How do I find the original number to a percentage? Reddit r/askmath

[@bprpmathbasics]

Mathematically, which of these numbers is the largest? (A) Number of hours in a year (B) Number of seconds in a day (C) Number of days in a decade (D) Number of minutes in a week kzbin.info/www/bejne/ZmexoqeiotCDgZI

[@ProtossOP]

Since this is about proportions you just think of them like this: $35 is 25% $X is 100% Then you write it like this(think “is” is “=“): $35 = 25% $X = 100% And then you divide one by another $35/$X = 25%/100% Alternatively you could write as(think “is” is “/“): $35/25% = $X/100% Then you solve it for X.

[@HxTurtle]

I'd use the first method, but simply flip the lines (so that you don't end up with x in the denominator, which is then even quicker to see what to do with one glimpse.)

[@UserT049.]

Why?

[@Dyne191]

You're nuking it

[@Sg190th]

Basically, you divide the number by its percentage.

[@incircIe]

Yeah, but the important part is the concept

[@Voperleed]

I have 2 methods. In the first i divide for the percentage itself and then multiply for 100 In the second, in case it is a simple fraction of 100%, i just multiply it until it reaches 100%

[@LaMirah]

That's the way to do it in a calculator, but it's not very didactic. Better to teach it the long way around, just like explicitly dividing both sides of the equations by the decimal equivalent of the percentage instead of just flipping the number into the other side's denominator. This is, after all, bprp math basics.

[@HxTurtle]

yes, because you start out with the form of, "a × b = c" and to solve for 'b', you end up dividing c by a.

[@demystify2022]

Yes but because it’s 25% which is 1/4 then you just have to do 35x4.

[@floofybear]

1) In maths when saying a of b, we write it as a(b). 2) % = 1/100 Using these two rules we can solve it. 25% of x is 35$ 25%(x) = 35 25(1/100)(x) = 35 (25/100)(x) = 35 0.25(x) = 35 x = 35/0.25 x = 140 ⭐

[@HenrikMyrhaug]

I disagree about converting to decimal. Instead, because a percentage n% literally means a fraction n/100, you should write the fraction down, then do algebra to find X. The reason why this is a better method is because you don't have to convert to decimal (which many struggle to understand), and because dividing by a number smaller than 1 is hard for beginners to understand. Multiplying by 100 and dividing by n on the other hand is really easy to understand. So the method: X*17%=X*17/100=42.5 -> X*17=42.5*100 -> X=4250/17=250 Is much more intuitively understandable and easily explainable than dividing by 0.17. The word "percent" literally consists of "per" meaning pieces of/ divided by, and "cent" meaning 100, so we should be teaching it as a fraction of 100.

[@brianhsu_hsu]

Also don't agree convert to decimal first. Multiply both side by 100 is much easier to work with and more intuitive.

[@brianhsu_hsu]

BTW, also want to add something as an additional information. Converting to decimal first not always work. For example, what if I told you that the owner of shop give me a discount and I only paid two-thirds (2/3) of the original price, and I paid 100, what is the original price? The idea is the same, but I only change the percentage part to a fraction. We just shouldn't convert to decimal point at all, because otherwise we will get 0.666666....., which no mater what we do, we will lose precision when we divide 2/3 with it's decimal form, because it's has infinite 6 after the decimal point. Instead, simply multiply both side by 3 first and everything is perfect. 2/3 * X = 100 2 * X = 100 * 3 = 300 X = 150

[@aralornwolf3140]

brianshsu_hsu, He was talking about percent not fraction. A number given in Percent form can be written in Decimal form without any complications. Fraction = Decimal = Percent = Ratio* * Not all Ratios are given in their fraction form. brianhsu_hsu's example reminded me of the one question everyone, other than I, got wrong when I was in grade 8. The question was about resizing a picture, the picture's sized was increased by 2/3rds. What was the original size of the picture? However, when you're forcing the student to divide by a prime number no matter what you do. In the long division format, the student is going to begin by converting the decimal to a whole number anyway. Adding that to the equation is not required.

[@rymq]

I think proportion is the easiest way to do that 25% of x is 35 and you put inside proportion what you have part as number part as % -------------------------- = --------------------------------------- whole as number whole as % (it is always 100%) So we have on this case 35 25% ------ = ------ X 100% and now you multiply on a cross 3500 = 25x and here you divide both sides by 25 ,and you have an answer x = 140 It is so easy and less complicated

[@Ninja20704]

Where I live this is how these qns are usually taught, particularly for the second example: 17% of original cost -> $42.5 1% “ “ “ -> $42.50 ÷ 17 = $2.50 100% “ “ “ -> $2.50 * 100=$250 Slightly easier both on the conceptual and the calculation aspect

[@Jedimeister17]

In the end, both are the same idea, but you took the „long way“. Despite being the long way, it‘s easier to calculate in your head.

[@cyrusyeung8096]

Thank you so much for such a great video. This reminds me of a common mistake: when students solve "What increases by 30% becomes 120?", they sometimes say "answer is 120 × (1 - 30%) = 84", but the correct answer should be "120 ÷ (1 + 30%) = 92.3076...". I usually explain this to students in an algebraic way, but I wonder if it can be explained graphically like 0:40 - 1:20

[@bprpmathbasics]

Glad to hear this! Thanks.

[@HxTurtle]

it's then best to say, 120 equals 130% seen from the original; or one point three "parts" and solve for one part, ta-da.

[@avirat716]

What i like to do is for example 15% of what is 225? In this case i like to do it like this: 15%=15/100 so, 15x/100=225 and then, x=225*100/15 so, x=15*100 or 1500

[@bprpmathbasics]

Ah cool I see. That explains why we move the decimal in the long division.

[@HxTurtle]

​@@bprpmathbasicshuh?! I didn't expect this hearing from you-but it's literally in the word itself, "per cent!" with cent being Latin for a hundredth, so one percent is just the same as one hundredth in plain English, which is written down as, "0.01“ in decimal notation.

[@Mark73]

It's really simple. 140 * .25 = 35. Therefore 35 / .25 = 140 Just divide both side by the percentage, and it will cancel out on one side.

[@romanyoutube3141]

We were taught a great formula: č x 100 = z x p where: č is the part of the whole number (in slovak: časť) z is the whole number or as we say the base (in slovak: základ) p is the percentage (in slovak: percentá) From this you can just find your missing variable easily.

[@abelwritesmusic]

(25/100) = (35/X) and solve for X Reduce (25/100) to (1/4) then use cross multiplication to solve for X (35×4)=(1×X) so 140=X

[@penothagoat2699]

it's actually not that deep, it's like wanting to know what 25% of 140$ is, if you wanna know that just multiply the percentage you want to know by the total number (in this case it's going to be 25x140), then divide the whole thing by 100 (in this case (25x140)%100 ), and the result will be 35 so let's do the same thing.... BACKWARDS, so (100x35)%25 and you're going to get 140$

[@nina531]

I also use the PRB triangle rule P ----- R|B If you're looking for the base (B, original value), just divide the percentage (P) by the rate (R). Same rule when you need to find the rate. To find the percentage, you multiply the base by the rate

[@terakoinfinity9523]

I like the concept of x% of y = y% of x. For example, if 25% of y = 35, then y% of 25 = 35. Then at that point i know that 140% of 25 = 35, therefore y = 140

[@starleaf-luna]

the way I was taught it: $35 - 25% x - 100% so we cross multiply. 25x = 3500 x = 3500 / 25 x = 140 so if 35 is 25% of x, then 100% of x is 140.

[@smartbeastgaming8913]

Don’t agree to this solution A better and easier solution-: 25% of x = 35 = 25/100 * x = 35 Dividing both sides with 25/100 (or taking 25/100 to RHS) = x = 35/ (25/100) = x = (35*100)/25 = x = 140

[@deltakyy3894]

LOL im in 5th grade (6th math) and our teacher actually taught us this yesterday but instead she said the word “of” means multiplication so you would multiply (25/100)x = 35 so then you would divided both sides by 1/4 or multiply by 4. and 35 times 4 is 140. edit: i watched the video and realized he said basically the same thing

[@Slayer0fSun]

Percenteges are my favourite and this is a problem i myself have had trouble with,and this was my solution: First,we find 1% by dividing the percentege to 100 100 / 25 = 4 And now that we know how much 1% is we multiply with the number we know so 35 × 4

[@Manker00]

As we work with percentages we can just do 100 / 25 * 35 = 140, and similarly 100 / 17 * 35 ~ 206.

[@JubeiKibagamiFez]

3:18 I said to myself at the beginning of the video I knew this, but then I doubted myself. I knew it was that simple. I always did the equation for percentage when I was a tutor way back when.

[@gilernt]

i love how as a mechanical engineering that just finished all the required math courses (calc 1-4, diffeq), it's the basic things that i've never learned and have to go back and learn 😭

[@wobaguk]

I prefer to write the percentage as 17/100 etc. rather than decimal, that way you can get an answer you can rationalise and solve more easily manually rather than just heading for a calculator.

[@brandonolak255]

Would it also be the same to take the percentage (%25) and convert to a fraction (1/4). Then you multiply the number ($35) by the denominator? So, 4 x 35 = 140. The only thing is, this would only work if the numerator was 1, because the 1 would represent the other number we know?

[@brandonolak255]

So it would be necessary to make simplify whatever fraction you have to make the numerator 1. You would get a decimal for a denominator more often if you have “not so clean” fractions, but it still works.

[@hamgification]

if you know it's something well known, like 25 %, it's a matter of seconds: 35*4 = 140, cause 25*4 = 100. ... You can do this with halves, thirds, fifths, tenths... makes it quicker a lot of the times

[@allenanderson2457]

I learned the "IS over OF" method. 25% as a fraction is 25/100 that will be equal the "IS" value over the "OF" value in other words: 25/100 = 35/x ; then solve for x

[@emilyesnyman]

I like this! I was taught similarly, saying "what you WANT" over "what you HAVE" Eg. I take the value 35 and multiply it by the percentage that I want (the 100) over the percentage that I have (25) So it becomes: 35 * 100/25 = 35*4 = 140

[@Dojaesd]

what are these weird acronyms lol, it's just basic algebra

[@allenanderson2457]

@@Dojaesd What weird acronyms?

[@Dojaesd]

@@allenanderson2457 the is and of

[@allenanderson2457]

@@Dojaesd They're not acronyms. they're just a way of remembering how to set up the equation. The number next to IS goes into the numerator, and the number next to OF goes in the denominator. That's all...

[@CuriousFocker]

$35 ÷ 25 x 100 = $140 Divide the amount [$35] by the percentage amount [25%] and multiply by the whole amount percentage [100%] to give you the total amount [$140]. It is simpler than the shown method, and works for any percentage. bprp math basics always overcomplicates things - keep it simple.

[@rateeshk8175]

1:07 , steve said 35 times 5, did anyone catch it? Yet he did do the correct steps, Now that's a teacher if i have seen one

[@UncleChrist]

No, he didn’t say 5 he said “$35 times four of them”

[@rateeshk8175]

@@UncleChrist yes, he edited that part out. Previously, he did say it, but he fixed it 💯💯

[@aryaman.kureel.1735]

Nah bro he actually said 4 , look at his lips, they say "four"

[@alicornxx6919]

You could also do, 25% = 35 then, you divide both sides by 25 1%=1.4 then, multiply both sides by 100, 100%=140

[@JT-he7fw]

It is amazing how many people forget division is reverses multiplication. I am also surprised when I am at a store and people calculate say 20% off they multiple 20% by the price then remember that number then subtract it from the original price versus just multiplying by the complement of 80%.

[@imightbeaperson630]

Well that has to do with mental math, where for most people it is easier to do multiple, simpler operations in their heads instead of one harder operation.

[@skie6282]

Isnt the result the same lol, its a simpler version with a few steps vs 1 harder version

[@JT-he7fw]

@@imightbeaperson630 I agree and I do it that way for mental math too but I see people do it with a calculator that way which is harder and more steps

[@JT-he7fw]

@@skie6282 one way is easier in your head one way is easier on a calculator all the same result

[@Maninawig]

Honestly, I had a math teacher in 8th grade teach us this way. To add tax, she'd have us calculate x•%=y x+y=total all the time, and got mad at me for suggesting that x•(1+%)=total as "some kids won't understand that" In 9th grade, we learned that most of the things she taught was false and backwards.

[@JayTemple]

When you were doing 25%, you accidentally came up with a good way to explain fractional division! Asking for 32 divided by 1/4 is the same as asking, 1/4 of what is 32? Then you can extend it. Asking for 27 divided by 3/4 is the same as asking, 3/4 of what is 27? Well, if 3/4 of the number is 27, then 1/4 is 27 / 3 = 9, etc.

[@afre3398]

Not wrong by any means but perhaps not a very good pedagogical explanation. I feel you skipped some important parts here. A percentage is a number or ratio expressed as a fraction of 100. So 17 hundredths of x is 42.5 (x*17)/100=42.5

[@tobybartels8426]

You can draw a picture even for 17%, although it's not as pretty. The picture for 25% is nice because 25/100 reduces to 1/4, so you only have to divide the circle into 4 pieces. Since 17/100 doesn't reduce, you have to divide the circle into 100 pieces. Of these, 17 are shaded in, so you divide by 17 to get the size of 1 piece. Then multiply by 100 to get the entire circle.

[@Otatoes]

A more "presentable" way I think might be: (17/100)y = 42.5 y = 42.5 * 100/17 y = 425/10 * 100/17 y = 425 * 10/17 y = 4250/17 y = 250 I only showed extra steps for the clarification

[@speedg]

I actually came upon a solution where you convert both into fractions, invert the percentage fraction and multiply it with the other fraction. (ex. for the second example: 100/17 * 425/10 = 250)

[@amanbhardwaj313]

So we don't know know the real value which is x and also x is 100% also 35 is 25 % of x we just do x/35=100%/25% => x/35=4 => x=4×35 => x=140

[@emilyesnyman]

That's basically how I do it as well

[@habbokoreiapix]

I know that: → 25% of x is the same as x% of 25 → x% = x/100 → x% of y = (x/100) * y Then if 25% of x = 35, 25% of x = 35 x% of 25 = 35 (x/100) * 25 = 35 x/100 = 35/25 [divide numerator and denominator by 5] x/100 = 7/5 [multiply both sides by 100] x = 7/5 * 100 x = 1.4 * 100 x = 140

[@DefenderTerrarian]

I'm currently taking Calc3, and only now, after watching this video, understand how to divide by a decimal. Conceptually, of course, I understood it, but the way I was taught to do it was really confusing and convoluted.

[@PuniBelserion]

Thats a cool way to do it, but i found it more easy to just use fractions. Les say i have 34% of 220. So. I Will just say "its a Percenage so it is divided by 100" 34/100. Then the rest is the same. So 34/100.220/1 = X 7480/100 = X. Then we simplify it or just do the actual divition. 74,8 = X. Knowing thats a percentage is ALWAYS X/100 helped me a lot in those Problems 😊 Then, if You just move the X arround, and do simple clear the X 74.8 is X% of 220. X/100.220 = 74,8 220x/100 = 74,8 We clear first the Denominator 220x =74,8 times 100 We resolve andThen we clear the 220 passing to the other side as the opposite Sign X =7480: 220 X= 34 I hope is helpfuul for someone Pd: i dont know if the same terms i used in school Back then Still called like that (denominator for example) so i just literally translated it from Spanish, sorry if some of them dont Make sense to you 😢

[@WorkEducation-ki6hu]

let the original no. be x --> 25% of x = 35 --> (25/100) * x= 35 --> (1/4)*x = 35 --> x=35*4 --> x=140 So the number is 140 Simplest question I have ever seen on the Internet

[@LeonardoBruno54]

25 = 35 100 = x Cross multiply 25x = 3500 x = 3500/25 x = 140

[@robj7532]

I love your videos. I havent had to do much math, myself, for the last 40 yrs. I'm amazed at how much i remember. I thought it was all gone.

[@brianhsu_hsu]

I don't like the convert to decimal part, it seems unnecessary to me. As long division with decimal is really tedious and easy to make mistake when moving the decimal point. Working with fraction is much easier when it come to percentage. We could simply multiply 100 on both side, and get a whole number without any decimal. 25/100 * x = 35 25*x = 3500 x = 3500 / 25 x = 140.0 In this way, you don't deal with decimal point until the last step. Yes, it is conceptually equivalent to the version in the video, but much easier to work with IMHO.

[@m1germsy784]

You can also cross multiply

[@JosefZeethuven]

x(100/y%) 35*(100/25) for this instance. which is 35*4=140

[@guerra_dos_bichos]

That one I knew, my education is not useless after all

[@mantasr]

You just divide by the percentage in decimal form. I have to do this a lot and this is the fastest way. In practice, with a calculator.

[@DiogoCebola]

1 - x 0.25 - 35 35 = 0.25x x = 35/0.25 x = 140

[@itzsoweezee9980]

4 x $35 = $140 4 x $30 = $120 (4 by 3 is 12) and 4 x $5 = $20 💁‍♂️ or 2 x $35 = $70 and €70 x 2 = $140 🤷‍♂️ You can do the math in your head in just a few seconds if you know your multiplication tables. 😉

[@Kirbster-D-Shroom]

35 × 4

[@tommyb6611]

This is learned at the age of 10. And can't forget such easy. 35$ .... 25 x $ ...100 x=(35*100)/25 = 140 Sad someone has to ask on forums

[@goldpotato1885]

Sad to see you exist

[@Zen_Phantom]

25% of x = 5 25/100×x =5 25x/100=5 25x =500 x =20

[@dakota5569]

When someone says they dont understand calculus, its because they dont understand algebra

[@JubeiKibagamiFez]

Now, just a thought... What happens if the percentage is more less than 1%? Do we keep moving the decimal place till it becomes a whole number?

[@brianhsu_hsu]

Since % literally means divided by 100, so you just multiply both side by 100 and do the algebra, it works in any circumstance. Don't convert it to decimal point. It's a mess. For example, 12.34% of X is 567.89, what is X. The solution will be: 12.34/100 * X = 567.89 1234 * X = 56789 X = 56789 / 1234 X = 46.0202... Of course sometimes we need to deal with a decimal point before the X or right hand side, but it still much more easier if you first multiply both side by 100. Because you only deal decimal point at the last step, and you only do division once, not twice. For example, if 12.345% of X is 567.89, what is X? The solution will be: 12.345 / 100 * X = 567.89 1234.5 * X = 56789 X = 56789 / 1234.5 X = 46.00162 Or if it's less then 1 percent, for example, 0.123% of X is 456, what is X. Still multiply both side by 100 and do the division. 0.123% / 100 * X = 456 12.3 * X = 45600 X = 45600 / 12.3 X = 3707.317 Or better yet, multiply both side by 100 repeatedly until you got decimal point out of both side, then you don't need to deal with long division with a decimal point at the divisor. 0.123% / 100 * X = 456 12.3 * X = 45600 123 * X = 456000 X = 456000 / 123 X = 3707.317

[@JubeiKibagamiFez]

@@brianhsu_hsu I was thinking a percentage like 0.005%.

[@brianhsu_hsu]

@@JubeiKibagamiFez Same, just multiply both side by 100 or 10 repeatedly until you get decimal point out of both side. 0.005 / 100 * X = 123 0.005 * X = 12300 5*X = 12300000 X = 12300000 / 5 X = 2460000

[@JubeiKibagamiFez]

Just an edit... I meant to just say "less than 1%." Some times my brain is to fast for my fingers and I will literally skip typing entire words.

[@Maninawig]

Does this work with additive totals? Like say you paid $19.36 after a 7% tax, would the answe to the sale price be $19.36/1.07?

[@yudiputra2595]

i simply do 35 x 100 then the result is divided by the 25%

[@prometheus1222]

What i do here is double it twice lol not that hard 25=35, 50=70, 100=140

[@bubblecqt5796]

x = y(z%)^-1

[@noexception9598]

140

[@akshatkaront8172]

140

[@tiagosoares3959]

Regra de três simples

[@casusbelli9225]

Just multiply in by 4, duh. Or multiply it to whatever is an inverse of the percentage.

[@Gust52]

Man if ppl have doubts on topics like this, everyone should go back to kindergarten. It's an absolute shame to have doubts on these when you're grownup; these should be om your fingertips. If ppl can't solve this, they are nothing for geometry and calculus m

[@lightningbolt9155]

Oop, why is this private? (Forgot the term, maybe it was unlisted?)

[@tomholand5573]

tan X = i find X plz

[@annawanna5995]

Why would anyone pick '$60' as their answer? O_o How?

[@lalabooty-p6x]

this guy is david howells 4th cousin...change my mind

[@kjk1185]

(x*100)/yy%

[@pauljohn5554]

You rock! Thanks for

[@mekaindo]

Can't believe they don't know this.

[@eidodk]

Way too complex... When working with percentages, first work out what the value of one percent is, then multiply by 100 in the end to get the full value.

[@The_Red_Scare]

Nvr heard of this method before, I don't think, but it worked! Thx for sharing!

[@marsrocket]

You don’t need 6 minutes to explain this. 0.25x = 140. Divide both sides by 0.25, x = 140/0.25. Done.

[@TheVivi13]

You're overestimating how good people are at math lol

[@GingeryGinger]

You haven’t actually explained anything. All that pretentious syntax for what?

[@The_Red_Scare]

You didn't even answer the question... They said how do you get the original number with ONLY the % (25%) and the amount that % actually is ($35). The answer would be to divide the number by the percentage after converting the percentage into a decimal (0.25). You could also turn it into a fraction if possible (not every number can be converted into a fraction, such as pi) and just multiply the inverse of that fraction to the amount you're given to find the original number. The point of this video isn't to just spit out the answer. He's trying to TEACH. 6 minutes isn't a long time.

[@The_Red_Scare]

@@GingeryGinger Just to give the wrong answer to the question. Bro's finding the percentage instead of the original number. 😔