 50%, you'll get the 39.60 (which is the 55% of 72.)You can check your answer by keeping in mind that 100 minus 55 equals 45. If you were to look for 45 of 72 you should come up with a number that, when added to your 39.60, should amount to 100% of 72. By multiplying 72 by .45 (percent - remember the decimal point) you'll get 32.40. If you add the 32.40 (the 45 percent) to the 39.60 (the 55 percent you got before), you'll find the two numbers add up to 72.00. That's because, again, 72 is 100% of 72 - and 45 and 55 add up to 100%.
Chikka, Math isn't always as hard as it can seem to be when you're in school. I'm not a math teacher, and math has never been my favorite subject (whatsoever); but when somehow all the things they try to teach in school just seem a lot easier once you get old enough to kind of see how easy things really are.
Something a lot of students don't realize is when they're "all nervous" and tense about homework or school subjects brain chemicals can actually change and make concentrating on what you're trying to learn more difficult.
What I recall about being around your age is not seeing math the way I eventually came to see it. As a student, I saw it as a bunch of unrelated things that were used to find numbers (or something like that). Once I got older I started to see that math is like a giant puzzles that makes one, big, picture (or whole) and that doing things like finding fractions and percents were really just different ways of seeing the pieces of that puzzle.
Another simple way to imagine math is to always kind of keep that picture of 100 pennies in your mind. You can imagine how you could multiply that dollar's worth of pennies by any number you want, or if there were a way to cut the pennies into tiny, equal, pieces, you'd be dealing with fractions (of 1). Math, though, is little more than ways of playing with those "pennies". Another way to see how math is nothing more than something that represents real stuff in the world might be to get something like a thousand Bingo chips or Poker chips; or else cut some paper into thousands of equal pieces and just play with it. Divide it into little groups of paper, add groups together, stack them up in equal stacks, and then make new stacks with different amounts of them.
I guess my point is that it's important not to think of numbers as "just numbers on paper" and math operations as "just isolated things you have to learn". While more advanced math can certainly seem a little trickier, in terms of drawing a connect connection to something like stacks of Poker chips or pennies, if you can get very comfortable seeing how 6th-grade math is pretty much a matter of that "whole" puzzle with all those different ways of altering the pieces of it; it may give you a sense of feeling more sure and ready to take on the more advanced math later.
I can give you some words to describe what I have on my desk right now, and you'll know that the words I type represent something very real and concrete. For example: cup of coffee, stapler, telephone. You have no problem knowing exactly what the words represent. Well, if I gave you a number that number would represent something every bit as concrete and real as the coffee cup, stapler, and phone are. If I tell you I have 4 books on my desk and tell you I'll take one away, you'll automatically imagine how I now have 3 books on my desk. The number of books I mentioned tells you nothing about what the books are, how big they are, or what color covers they have. Numbers represent, as you know, how many of anything there is, was, or will be. Numbers do a separate job than words do, but the thing with math is that it is about learning tricks for playing with numbers.
Maybe it would help if you could try to always imagine how every number in the world represents a poker chip or a part of poker chip.
Finally, something else that may possibly help you get a stronger feel for the way numbers fit together: Take a piece of paper, rule off ten or eleven vertical colums and, maybe, 20 horizontal rows. If you haven't already done this (or if it has been a while) start by making a multiplication chart with numbers 1 through 20 down the left-hand side, and numbers 1 through 10 or so across the top.
You'll find filling in the chart fairly easy, but as you fill it in notice there's a real "system going on" to the whole thing. Then try a different kind of multiplication chart. Try setting it up the say way but imagining, say, that you'll be paid 5.00 an hour for work. Down the side put something like "Week 1", Week 2", "Week 3" etc. and across the top head the columns with, say, 1 hour, 2 hours, 3 hours, etc.
Imagine how much you could make working different numbers of hours each week, and then once you have your whole chart done you could notice how you could do easily check on something like, "If I worked for 20 hours a week how much will I have at the end of Week 4?" "If I worked for 12 hours a week how much would I have by the end of Week 3?" It doesn't have to be hours worked. It could be number of DVD's you'll be collecting, number of music files, or anything. The point is if you make yourself some charts when you have a little fre e time you'll start to get a real feel for how math is that bunch of puzzles pieces that fit together.
Someone hasn't managed to help you feel sure of math. If you take a little time to make yourself some multiplication tables (strange as that may seem) you'll be using what you already know, as well as noticing a few things you may have missed along the way. You'll be the one in charge of setting up your own math problems and what you'll do with them. It's one of the best ways to get that proverbial "hands on" experience and knowledge.
I hope all these words haven't just been a giant bore to you (or anyone else), but when people can really see the relationship of numbers to real life things (even though sometimes though things are abstract) math can be pretty easy.
Not sure if this went through the stystem, but i just wanted to say that you should have a donation button on this page for all your hard-good work your doing!!
Good job;)
It did go through, but after I replied to your first post I thought of something I should have included:
Actually, yesterday I did run into a $700,000 house I wouldn't mind buying if I had the extra money. Do you think I could hire myself out as a "Sixth-grade, math-homework-doer" and earn enough to buy that 14-room house, which always looks so great at Christmas time? :)
In the interest of full disclosure, I was a kid who had no trouble learning math in elementary school, but when I got to seventh grade I was put in an "experimental modern math" class (which came to be the math that is now taught in schools). I did ok until my family moved, and because the new school didn't have the same math program the other school had, I was put in yet another and more advanced "modern math" class for a couple of years.
Maybe it was the sudden jump, or maybe it was the teacher, but from then on I never could see how that particular math "related to real life". I had my good grades in high school math under certain circumstances, but my inability to find high-school math "applicable to real life" (bizarre as that sounds to anyone who knows better, including my more mature and present self) made it close to impossible for me to "waste my free time" on math homework (!!!). So, whatever homework I did I did in English class (where the material came easily to me and didn't require paying attention).
As a kid, I blamed myself for not being able to make myself do what I truly wanted to do and knew I should be doing. I was about 40 years old when I finally figured out that I hadn't been lazy or careless. I had been without a teacher who knew enough to just point out how math applies to real life and gives us a new way to approach problem solving - even when the problem isn't a mathematical one.
Kindergarten and first-grade children are routinely shown the "apples and oranges" problems, but when kids get to sixth grade or so, and the math is no longer about simply adding and substracting, I think adults sometimes don't realize that some kids (maybe most) still need to see how something like Algebra is used in real-life problem-solving. Sometimes, too, maybe kids need to learn not just one way to find something like percentages, but a number of different little tricks that - when they see them - will help them see how it all fits together.
I grew up to be a person who is ok with math. In fact, I grew up to be a person who actually uses Algebra in my real-life problem-solving, even though I've chosen to work in areas that are more words- or people-focused. Still, I know the schools are full of kids who are - to one degree or another - like I was, with some having their grades only mildly affected but others having their academic journey more seriously harmed.
In a way I feel like a fraud, presuming to attempt to offer tricks on even something as elementary as percentages; but then again, there's a part of me that thinks there's a chance a "non-math" person may be able to explain things to another "non-math" person in a way the other person relates to more.
I don't over-estimate the degree to which my little percentages hub may be of any help to anyone; but if it turns out that it's of a little help to a few students who, for one reason or another, didn't quite catch on in class, then, to me, that makes the half hour or so I spent writing so much more well spent than it would have been on some other activities.
Again, thanks for your kind words. (I suppose, though, I'll have to wait on that 14-room house for now. Maybe if I'd had a better love of math when I was in sixth grade I would have become an architect or engineer, instead of dreaming of becoming an English teacher or social worker. :))
Thanks for all your help needed to look up on percentages for a test im taking and youve really helped :-)
We usually grab a calculator when we need some math. This info is so useful when there is no calculator at hand. Thanks
G'day Lisa
I finally do get it - you've put it so simply & I could use my calculator (at last!) to follow. You have a gift & it's so generous of you to share it with people.
My question is - Please can you tell me how do I get 2.4% of something - I thought about cheating and rounding it up to 3% to make it easier - but that doesn't improve my knowledge at all. I can understand when it's .25% or .75% but what about this sort of thing how do I calculate that?
Thank you so much for being you
Jen
Thanks for your nice words, Jen (but - believe me - it's no gift. It's more a matter of survival at the supermarket. :) )
Generally, I'd find 2.45% of any number by using the above "tricks" to find 24% of the number, and move the decimal point over one play to the left-hand side. For example, if you know that 24% of $100 is, of course, $24.00; then moving the decimal over one place to the left would give you $2.40 (which is the 2.4% of $100.00).
Another approach (that's easy but more complicated than the above quick approach) is:
Turn the 2.4% problem into two different problems: Since 2.4% is 2% plus 4 tenths of a percent, you could easily do it by first thinking of the number you're trying to find the percentage of, moving the decimal point over to get what 1% of that number is. Once you have the 1% you can then make the two different problems.
For example, if the problem is 2.4% of $100.00, you know immediately that 10% (or 1/10) of $100.00 is $10.00. That means that moving the decimal point over one place to the left will show you $1.00, which is, of course, 1% (1/100) of $100.00. (All the words I'm using to describe this initial process make it seems like a far bigger deal than really doing it is. )
Once you have your 1% keep that in mind (or write it down), because that's what will let you find your answers easily.
This is when you break the problem down into two very easy problems:
Since you want to find 2.4% you want to find 2% plus 4/10 of one percent.
The first thing is to find 2% by simply multiply the 1% by 2. In this simple case, since 1% is $1.00, mulitply that $1.00 by 2 is, of course, $2.00. You've got your 2% of $100.00. Keep that figure in mind, or write it down, until you do the second simple problem, which is:
Think about that 1% again ($1.00). Move the decimal point over one place to get get one-tenth of a percent (because now you're working with the numbers on the right-hand side of the decimal point 2.4%). Moving the decimal point will turn the $1.00 into .10 (ten cents). Since you now know that .10 is one-tenth of one percent, all you have to do is multiply it by the 4, and you'll get the .40 cents, which is 4/10 of a percent of $100.00. (Again, all the words make the problem look like a far bigger deal than it really is.)
Now that you know that 2% of your $100.00 is $2.00; and that .4% of $100.00 is .40 cents, all you have to do is add them together. You get $2.40 (which is, of course, the $2.40 you would get by figuring out 24% and moving the decimal place over one place).
In other words turn the problem into two little problems, dealing separately with the numbers on each side of the decimal point . Then add them together.
Thanks again, for your kind words. :)
Hi Lisa, i wanted to work out the difference in percentage between two figures. How would I work out the difference (in percentage) between 29,000 and 3,500. Basically both those figures are average attendances for football matches between 2006 and 2007, i wanted to find out how much in a percentage the attendence has dropped in the year. Thanks for your help :)
Hi, James. This particular type of calculation goes a little past the kind of "quickie mental tricks" I have for percentages that apply to grocery shopping, tips, and sales taxes. Most people would prefer to use a calculator for this type of calculation.
What you would need to do is figure out the difference between 29000 and 3500 (which is 25500). Because you're interested in what percentage 25500 is of 29000, you would divide the 25500 (the difference) by 29000. After calculating that, you would multiply the answer by 100. Depending on what you're doing you may choose to round, but if you do there will always be a slight discrepancy if you try to "back check" your figures.
(In other words, it used to be 29000 but went down by 25500, so what you need to know is what percentage of that original number (29000) is that 25500. )
You can check your calculations by figuring out what percentage of 29000 the 3500 is (divide 3500 by 29000 and multiply the answer by 100). Once you have what percent (parts of 100%) 3500 is, you can substract that percent from 100 - and you should get an answer that shows what percent of 29000 the 25500 is. (The 3500 is x percent of the original 29000, and the 25500 difference is x percent of the original 29000, and those percentages should add up to 100% of the 29000).
I got 87.9 for 25500; and 12.1 for the 3500. The 87.9 and 12.1 add up to 100%.
I'm including here links to a few sites that do a more "professional" job of explaining how to do this type of calculation (in order of helpfulness, in my opinion). I'm also including a "non-professional" link that adds a simple remark that may be worth including.
This is an excellent one (scroll down to where this type of calculation is done):
http://www.copydesk.org/words/math.htm
Here is one that shows it in a different way:
http://mathcentral.uregina.ca/QQ/database/QQ.09.06
These three links are also good:
http://www.helpingwithmath.com/by_subject/percenta
http://download.oracle.com/docs/html/B13915_04/per there's someone's simple remark on a non-math site:
http://answers.yahoo.com/question/index?qid=200708
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Comments
I think you should have a Donation button on this page for all your good-hard work your doing!! really!!
Good job:)
Thank you. A donation button sounds good to me, but I don't think HubPages would approve. :)
Timely topic, thanks! WHo can't use this?!
working
Albert says:
8 months ago
wow thanks alot u helped greatly. i owe u.