# How to Work Out Percentages - Some Tricks to Help You Work Out Percentages Without A Calculator

Updated on June 22, 2015

"Lisa" , a "social sciences enthusiast" and Mom of three grown kids, writes from personal experience/exposure and/or past research

## Author's Note

If you're looking for conventional/standard ways to do percent problems you'll find several links to "real" math sites by scrolling down toward the end of the main part of this Hub. That isn't the purpose of this Hub; and although I've considered including more conventional approaches here, I think it's most fair to people looking for help with percent problems to direct them to sites that do a better job showing those conventional approaches than I can. After all, that's the sole purpose of those sites. For more on the purpose/intent of this Hub see "More About This Hub" below.

## Some Handy "Tricks" for Doing "Percent Problems"

A Few Notes On The Basics:

In 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

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 multiply 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.

This Hub was originally written to show "quick mental tricks" for doing percent problems. It was written with adults in mind and in response to a request. It was not intended to offer more than those quick tricks for common percent problems. The aim was to offer people those tricks they could use in situations involving things like shopping and tipping. Sometimes we need a quick way to figure a tip or sales tax. Sometimes we want to know how much a product will cost when we learn it has a "75%-off price". The aim was to offer a few simple ways people can do percentage problems in their head that can come in handy, and that don't show up too frequently in the "standard" search on doing percentage problems.

When I wrote the Hub I didn't change the wording in the request, and now that it has taken on a nature/life of its own it is clear the title is no longer appropriate or sufficient (to describe the content). I could change the title, of course, but the Hub has found its place in search engines and has turned out to help a lot of people (usually young students) who were having some trouble "getting" how to do percentages. As a result, I don't want to change the title and risk the Hub's "getting lost to the ages".

The nature of the Hub evolved, though, because readers began asking for elaboration on the original approach (the "mental tricks") . From there, readers began asking about percent problems that went beyond the kind one would do using those "mental tricks".

Originally, I had approached writing this Hub (in answer to that question/request someone had posted) as if I were sitting at the dining room table, trying to help a middle-school or junior-high student understand percentage problems. So, it started out "folksy" and in terms that wouldn't show up in math books; and as things evolved and all those questions/comments continued to be posted, I continued to use the same approach.

The way I've seen it, if someone is asking how to figure a percent problem there's a good chance it's because they haven't already become comfortable "doing percents" as taught/being taught in school. So, as questions about finding percents have continued to come in (and as a lot of them have gone way beyond the original intent of this Hub), I've found myself using whatever words or combination of words and techniques I can "pull out of the air" in an attempt to make understanding what "is going on behind a percent problem". People who have trouble "getting" some things in math have that trouble because things like equations on paper don't mean anything to them.

In any case, the Hub has taken directions that weren't the original intent. At the same time, when new questions have been posted I've just figured, "It's easy enough for me to just answer them." As a result, the comments section of this Hub has become very much aimed at people for whom math class and math books haven't happened to be very effective (or wasn't effective enough for them to remember if they were students years ago).

The point is, if you're comfortable with math and having no particular challenge learning from math teachers or books, 1. You either don't need this Hub or else you need one of those conventional "how-to-do-math" sites, from which you can easily find that little extra bit of information you need., and 2. There's a good chance you'll find this particular absolutely "wacky".

If you've always been comfortable learning math there's also a good chance you can't imagine how a perfectly "smart" student may have trouble learning one thing or another, only because an adult hasn't figured out that he needs someone to think up a different way of presenting one thing or another.

Adults who may have, as students, once hit a "stumbling block" on one math thing or another, and adults who have ever had to watch a student struggle with one kind of problem or another (or most of them), will understand why I've left all the questions and answers in the "Comment" section on this Hub.

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• ### Standard Deviation and Variance By Hand: Steps to Calculate

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• AUTHOR

Lisa HW

7 years ago from Massachusetts

Thank you, everyone for your comments, kind words, and questions. They've helped raise issues beyond the original intent of this Hub, and if it weren't for the comments and questions I wouldn't have thought to include a whole lot of things that I hope may have been helpful to someone. Sincerely appreciated.

• llololollollo

7 years ago

omg tanks i was strugaling!

• AUTHOR

Lisa HW

8 years ago from Massachusetts

Shannon, if, by any chance, you're having trouble finding your own comment (Oct 11, 2011) and my reply, look farther up (toward the middle of the comments). I've discovered some "technical issue", and I don't know what to do about it right now.) In any case, your comment and mine are both there.

• AUTHOR

Lisa HW

8 years ago from Massachusetts

Shannon: I approved your comment for posting here, but for some reason it isn't showing up. (Technical problem I'm having.) I was going to re-type it here, but now I can't seem to find your version of it either.

In any case, you asked about problems such as finding out what percentage of 40 27 is, or how to find out something like what percentage of 50 13 is.

You would find the answer to that kind of percent problem this way:

First you divide the 27 by 40.

Then you multiply the answer by 100.

In the example of what percent of 50 13 is,

you would divide the 13 by 50.

Then you multiply the answer by 100, and you'll get 26%. (13 is 26% of 50).

You can check this one easily by thinking of this:

13 is 13% of 100. So, because 50 is half of 100, 13 would make "twice as much of a percentage". (Two times 13 is 26.)

Basically, what you want to figure out (for example, in the one with 27 and 40) is, "How can I chop this 40 into equal 27 equal little bits. That's why you divide the 27 by 40. Once you see what each of those equal little bits are "worth", you need to multiply them by the 100 because that's what will show you what percentage of 40 the number, 27, is.

I hope this helps. (And I'm sorry that I seem to have done something to make posting your comment a "technical problem". We've had some changes in settings on HubPages, and maybe I've done something wrong with my setting.)

• Shannon.

8 years ago

I'm doing a test tomorrow on this stuff, and I'm not sure how to work out things like 27 out of 40 as a percentage, I understand that to find 13 out of 50 as a percentage is just how many times can you fit 50 into 100 which is 2 then times 13 by 2 as well to get the answer I'm just very confused on how to find out numbers like 40 and others that you cant fit equally into 100 :/ Can anybody help pleaseee!

• ruach

8 years ago

it is a awesome site

• AUTHOR

Lisa HW

8 years ago from Massachusetts

Note to "Lost" (I don't really know what you're comment isn't showing up, but I'll reiterate it for anyone reading: "Lost" commented that s/he is "lost" because it "seems like the above info skips some steps").

Reply: Hi, Lost. I'm sorry the info isn't helpful. The Hub does skip steps because the aim was to try to offer people "quickie" tips for finding percentages in their head. A better resource for the conventional way to work out percentages can be found in the gray block near the top of this Hub, which contains links to math help.

If you have a question about any of quick-trick examples I've included here, feel free to ask; and I'll do my best to clarify anything. :)

• Chris

8 years ago

Lisa HW, Your dedication to this posting has been astounding to me. Your efforts are definitely appreciated!

• anonamous

8 years ago

exuse me, how do you work out 21 percent of something? i'm very stuck and urgently need help! thank you. :)

• AUTHOR

Lisa HW

8 years ago from Massachusetts

Sim, probably the quickest way to find something like 35% of anything, might be to do something like think of what 10% is and then divide that in half to get 5%. For 35% (because there are 7 5's in 35), multiply what you got for 5% by 7.

With something like 25% of anything (or, as you say, 50% of something), just dividing by 4 or 2 (whichever applies) is easiest.

• Sim

8 years ago

Sorry the example was for you to let me know what the 65% and the 69% would be as they are both only worth 25% or 35% of 60%.

So what would 65% be as a 25% of 60% and

what would 69% be as a 35% of 60%

if that makes sense?

obviously if the grade was 25%,25%,50% it would make it easier as we would merely half or quarter the grade to find out what it is of the %age.

Thanks.

• Sim

8 years ago

Yes Lisa,

You are quite right in your second-guessing.

40% of the whole module comes from the one exam result

and the other 60% is coming from two parts - online test 35% of that 60% and the assignment being the 35% of the 60%. Each of the pieces of work are worth 100 marks.

40% and 60% adding together to make the whole 100% for the module.

Ok so let's just say I throw some random numbers out here for you to make understanding a bit simpler for me as im currently not well AT ALL so this is all still a bit confusing,

These are examples;

For the 25% of the 60% online test I got 65%(MARKS OUT OF 100)

For the 35% of the 60% assignment I got 69%(MARKS OUT OF 100)

For the 40% exam I got 73% (MARKS OUT OF 100)

Thanks for the help so far..!! x

• AUTHOR

Lisa HW

8 years ago from Massachusetts

Sim, I shouldn't be second-guessing what you say here; but I'm wondering if what they're saying is that 40% of the grade will be based on a test; and the other 60% made up of the other two (assignment and exam) combined (with the assignment making up 35% of the whole grade, and the test making up the 25% of the whole grade. (25% and 35%, of course, add up to the 60 - so I was just wondering if that's what they doing.)

Having said that (and if it's going to 25% of 60, etc.), if I were aiming to do it quickly I'd think of 10% of the whole grade and first multiply it by 4. That's the 40% quickly. What's left would be the 60%.

From there I'd find 10% of that number (the 60%)and multiply it by 2 to get 20% of the 60%. Keeping in mind what that 10% of the 60% was, I'd think of half that (5% is half of 10, of course) and add it to the 20% to get the 25% of that 60%).

I'd do the same kind of thing to get the 35% of 60% (get the 10%, multiply it by 3 to get 30%; then after half of 10% to get the 35).

(I still suspect they're saying 40% of the grade will be based on the exam, 35 based on the assignment, and 25 based on the test. Maybe I'm wrong, of course. :) )

• Sim

8 years ago

For my university grades this year in one module they have decided to make life difficult for us.

The total marks come in the form of

a test (25% of 60%)

an assignment (35% of 60%)

an examination (40%)

Quite clearly the 40% won't be the difficult one to figure out, but I'm a bit baffled on figuring the 25% and 35% of 60%.. Help here please?

• Diane Inside

9 years ago

Hey lisa just loved the refresher. I always get befuddled when I go to the market and it is a 30% off sale. Ha Ha. Now I can remember how to work that out to see what the savings would be. Thanks.

• wt1s3rv3r

9 years ago

Good Post!

• BESBES

9 years ago

If you know what 15% of an amount is, how can you find out what the total amount is (100%)? I use to know how to figure it when I was in school but don't remember it now.

• AUTHOR

Lisa HW

9 years ago from Massachusetts

ss sneh, I was unaware of that particular percentage. LOL

• ss sneh

9 years ago from the Incredible India!

Hi! Do you know the percentage of Google finding- "how to work out percentages" - this hub? 99.999999% ! -- Thanks

• rajeev

9 years ago

18 people as top management working in a company of a total manpower 1570

what is percentage of the management

how it calculate

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Ivan, it does affect me. It's nice to think that the Hub has helped someone with a test in school. Thank you for coming back to share that nice piece of information.

• Ivan

9 years ago

Hi Lisa. This may not affect you but thanks to ur site I got 97% on my percentage and decimal test I showed my friend the site and he showed the teacher now the page is in our school bookmarks lol

• AUTHOR

Lisa HW

9 years ago from Massachusetts

sean w, thanks. The way you posted isn't just "an easier way" - it's pretty much THE way (as in "the way people learn in school how to do that kind of percentage problem). :)

I'm not so much addressing you here (since you seem to be all set when it comes to percentages now :) ); but you raised a point worth addressing about how there are pretty easy ways to do math problems; and how about how, in some ways, I've made things appear a lot more difficult by using a lot of words to try to explain how things are done.

This Hub began only as a "quick-mental-tricks" Hub, and it turned into one with people asking percentage-problem questions beyond quick mental tricks. Questions have come from young students, people who are having trouble with percentages, had trouble with that particular type of math problem in school, or just forgot.

Pretty much most of what I've offered in the Comments section (anything outside the "main Hub" here) is a matter of my assuming whoever has asked how to do one kind of problem or another could use someone to explain in a way other than the way math books or math teachers explain (because the "more conventional way" of teaching how to a percentage doesn't always work well for some people).

So what's here (as far as my responses to questions goes), is a whole lot of wordiness (and even "wackiness", at least within the context of math) that comes from my kind of stabbing-in-dark and trying to think of some "non-standard" way to make what's going on with percentage problems clearer to anyone who isn't comfortable with them.

One reason people forget what they learned in math (whether it's with percentage problems or other kinds of problems) is that they don't see "what's going on behind the written equation". It can look like "nothing but numbers/letters on paper" (even if they know what each number/letter represents and so can do the equation). What often happens is people learn how to do one kind of math problem in school, and then they forget a few years letter because they never really learned "what was going on behind the equation" enough for it to stay with them. It was just "one more kind of math problem to memorize".

I just thought it might be worth pointing out that if someone is looking for the "standard way" to do a percentage problem they'll be better off going to one of the links offered here. People looking for any quick mental tricks for doing percentages usually understand they won't be getting the "standard" way of doing things.

How all the comments seemed to evolve into being "regular" percentage-problem questions, I'm not sure - but that explains why there's so many unconventional approaches to doing things on this particular Hub. :)

sean (although the above wasn't particularly aimed at you and was instead aimed at kind of explaining to anyone else who reads from now on); thanks for pointing out something that never occurred to me (as a result of how this Hub started out as one thing and evolved into something else). This Hub has been up for awhile, and it has kind of evolved over time. You've given me some ideas of for making it better than it is now, so thanks.

• sean w

9 years ago

hi Sean

original price 240 special offer price 210

240 - 210 = 30

then 30/240 = 0.125 x 100 = 12.5%

cheers

sean w

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Sean, this gets beyond the "mental-tricks" category, but what you'd do is first see that at \$210, you'd be paying \$30 less. That \$30 is what you'd be focusing on.

You either want to know what percent of \$240 the \$30 is (because that will tell you what percent the price was reduced), or else you want to know what percent of \$240 the \$210 is (because that would tell you what percent you'd be paying - with whatever the difference between that and 100% is showing the percent reduction) (But forget this approach for now. I'm only mentioning it as something to keep in mind if a problem is ever easier to do by doing it this way.)

If you think of "percents" as "units" instead (or too), it can make seeing how this kind of problem works seem less complicated. I'm going to use the word, "units," because I think it can make it easier to describe what's happening in this type of problem.

Since you want to know what percent of \$240 the \$30 is, you first want to think about dividing up that \$30 into 240 equal "pieces". Why? Because you need to know the relationship between 30 and 240.

As you know, to figure out how many equal "pieces" you could divide the 30 into, you'd divide 30 by the 240 (and it would be easier to do that on a calculator, although you don't have to. It's just that I don't have a quick mental trick for this kind of percent problem).

Once you divide 30 by 240, you see that it comes out to 0.125

Here's the word, "units", comes in: The way to remember that you have to divide the smaller number by the larger one is to imagine how you have to come up with however many equal "units" ("pieces") would "go to"/"go with" each of the (in this case) 240 individual dollars (or "units"/"pieces").

So, you divide the \$30 difference in price by the original \$240 price, and you get the 0.125

Then just multiply that 0.125 by 100 because you want to know what relationship 100 of those 0.125 "units" would have to \$30.

Just by moving the decimal point over two places you can see that 0.125 by 100 is 12.50. If you feel more comfortable with doing it on a calculator, you'll get the same thing by multiply by a 100 on that.

You can double-check your math by finding 12.5% of 240 - and you'll see that it's 30.

Looking at the problem the other way (seeing what percent 210 is of 240), you can see that if 30 is 12.5%, 210 is 87.5% of the original 240 (because you're subtracting the 12.5 from 100% and seeing that what's left is 87.5)

Hope this helps.

• Sean

9 years ago

So how would you do a percent decrease or increase with an unknown percentage. Lets say you went to buy a dining room table that originally sold for \$240 and since it was a floor model it was reduced to \$210, what is the percent decrease from the original price?

• AUTHOR

Lisa HW

9 years ago from Massachusetts

sian-a, before I leave this for now, there is one quick mental trick that's different from the approach I used above:

With something like 40% of 45 I might "turn that 45 into 90", because that's divisible by 10 and would make using the above "tricks" easier.

Of course, since 90 is two times what 45 is, I'd have to divide the answer I got by 2.

So, I might do something like:

Turn the 45 into 90.

Think of 10% of 90 (which is, of course, 9)

To get 40% of 90 I'd know to multiply the 9 by 4

(because 9 is 10% and there are 4 10%'s in 40%)

So, since I know that 4 x 9 is 36, I'd see that 40% of 90 is 36.

Since I didn't really want 40% of 90 and really wanted 40% of 45, I'd have to think of what half of 36 is (and that's 18).

18 is 40% of 45, and you'll see (be able to check) that if multiply 45 by .40 on a calculator or paper.

There you have the 40% of 45 (with a somewhat odd approach, I know. :) )

• AUTHOR

Lisa HW

9 years ago from Massachusetts

sian-a, (I don't know if you're asking for an example of a "mental trick" or just how to figure out that particular kind of percentage problem). I'm going to go with just "how to figure it out" (no mental tricks for now), because I want to answer you but I don't quite have the time right now to write out how, exactly, I'd do that kind with a "mental trick". It takes a little time to think up how to explain something in a way I think may be easy to read) I figure, if you're asking how to do that percent in general, you need a quick answer. If you're just interested in a "mental quick-trick" to do it, I imagine it isn't any emergency. :)

Mental tricks aside, the simple answer to that one is multiply 45 by .40 either on paper or with a calculator.

Another way might be to move the decimal point to get 10% (4.5), and then multiply that by 4 (because there are 4 10%'s in 40%). (Someone might wonder what would even be the benefit of doing something like this approach on a calculator or paper, and the only benefit might be that for a student who's not comfortable with percentages, it can sometimes help to make a problem seem simpler (and then to change it back to what may have seem like a more difficult problem).

• sian-a

9 years ago

how do you work out 40% of 45 ?

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Ivan, not only do (and will) I remember you, but I mentioned you (and your "thing" about my age) to my sister over the weekend. LOL (She's around my age, so she sees the humor in my discomfort with admitting my precise age on the Internet.)

• Ivan

9 years ago

Dang Lisa you so smart lol I hope you remember me from comments above you rule

• AUTHOR

Lisa HW

9 years ago from Massachusetts

PC, Hi. I think there's a chance you just did a little something wrong with the calculator or missed a step (or something like that). I'm assuming you may have done a "percent trick" and were then checking it on the calculator?

If you were finding 5% of 763 you could do it first by thinking of how 10% of 763. All you do to get that is look at the 763, know it would have a decimal point after it (if the decimal point weren't invisible) (so it would be 763. ) and then move that decimal point you put in over one place toward your left hand. (so 10% would be 76.30)

Then all you do is divide that 10% (76.30) in half (because you know that 5 is half of 10).

Anyway, I'm going to guess about what you may have done (although I can't guess about that 1678-thing; I think that was a calculator thing, maybe):

If the problem were to find 50 percent of 763, to do that on a calculator you'd multiply 763 by .50 (which is what 50 percent would look like if you wrote it out). If you multiply 763 (punch that in first on that calculator) by .50 (forget the percent key on the calculator for now and just use the multiplication key) by .50 you'll get 381.5. Sometimes it's easy (in your head) to just think of dollars while you're doing percents. Turn everything into dollars - and if you weren't really dealing in dollars with the original problem, you can "turn things back into non-dollars" after you've done the math. It just helps you keep in mind where the decimal points and zeros go along the way).

Since 50% is half of 763, to check that 381.5 answer all you would do would be multiply the 381.5 times 2 to make sure there are really 2 381'5's in 763.

If you were finding five percent of 763 the five percent should look like this .05 (and you'd multiply the 763 by .05 either on a calculator or on paper).

For the most part, I can't really think of too many times you'd need to divide if you were either using the mental tricks here to find percent, or else using a calculator or paper to find percent. Usually, it's a matter of multiply by whatever percent you need to know.

The one reason I think you may have been dividing (if you were trying to do a percent problem) was if you were trying to approach the problem by finding 10% first and then dividing that in half to find 5%.

If you were trying to find half of 10%, you would have first seen that to get 10% of 763 you'd move the decimal point over one place toward your left hand (after you pictured an invisible decimal point being after the 3), you get 76.30. So if it were dollars, 10% of 763.00 would be 76.30.

If you originally had wanted to find five percent (.05) of 763, you'd need to divide that 76.30 (10%) you got in half (because 5 is half 10).

If you divide the 76.30 (ten percent) in half you get 38.15 (so that would 5 percent of 763).

Another guess about why you may have been dividing:

If you were trying to find fifty percent of 763 you could get that by dividing 763 by 2 - not by fifty percent. Again, if you're finding percent on a calculator, you multiply, putting in the "starting number".

If you trying to find fifty percent of 763, the reason you'd divide by 2 is because fifty percent is half of one-hundred percent.

There are four kinds of percent problems that are super easy to do in your head (which is why you can sometimes start with one of them and take it from there):

100% is all done for you with any number.

50% always means "just divide in half"

10% is easy because you just move the decimal point.

1% can be found by moving the decimal point 2 places over.

Keep in mind that if you find 1% you always multiply by whatever percent/number you want to find (that can help you feel like you understand percents better and can make what's happening with percents a little clearer for you).

Hope some of this helps.

• PERCENTS CHANGE!!

9 years ago

Hey, Im a 6th grader, I suck at math. So I read a few comments and stuff and went oh, I can do this!! so using my calculator I divide .5 into 763...and got 1678...I DONT KNOW HOW!!! Help!!

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Ivan - nope. Not 60, 70, or 80. LOL If you really have to push the age thing, I'm in my 50's (and still getting over the fact that I'm in not in my 40's, so that's as much I can make myself admit. LOL ) I'm not all that knowledgeable, but thanks for the compliment. I just try not to write or talk about the stuff I don't know and stick with the stuff I do. LOL

• Ivan

9 years ago

Lol sorry so are you like 60? That sounds right lol I'm just wondering cause iv never met a person as knowledgeable as you haha

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Maybe what the 15% confusing thing was that it showed up in the kind of problem that could be done most easily in a couple of different steps. The "tricks" I'm offering here are based on the more basic math facts that a lot of people are really comfortable with, even if they aren't finished with school or aren't "math people".

As I showed above, it's easy to find 10% of something. Since you can't find 5% the same way, the next-easiest thing to do is find 10% and divide it half (because finding 10% is simple, and because you know that 5 if half of 10).

Or, the other easy way would be to think of 1% and multiply that by 5.

What I'm trying to offer are "tricks" or different ways to figure percentages either in your head or without a lot of figuring on paper. I'm not offering the "usual" way of figuring percentages a lot of times here, because I was aiming to show those "quick tricks". So I can see how there are places where such odd tricks may not make sense to some people. :)

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Ivan - LOL. Nowhere near 80! I was in elementary school in the 1960s, and those teachers were - like - my grandmother's age (and she was born in 1881, so that's where I came up that era). My mother was in her 40's. If her mother had been alive she would have been in her 70's. With the exception of one, young, kindergarten, teacher; the youngest of the teachers in that school was way older than my mother - and the rest of them only got older from there!! A couple/few of them may have been born between, say, 1900 and 1920.

confused kid, I'm kind of confused about your post too. I'm just going take a couple of guesses about what you're asking. Please overlook it if I don't understand what you mean exactly:

If what you're asking if how to find 10% that's a really easy thing to do. 10% is always one-tenth of any number. All you have to do is look at (or think of) the number you want to find 10% of, and move its decimal point over. Since numbers don't always show up with decimal points (because the decimal point isn't really required for whole numbers), first you just have to think where the decimal point should.

For example, if the number is 33 you need to (at least while you're figuring ten percent) think of how the decimal point would be 33.0. Later you can take out the decimal point, but for figuring 10%/one-tenth, it makes things easy.

If the number you wanted 10% of was 105, you'd add the decimal point like this: 105.0

Once you know where the decimal point (even an invisible one) is in any number, all you have to do is move it one place over toward your left hand to find one-tenth (10%) of it. So, if you wanted 10% of 450: First you put in the decimal that you can't see (450.0). Then you move that decimal point over one place toward your left hand. It will look like this": 45.00 Since you're dealing with a whole number (like 450) you don't need those zeros after the decimal point. Because, when there is nothing but zeros after a decimal point it means you have a whole number.

So, once you see that 10% of 450(.0) shows up to be 45.00 you can drop off the zeros. You now have 45.

If you're looking for 10% of 15: You can see that 15 is a whole number. It's not 15.5 or 15.7, or anything like that. It's just plain, old, 15. All you do is add that invisible decimal point to 15. You add it right after the 15, so it should look like this (at least while you're doing your figuring): 15.0

Now, you move the decimal point over one place toward your left hand, and it will look like this: 1.50 That's 10% of 15. Since you can't drop off the 5 (because the only thing you can ever drop off are zeros that follow a decimal point); you'll see that 10% of 15 is 1.5. (You can drop off that zero because it's at the end).

In other words, any time you want to find 10% of any number all you have to do is divide that number by 10.

To find 1% you move the decimal point TWO places over toward your left hand. The good thing about finding 1% is that you can multiply 1% by whatever percentage-number you need to. If you want to find 4% of 50, all you have to do is find 1% of 50 (the way I showed above) and then multiply that 1% by 4.

There are other ways of finding percents that may make sense for a lot of people (especially someone who uses a calculator), so the only benefit to the approaches I'm showing here is they tend to make finding percentages easier (and something you can often do in your head).

Hope some of this is a little more helpful. Feel free to ask for further clarification if there's a chance I can make it any less confusing. :)

• confused kid

9 years ago

this is stupid i said suppose u don't no the percentage eg.10% and they just say find the percentage of 15

• Ivan

9 years ago

Hehe this is great Lisa but if your teachers are born late 1800s aren't you like 80? Not that it's bad because you know so so much

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Ivan, thank you for such nice words. I'm glad it was helpful (because sometimes people come to this Hub hoping to find it helpful and seeing it didn't help them very much). We (HubPages) writers get comments sent to us through e.mail, so when I see a question show up I'm always glad to at least try to answer it. This Hub is a different kind of Hub than a lot of the other Hubs I've written. I wrote in because someone asked how to do percents, so I figured these "tricks" might be helpful to someone. It turns out there are a lot of people (often students) looking for help on how to do one kind of math problem or another.

I'm not all that "smart" (trust me on that LOL ). With something like basic math stuff, though, a person doesn't need to be particularly great with math to find a few handy tricks.

I'd describe myself as "being confident with basic math problems", and because students and learning are something I've spent a lot of time thinking about (I have three grown kids who went through the public school system), I'd like to try to answer your question about how I got "confident" with this particular kind of math thing.

One thing that I think got me off on good footing with basic math was that I went to an old fashioned elementary school (no frills and not even a lot of the most common things, like a cafeteria or gym). The teachers were elderly (and I mean "elderly" - like born in the latest 1800's). They taught the basics in all subjects, but they were pretty good at it. So I think it's important that kids in the first few years of school learn the most basic things, like "math facts" (multiplication tables). Everything after learning those basic math facts is based on them.

Sixth grade was a lost year for me because the teacher was senile (truly senile - I'm not being funny). In seventh grade I was put in an "experimental math class", but then my parents moved and the new school didn't have the same kind of "experimental math". So halfway through the year I was "completely turned off" of math because I was fed up that I hadn't just been put back in a "regular" math class, rather than being jumped ahead to math that was more advanced than the the "experimental" math had been. I stopped doing all math homework for 7th and 8th grade. I was a thirteen-year-old girl with "better things to think about". LOL For high school I had matured, and so I "shaped up" once I got into math like Algebra and Geometry. I even took an extra math course (Business Math) because I thought something that "practical" might be useful.

Once I had been "separated from my earlier interest in math) when that sixth-grade teacher was as ineffective as she was, I never regained any particular enthusiasm for, or interest in, math. Maybe it was me (although I think it's this way for a lot of students, especially girls), but there were never any teachers who managed to know how to share their own enthusiasm (if they had any in the first place) for math.

Although I somehow managed to often get good grades; to me, math class was always a matter of teachers "droning on and on", or else (because math teachers usually used the board to show how things were done) I'd get aggravated because I'm not a "visual" learner. I'm an "auditory" learner.

I'd pick up a good part of what the teacher was saying, but I wasn't super confident with a lot of it. Then, because I wasn't interested in math, I'd get agitated when homework time came (and being agitated means being stressed; being stressed means having trouble concentrating because "stress hormones" rise and actually affect our ability to concentrate).

What I realized I needed to do was "never mind about the right terms" and even "never mind about how teachers say to do one thing or another"; and instead, put things (in my head) in my own terms and "find my own way to being more comfortable with" different things in math. Of course, that doesn't always cut it with a "show-your-work" kind of quiz or test; but where it did "cut it" was that I had the confidence to think I had "the right" to figure out my own ways of "getting to know math better" (rather than seeing it as a subject that "belonged" only to people who love it.

The words used in math aren't interesting words to a lot of students in the process of trying to learn it. Students who lean toward having stronger verbal-related skills can find math words so boring it can seem as if they all run into each other, and none of them particularly stands out as "memorable" or "interesting". A lot of the "droning on and on" just doesn't capture the attention of some students, and a lot of the people who teach math aren't particularly "verbal" people. They're "math" people.

My tip to any student who sometimes feels like he's "drowning" with one kind of math problem or another would be to "make yourself a life-line" by taking whatever you already have learned about math, putting things in words that make whatever you do already know seem more "catchy", and using that to pull yourself to "dry ground".

If you take whatever you already DO know, and "make it yours" by "mentally playing with it" (on paper if you need to), it can put you on that much better footing to then use the "sureness" you've built for yourself for learning the next thing in math. I guess the thing is there can be a gap betweeen what teachers try to teach and what students actually completely learn. Students (maybe particularly "verbal" students) need to find a way to fill in that gap in some way that works for them.

Students can't fill in that gap with anything but what they already have (in terms of knowledge of math). What they usually "have" is SOME knowledge of the subject and their own way of using words, as well as their own set of things that will make "seeing" the subject easier for them.

A lot of students don't have the confidence to try to think of their own ways of filling in that gap. In fact, a lot of students are not encouraged to do that. They're often told, "Here's what you need to do, and you need to do it this way." A lot of students think, "There's the teacher. The teachers knows the subject. Here's me. I don't like this subject, and I don't know it. End of story."

One student may never eventually "love" the subject; but trying to make it more "catchy" in one's mind by "playing with" what one already knows can at least eliminate having to overcome the fact that a student finds math tediously uninteresting. If a student can get to the point where he's at least comfortable with whatever he already knows, math no even needs to be interesting. It's then "turned into" something that's "matter-of-fact" to learn.

I think the challenge, though, is that students are pretty much on their own when it comes to that "figuring out ways to fill in that gap". They need to know how they best learn, how they can best recall things, and how to make something more interesting for themselves. They need to have enough confidence to say, "I need to do this my way, just for now, until I learn it better." I think they also need teachers and parents who understand that, for some students, "doing it my way first" helps fill in that "gap" (so they can then go on and do it "the right way").

I don't know if any of this is at all helpful. The length of my response probably very much backs up my claim that I'm more of a "verbal" person than a "math" person. LOL

• Ivan

9 years ago

Wow thanks for answering I get it now your the best and also it's cool how you still answer questions even though you made this 2 years ago!!! Lots of people just make a site answer 2 questions and leave. You need a donation button lol how are u so smart? How did u learn I really need to know because I get slot of presure from parents cause there both doctors but anyway I really appreciate what you do for us ur a legend u rock

• AUTHOR

Lisa HW

9 years ago from Massachusetts

I'm not completely sure if I understand your question correctly, but finding 45 percent of 20 in your head (of, if you need it, making a couple of quick notes on a scrap of paper) is easy. There are a few different ways you could use "quick tricks".

One easy way would be to aim to first figure out 5% percent, and because you already know that there are 9 5's in 45, all you'd have to do is multiply 5 percent by 9.

The quick way to find 5% if to think of 10% (because you know that there are 2 10's in 20.

So, first you see that 10% of 20 is 2. That means, of course, that half of 10% (5%) is 1.

Since you started out knowing that there are 9 5's in 45, all you have to do is multiply 9 by 1 in your head - and you've got your 45% of 20. 9 x 1 is, of course, 9 (which is 45% of 20).

-----

Another approach to some problems like this one:

When I first look at the 45% of 20 problem, my instinct is to think of how I already know that 45 is half of 90. That means if I figure out 90% all I have to do is think of what half of that is (or figure out what half of it is) to get 45%.

Finding 90% is easy because 90 is 10 less than 100, so all I have to do is see what 10% is - and then substract that from 20 to get 90%. Since it's easy to know that 2 is 10% (one tenth) of 20, and it's easy to know that if I substract 2 from 20 I'll get 18 (and, again, since 45% if half of 90%), I can easily see that 45% of 20 is 9.

-----

Another approach might be this:

Find (or think of) 40% of 20 first, then find (or think of) 5% of 20 - and add them together.

It's easy to find 40% by thinking of what 10% (one-tenth) of 20 is; and then multiplying it by 4 (because 40 amounts to 4 times 10).

So, since you know that one-tenth (10%) of 20 is 2, all you have to do is multiply 2 times 4 to get 8 or 40%. (Some people may want to jot that down until they get the 5% that they're going to add to the 8 they came up with when they figured out the 40% of 20.

Figuring out 5% is easy with this approach because you already figured out 10%. So, you just think of how half of the 10% (2 in the problem here) is 1.

Now all that needs to be done is add that 1 you just got to the 8 you got when you figured out how much 40% of 20 is - and you've got the 9.

In answer to your question about "timing by 100" you wouldn't do that if you had a problem like "find .45 of 20". You'd do that if the problem was one like: "What number is 9 45% of?"

If you're doing a problem like the 45% of 20 one, you don't really need to think about the decimal point unless/until you see that one is needed later. Calculators show percentage with the decimal point, so you can see exactly where the calculator is at any point in your calculations. When you're doing a problem like this in your head you can just think of 45% as "45" and deal with adding any decimal points later. For example, with a number like "20" the decimal point is "invisible" but would be after the zero.

If the problem were different, and were "find 0.045 of 20" you would use the same mental tricks as for 45% (.45) of 20, but then you'd know that you had to move the decimal point (even if you start out with an invisible decimal point in 20). The reason you'd move the decimal point over one place would be because you wanted to show that "9" (45%) divided by 10. So, instead of 9 (9.0), .045% of 20 would be .09 (because you moved that invisible decimal point that we don't see after 9 over one place (and added a zero in order to show that the decimal point had been moved over one place).

When the calculator shows that decimal point it's showing that you're finding 45 one-hundredths of 20 (because one-hundredths are "one-percents"). If there wasn't a decimal point it would look like you're multiplying 20 x 45.

When you do these "quick tricks" to find percentages, you kind of already have it in your head that finding percent; and when you do something like find 10% (one-tenth) because it's easy, you've already done the "dividing" you need to "get you into a percent mode" with whatever you do from there.

• Ivan

9 years ago

Lisa you have a great site your really smart! But is doing a percentagethe calculaterway which is making it a decimal like .45 of 20 really hard? Because i don't get the timeing by 100 thing please reply!!!

• AUTHOR

Lisa HW

9 years ago from Massachusetts

pam, the way you have the .10% written, that's one-tenth of a percent. Ten percent could be written .10 (one-tenth) or else 10%, but since, if you were to add the "invisible decimal point", you'd write 10.0 for ten; with both the decimal and percent sign it makes it one-tenth of a percent. (With both the decimal and percent sign, there's an "invisible zero" before the decimal point.

With the problem you posted, I'm going to use 10% to keep things simple. You can always move the decimal point later if you really want one-tenth of a percent.

I'm also going to use the word, "units" instead of "percents", because it can seem simpler:

If some original number was reduced by 10%, that would mean the 1,605,837 is 90 percent (or 90 "individual percents/units") of that original number.

Since you the 1,605,837 makes up 90 "units" of the original number you need to divide the 1,605,837 by 90 in order to see what one "unit" is.

Once you know what one "unit" is you can multiply that number by 100 to figure out what the original 100% was.

When you divide the 1,605,837 by 90 ("units") you get 17,842.63. If you multiply that by 100 (which you can, of course, just do by moving the decimal point over two places), you get 17,84263.

You can check your answer by finding 90% of 17,84263 and seeing that it's 1,604,837.

The above example is going with the problem that the 1,605,837 was what happened when you reduced a larger number by 10% (ten percent).

If it was reduced, instead, by a tenth of a percent you'd move the decimal point accordingly. You'd still start out by finding what number each of those 90 "units" represents.

There are other ways to do this kind of problem, but I think this way is the simplest for someone not entirely comfortable with percents, or just someone who likes to reduce the risk of making a mistake with a zero or decimal point somewhere earlier in the problem.

I just always find kind of using 10% as a "base" if possible makes things a lot simpler.

• pam

9 years ago

If your beginning amount is reduced by .10% and the result is 1,605,837; what was the beginning amount? Also is the .10% 1/tenth of a percent or is it 10 percent?

• AUTHOR

Lisa HW

9 years ago from Massachusetts

karina, I never thought much about them (I have other math things I hate, but not percentages). From what I've seen, though, I guess you're far from alone. :)

• karina

9 years ago

omg i totally hate percentages well anyway thanx 4 the lesson i learned something about this subject!....

• AUTHOR

Lisa HW

9 years ago from Massachusetts

To increase by a percentage, you would simply multiply the number by 100 percent plus whatever the percentage is. For example, if you want to add 20% of 100 you would either use a calculator to get 120% of 80; or else you could do some such problems in your head:

Since you already know that 80 is 100% of itself, you just have to figure out what 20% is and add that. An easy trick is to think of how 2 times 8 is 16 (if you do that you're leaving off the zero in the 80 in your head, but it makes it easy).

Then all you need to do is add 16 to 80 (which is 100% of itself).

Another quick trick to find that extra 20% is to think of 10% of 80 (easy - it's 8) and multiply that 8 by 2 (because you know 20% is 2 times 10% percent).

To decrease a number (as in the example of 20% and 80) you could either use the tricks to get the 20% and just substract that.

Or else, you could substract the 20% from 100 (which you can easily do in your head) and come up with 80. Once you have that you know you'll be looking for 80% of 80.

You could, of course, either use a calculator or write it out on paper and find find 80% of 80 the "usual way". Or, you could do one that easy in your head:

Since you know you'll be looking for 80% of 80, you go back to thinking up 10% of 80 (8) and multiply it by 8 (since 80 is 8 times 10).

So the only difference with a decreasing-by-a-percentage problem is that you first subtract the percentage from 100 to figure how what percentage you're really looking for - and then you use the tricks to find that percent.

• nathan

9 years ago

How do you work out the percentage increase/decrease from one number to another?

• AUTHOR

Lisa HW

9 years ago from Massachusetts

stephanie, it's not clear to me what you mean. If you're looking for percents that are related to the price of something, it's all kind of the same thing.

Please overlook it if my attempt to clarify/be helpful shows that I don't really know what you were looking for: If you're looking for prices (for example 50 percent of ten dollars) the ten dollars would be written as 10.00 (with that decimal point showing 10 dollars and no cents/change).

If you're writing prices you always know that there are spaces for however many dollars are in the price, then there's the decimal point, followed by however much change is also in the price. Ten dollars and ninety-nine cents would, of course, look like \$10.99

So, to find any percentage of any price, you would picture how it would be written first (or imagine it in your head); and you'd figure out the percentage with the decimal point in mind.

If the problem were simple enough you wouldn't have to do that, though. For example fifty percent of ten dollars means "half" of ten dollars dollars. Since you know that five is half of ten, you'd easily known that five dollars (\$5.00) is fifty percent (50%) of ten dollars (\$10.00).

One reason for using decimals (besides needing to use them when change is involved) is that it makes figuring out the percentage pretty easy. All you have to do is picture (or write down) how the price would look in numbers, and use that decimal point that's in all prices (if they're written out correctly) to help you figure the percent you're looking for.

Again, apologies if I don't "get it" with regard to the kind of thing you're looking for. I've just taken a wild shot at guessing what additional information may possibly be helpful.

Feel free to post with an example of the kind of problem you want to solve. I may or may not see it right away (depending on if you post at all, but I'll be back to try to answer as soon as I can).

• stephanie

9 years ago

this isn't the one i am looking for.i am looking for the one that is for the price nat decimals

• AUTHOR

Lisa HW

9 years ago from Massachusetts

whatever: Looks to me, then, like you fit real well here.

• whatever

9 years ago

losers al of u

• meet

9 years ago

thanks for ur help

• Dot I

9 years ago

Hi I am wanting to know if a question asks;if you got \$60.00 and spent \$14.50,what is the percentage you spent(14.50)what's the fastest way to calculate this?thank you

• AUTHOR

Lisa HW

9 years ago from Massachusetts

kenny, thanks.

• kenny

9 years ago

thanks this is really nice way very eassy.............

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Dan, to find out what percent of 1199 the 700 is you would divide the 700 by the 1199 (on a calculator - this one I don't have a quick mental trick for) and multiply the answer by 100. It comes out to 58.38198 (and if you round you'll get 58.4%).

If you check for 58.4% of 1199 you'll see that it's a "hair over" 700.

If you wanted more accuracy you can, of course, use the calculator for the above steps and instead don't round anything up or down.

(I hope I worded this right and didn't "do any oversights". It's 7 in the morning here - no coffee yet. LOL.)

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Rod, hi. I'll try (although sometimes it can be tricky to figure out how much or how little to say and still hope to make something easy). I'm not sure I can make it shorter, but maybe I can make it simpler. I'm going to try to separate all the ideas with a lot of spacing, to make reading easier.

If you don't do this already, sometimes when you're reading about math stuff it can help if you whisper what you're reading to yourself (or even read aloud). That helps you get the information in through your ears, and sometimes listening to "math stuff" is easier than try to "make your eyes" get the message to your head.

I guess the main idea is to try to make all the numbers smaller, so they're easier to work with in your head (if the problem is one that you can do that with).

The one thing you have to know (or keep in mind if you already know it) is that every number has a decimal point, whether it shows or not. If you have something like \$5.00 (to find some percent of) you can see the decimal point. If you're talking about 500 apples you can't see the decimal point, but you know it comes after the second 0, and just doesn't show up.

So, if you had to find 20% of 500 apples you could come up with 10% easily, because all you have to do is move the decimal point (either on paper or in your head) over one place (toward your left hand).

First you picture that 500 (apples) really has an invisible decimal point after it (like 500. - but you can't see it.)

So, even though you really want to find 20%...

First find 10% because it's really easy to do. (If you move the decimal point over one place toward your left hand you'll get 50 (or 50. if you imagine the invisible decimal point).

Now that you know 10% of 500 is 50 it's really easy to just think of two times 50 in order to find 20% (because you know that two 10's make 20). 2 times 50 is 100. That means that 20% of 500 is 100.

If you want to make the numbers even smaller and easier to deal with (on a problem like this one)...

Instead of finding 10% to make things easier, find 1%.

The reason it can help to find 1% first is because all you need to do to find the 20% (which is really what you want to do) is multiply 1% times 20 (because 20 1%'s will be 20%).

For example, with the 500 all you have to do is know that because percent always involves hundredths, 1% is 5.

(1% of 300 would be 3. 1% of 600 would be 6. etc. etc.)

If you need to move the decimal point toward your left hand in order to find 1% you would move it two places. At the bottom I'll make a comment about moving the decimal point over.

So, now that you've figured out that 1% of 500 is 5; if you want to know what 20% is you just multiply that 5 times 20. (5 "single/1 percents" times 20, because you really want to end up knowing what 20% is).

Why? Because there are 20 1-percents in 20 percent.

To check that the answer is right here's what you can think of:

100% always means ALL of something. 20% means PART of something. If you know that there are 5 20's in 100, the way to check your answer is to think of how many 20's (or how many "twenty percents) there are in 100. You probably already know in your head that there are 5 20's in 100.

That would mean that if you think of how of the answer you got for 20% (which was 100) and multiply times 5 it will show that you end up with the 500 (apples) you started with.

Moving the decimal point over one place toward your left hand means "dividing the number by 10". "Dividing by 10 is the same thing as finding 10%.

Moving the decimal point over two places toward your left hand means "dividing the number by 100". Dividing the number by 100 and finding 1% are the same thing.

With a little trickier kind of problem like: 13% of 500 you could do something like...

Think of 10% of 500 (by moving the decimal point so to get 50 instead of 500). So now you know that 50 is 10% of 500, but you really need to know what 13% is. Remember that 50 is 10% and then do step two:

Think of 1% of 500.

(Either by picturing moving the decimal point over two places and getting 5; or else by thinking of one tenth of the 50 you got (because there are 10 "single percents" in 10%).

1% of 500 is 5.

Now that you know 1% is 5 all you need to do to figure out how much that extra 3% is (that we left out of the 13% when we only figured out how much 10% is).

Just multiply the 5 you got for 1%) by 3 (because you really want 3%, not just 1%). 5 times 3 is 15.

To figure out 13% of 500 then, just add the 10% and the 3% you got (which was 50 for the 10% and 15 for the 3%).

Since 50 plus 15 equals 65, that means that 65 is 13% of 500.

Rod, I know this one example of percents of 500 doesn't really do it; but what would probably help you get how to figure out many percentages in your head would be if you think up problems yourself, finding different percentages of 100.

Find 10% of 100 (it's easy - remember? Just move the decimal point over one place).

Find 20% of 100. Just find different percentages of 100 (simple ones at first, like 40%, 50%, etc.).

Then try to find things like 45% of 100 or 65% of 100.

(To find 45% find 40% and 5% and add them together. To find 65% find 60% and 5% and add them together.)

(To find 40% think of 10% first and then multiply it times 4. To find 60% think of 10% first and multiply that times 6.)

To find 5% of a number think of what 1% and then multiply that by 5. To find 6% of a number think of what 1% is and multiply that by 6. etc. etc.

Hope some of this helps.

• dan

9 years ago

oh and one more think sorry Lisa

1199 is the price and i picked it up for \$700 what is that as a discount off 1199? I know 30% off 1000 is 700

• Rod

9 years ago

I'm a 6th this year and when i read your working out strategy, I didn't really get it. Can you explain it a little shorter and easier to understand?

Thanks!

• dan

9 years ago

Thanks a lot for that Lisa

I think i might have made a mistake in my question though here is what i'm trying to do:

I sold 37 units this month and the same month last year i sold 33 so what is the % increase here? Also lets say i sold 875 last year and only 370 this year how do i wrk that out as a negative??

Sorry and many thanks!

• AUTHOR

Lisa HW

9 years ago from Massachusetts

dan, you would divide the 310 by 387 (first) and then multiply the answer by 100. In this case, you'd have to round up at the end. (More later).

First, as a way of helping show what's going on, the reason you need to divide the 310 by 387 is that 387 represents "the whole", so you have to "assign" equal 387 "equal parts" in relation to the 310 "units". It's Step 1 in seeing the relationship between each of the 310 "units" to the "whole", 387. In other words, in order to know what number you'll be dealing with, you have to "break up" each of the 310 "units" in a way that relates to the 387.

So, if you divide 310 by 387 you get: 0.801034 (rounding down would get you 0.801. The next step is to multiply that by 100 (by simply moving the decimal point two places toward your right hand - or by using a calculator if you want).

From there you have: 80.1%

If you check to find 80.1% of 387 you'll get 309.987, and if you round up (to make up for the fact that you rounded down earlier), you'll see that 310 just about 80.1% of 387.

If you hadn't rounded down above, and if you multiply 387 by the 0.801034 you'll get just a tiny bit over 310 (but not enough to round up).

So - with a problem like this, divide the smaller number by the bigger number, and then multiply what you get by a 100.

Essentially, what you're doing with this kind of problem is trying to see a relationship between 310 "units" and 387, so you have to divide. The problem is that there isn't even one "387" in 310, so you're going to get equal "pieces" that don't amount to one whole "piece". If you picture trying divide 310 cookies by 387 you can imagine the bits you'd have to break them into. Because, with percentages, you're dealing with a larger number than "all those bits", and because percentages are about hundreths, that's why you multiply by 100 after dividing.

• dan

9 years ago

hi Lisa

i need to work out what 310 is as a percentage of 387

I'm not sure how to work out negative percentages??

Thanks

• nawid

9 years ago

thank you

• grace

9 years ago

great thanx yo rock i totally get it

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Artisan, thank you. If you are, you're not alone - that's for sure. :)

• Artisan Walker

9 years ago from Springfield, Oregon

Thank you for this. Clearly written and easy to understand -- even for someone mathematically challenged such as myself.

• emather

9 years ago from United Arab Emirates

i really had problems. thanks for this great hub

• AUTHOR

Lisa HW

9 years ago from Massachusetts

dogboy, to find something like 10% of, say, 50 you'd imagine that with the 50 the decimal point (which isn't ever written for whole numbers) would be after the zero (like 50. ). If you were dealing with 50 dollars it would, of course, be written out 50.00. So, keeping in mind where the decimal point (written or not written) is with any number...

To find something like 10% you would move the decimal point over once toward your left. With the 50. you'd move it from being after the zero to being after the 5, which would give you the 5 as 10% (1/10th) of 50.

• dogboy

9 years ago

you keep mentioning move the decimal point over one....LEFT OR RIGHT ? Just to make it perfectly clear.......Ü

• AUTHOR

Lisa HW

9 years ago from Massachusetts

Del, great. :) Thank you.

• Del

9 years ago

Just what I was looking for thanks a lot:)

• Deccan Chargers

9 years ago

very nice article.....

keep up the good work ....

thanks ....

10 years ago

Good article on working out percentages thanks, maryladd

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Author's Note: Somewhere in my account I ran into a comment that pointed out an error. That comment isn't showing up here, even though I approved it; so I don't quite know what's going on there.

In any case, I will return later to look for both the comment and the error pointed out by it. There's been a lot of a quick typing and "math gymastics" going on when I've tried to do things quickly here - so, again, I'll be back to correct the error and see whatever happened to that comment.

• AUTHOR

Lisa HW

10 years ago from Massachusetts

William, I'm not sure how your comment relates to the subject; but I have to admit it adds a little "lightness" to an otherwise boring topic. :)

• William

10 years ago

In the words of R. Kelly, "Everybody feelin freakyyyyy!!!!!"

• AUTHOR

Lisa HW

10 years ago from Massachusetts

andromida, thanks. :)

• syras mamun

10 years ago

Excellent hub topic.I think your tips gonna help me to figure out restaurant tip in a few seconds.

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Sexy jonty, thank you for the kind words. :)

• Sexy jonty

10 years ago from India

Very well written hub .....

very much informative ......

Thank you very much for your great hub, for good advice, good wishes and support. Thanks for sharing your experience with all of us.

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Chris, just another overlooked "grounding" tip:  Since you know that 4 x 80 is 320 (because you know that 4 x 8 is 32, and you're just dealing with the extra zero/tens), you'd also know that 320 is higher than 300.  That means  you can know that the answer to "what percent of 800 is 300" is going to be between the 30 and 40 (%) - in other words, in the 30's.

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Chris, you need to figure out what percent of 800 300 is.  The way to do that is to divide 300 by 800, and then multiply that by 100.  What you're essentially doing is figuring out how "800 units" can be equally divvied up among 300 "units".  Then, because percent is hundredths, that's why you multiply by 100.

In this case, you'll find that 300 is 37.5 percent of 800, so that's  your answer.

A different way to do it is to realize that 8 is 1% of 800 (percent is hundredths, and you get that by moving the decimal over two places; so you can do it in your head).  Once you know what 1% is you ask, "How many 1%'s go into 300?"  If you divide 300 by 8 you'll see that you get the 37.5 as well.

Just as a tip for getting a rough idea of how big a number you're looking for: You know that half (50%) of 800 is 400, so you'd know ahead of time that because 300 is less than 400 you'll be looking for a percentage under 50%.

Another "grounding" tip: You know that 10% of 800 is 80, so it's easy to know that 20% would be twice that (160). 30% would be three times 80 (240). At this point you may see that the 240 is getting kind of close to the 300; and, again, you know that 50% is 400. Again, this kind of thing can give you some "grounding" about the ballpark you're looking for.

• chris

10 years ago

im really struggling the best way to work out this problem please, please help out of 800 shoppers 300 shop more than three times a week. What percentage of the shoppers shop more than three times a week? i know theres got to be an easy way

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Kristi, I don't have any quickie mental tricks for that (and actually, I've been sick for a couple of weeks and can't really concentrate to write). So, I'm including this link, which shows the conventional way to figure out that type of problem:

http://www.ehow.com/how_2364017_percentage-numbers...

Actually, here's a site that will do the calculation for you:

http://lachie.net/maths/percent.html

I may think of a mental trick for that in the near future. Sorry not to be of more help.

• Kristy

10 years ago

Ok, how do I find out what the percentage is of something? If I am making something and I add 3.5 oz. base ingredients and add.5 oz. of another ingredient, what is the percentage of the .5 oz to the whole thing?

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Serina, first you'd figure out how much 25% is. A quick way is to divide the number you're dealing with by 4.

Another way is to figure in your head: What is 10% of the number in question. Then think of half of that 10%. (which will tell you what 5% is). Multiply whatever number is 10% by 2 (because you want 20%) and then add the number you got for 5%.

Now that you have whatever 25% is, you want to find 22%. The easiest way is to think of what 10% is by moving the decimal point over one place. Multiply the number you got (for 10%) by 2 (because 20 is two times as much as 20).

Now think of what 1% is by moving the decimal point over one more place (from where it was after you got the 10%). Again, multiply the number you get (for 1%) by 2 (to account for that extra 2 over the 20%).

Add the number you got as 20% to the number you got as 2%, and that's 22%.

• serena

10 years ago

How would you work out 22% of 25%???

• meggie moo

10 years ago

all sounds like archish to me (language bezzies made up don't get it) thanx though

• abc

10 years ago

i still dont get it (:sos:)

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Tiffany, you'd need to know the total number of votes in addition to how many votes someone got. From there you would use the same approach you use to find out what percent of one number another number is. In other words, if there were a total of, say, 500 votes you'd need to figure, "161 is what percent of 500". If I understand the type of "product discount" percentage problem you mentioned correctly, this would be an example of that:

Product used to sell for \$100. Today it's on sale for \$80. To find out the percentage of the "discount" you'd first consider the \$20 difference; and then ask "what percent of \$100 is \$20". That step, there, is the same as you'd use for the voting question (minus the dollar/cents factor).

• Tiffany

10 years ago

How do I determine the percent of each person's percentage of the vote. For example, if a person got 161 votes, how do I get the percentage of that number of votes. It might read 161 or "percentage. What are the steps?

I know how to get percentage of a product discount and so on, no problem.

thanks

• AUTHOR

Lisa HW

10 years ago from Massachusetts

Ibro, this site was prepared in answer to someone's request about how to find percentages.  It was the aim to show some quick tricks to help people figure it percentages easily (maybe at the supermarket or when figuring out a restaurant tip, etc.)

I used a casual, "non-math", style of wording because I figured if someone has trouble with figuring percentages they are either very young or else people who benefit more from "non-math"/more casual explanations.

I have no doubt that this page is not what a lot of people, looking for math information, will be looking for.  Based on feedback/traffic it gets, however, it is apparently what has answered some people's question about how to figure percentages easily.   Based on several nice e.mails I've gotten from junior-high age students, they are generally the "audience" for this site; but based on those e.mails, I have to say that I don't call it "BS" if a page has helped even a few kids learn their math.  My thinking has been that the world is full of more "formal" or "advanced" sites/books and even people who teach math, and none of it apparently got through to some of those kids who e.mailed me (at least when it came to figuring out percentages).

So, this page is an "unfancy"/"folksy" attempt to share some quick percentages tricks with anyone who has/had trouble with doing that.  Nobody is pretending it's anything more important or useful than that.  I have no doubt many people will find it is "BS" (that's ok), and I do think it's unfortunate if it hasn't been helpful to you, as you had thought.  I hope you found the kind of helpful information you were looking for, and remind  you that search engines don't always "know" exactly what you're looking for, and send you a bunch of different sites in search results.

• ibro

10 years ago

i think this site help me a lot but the site was BULLSHIT

• Anuj Tripathi

10 years ago

That is excellent. I liked it Lisa. As I am looking forward to the Management aptitude exam , this tutorial would be the boon for me.

Please do write some other articles on various other tricks.

• AUTHOR

Lisa HW

10 years ago from Massachusetts

wonderful, sorry if it didn't help. If you have the time, and want to ask a specific question, I'd be happy to try to be help.

10 years ago

you really help me thank you

• wonderful

10 years ago

i hate it does not helr

• AUTHOR

Lisa HW

10 years ago from Massachusetts

JPSO138, this hub has surprised me. It was a request I saw ages ago, and I thought, "I can answer that easily enough - think I'll answer the request." It has surprised me that anyone other than the person who made the request has even looked it. Based on the surprising number of e.mails I've gotten from this hub, I guess a lot of junior-high aged students seem to have liked it. It's not my best piece of writing, by any means, but I kind of like that it has apparently been useful to some students.

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