We can make a proportion to have. Percentage problems: standard calculation using proportions

Proportion translated from Latin language(proportio) means ratio, evenness of parts, that is, equality of two relations. The ability to calculate proportions is often necessary in everyday situations.

Sponsor of the placement P&G Articles on the topic "How to calculate a proportion" How to fold square roots How to find the diagonal of a square How to find the coordinates of the vertex of a parabola

A simple example where you need to apply knowledge about solving proportions: how to calculate 13% of your wages- the same interest that goes to the Pension Fund.

Write two lines of proportion. In the first, indicate the total salary amount, which represents 100%, that is, for example, 15,000 (rubles) = 100%.

In the line below, indicate the amount that needs to be calculated with the sign “X”, which is equal to 13%, that is, X = 13%.

The main property of proportion is this: the product of the extreme terms of a proportion is equal to the product of its middle terms. This means that if you multiply 15,000 by 13, the resulting number will be equal to the value of X multiplied by 100. That is, multiplying the terms of the proportion crosswise, you will get the same value.

To calculate what X ultimately equals, multiply 15,000 by 13 and divide by 100. You will get that 13 percent of your salary is 1,950 rubles, so you get 15,000 - 1,950 = 13,050 rubles net salaries.

If you need to take 100 grams of powdered sugar for a pie, and you know that 140 grams fit in one faceted glass, make the following proportion:

Calculate what X is equal to.

X = 100 x 1/140 = 0.7

That is, you will need 0.7 cups of powdered sugar.

It happens that you need to calculate the whole, knowing only the percentage part. For example, you know that 21 people at the enterprise, which is 5% of the total number of employees, have secondary specialized education. Set up a proportion to calculate total quantity employees: X (person) = 100%, 21 = 5%. 21 x 100 / 5 = 420 people.

Thus, having written down the available data in two lines, the value of the unknown term must be found as follows: multiply among themselves those terms of the proportion that are next to and above the unknown and divide the resulting number by the value that is diagonally from the unknown.

A = B x C / D; B = A x D / C; C = A x D / B; D = C x B / A

There are several types of diagonals in geometry. A diagonal is a segment that connects two non-adjacent (not belonging to the same side or edge) vertices of a polygon or polyhedron. There are also diagonals of faces considered as polygons and spatial

The cube represents special case a parallelepiped in which each of the faces is formed by a regular polygon - a square. The cube has six faces in total. Calculating the area is not difficult. Sponsored by P&G Articles on the topic "How to calculate the area of a cube" How to fold

What is proportion? From a mathematical point of view, proportion is the equality of two ratios. All parts of the proportion are interdependent, and their result is unchanged. You will need - Algebra Textbook for 7th grade. Sponsor of the placement P&G Articles on the topic "How to calculate the proportion" How

Often in life you have to apply simple mathematical operations quickly and without the help of electronic computers. For example, when calculating wages, you need to subtract from the total sum of money thirteen percent. How to do this? After all, subtract different types numbers are not allowed, without a specific

Everything is learned by comparison. The ratio of some quantities to each other can be expressed as a percentage. For example, by calculating what percentage of liquid from the main mass is contained in 1 kg of tomatoes and cucumbers, you will find out what will be juicier. You will need 1) Paper 2) Pen 3) Calculator Posting Sponsor

The arithmetic mean is an important concept used in many branches of mathematics and its applications: statistics, probability theory, economics, etc. The arithmetic mean can be defined as general concept average size. Sponsored by P&G Articles on the topic "How to calculate the average

The ability to solve proportions can also be useful in everyday life. Let's say you have vinegar essence in your kitchen containing 40% vinegar, and you need 6% vinegar. There is no way to do this without drawing up proportions. You will need a pen, a piece of paper, analytical thinking Sponsored by P&G Articles on

From the need for complex mathematical calculations ordinary person My head is spinning. Try to calculate what the amount is income tax from your salary. In this case, a simple action will help you - drawing up a proportion. A proportion is the equality of two quotients. It is written in the form

In mathematics, a proportion is the equality of two ratios. All its parts are characterized by interdependence and unchanging results. It is enough to consider one example to understand the principle of solving proportions. Sponsor of the placement P&G Articles on the topic "How to find a proportion" How to subtract a percentage from an amount How

Already from the first grade, children learn in mathematics lessons such concepts as equality, “greater than” and “less than” signs. Over the years, the tasks become more and more difficult, but the requirement to create an equality is also found in them quite often, since the “equal” sign is the basis of any transformations in mathematics.

How to make a proportion? Any schoolchild and adult will understand

For solving most problems in mathematics high school Knowledge of drawing up proportions is required. This simple skill will help you not only perform complex exercises from the textbook, but also delve into the very essence of mathematical science. How to make a proportion? Let's figure it out now.

The most simple example is a problem where three parameters are known, and the fourth needs to be found. The proportions are, of course, different, but often you need to find some number using percentages. For example, the boy had ten apples in total. He gave the fourth part to his mother. How many apples does the boy have left? This is the simplest example that will allow you to create a proportion. The main thing is to do this. Initially there were ten apples. Let it be 100%. We marked all his apples. He gave one-fourth. 1/4=25/100. This means he has left: 100% (it was originally) - 25% (he gave) = 75%. This figure shows the percentage of the amount of fruit remaining compared to the amount initially available. Now we have three numbers by which we can already solve the proportion. 10 apples - 100%, X apples - 75%, where x is the required amount of fruit. How to make a proportion? You need to understand what it is. Mathematically it looks like this. The equal sign is placed for your understanding.

It turns out that 10/x = 100%/75. This is the main property of proportions. After all, the larger x, the greater the percentage of this number from the original. We solve this proportion and find that x = 7.5 apples. We do not know why the boy decided to give away an integer amount. Now you know how to make a proportion. The main thing is to find two relationships, one of which contains the unknown unknown.

Solving a proportion often comes down to simple multiplication, and then to division. Schools do not explain to children why this is so. Although it is important to understand that proportional relationships are mathematical classics, the very essence of science. To solve proportions, you need to be able to handle fractions. For example, it is often necessary to convert interest into common fractions. That is, recording 95% will not work. And if you immediately write 95/100, then you can make significant reductions without starting the main calculation. It’s worth saying right away that if your proportion turns out to be with two unknowns, then it cannot be solved. No professor will help you here. And your task most likely has a more complex algorithm for correct actions.

Let's look at another example where there are no percentages. A motorist bought 5 liters of gasoline for 150 rubles. He thought about how much he would pay for 30 liters of fuel. To solve this problem, let's denote by x the required amount of money. You can solve this problem yourself and then check the answer. If you have not yet understood how to make a proportion, then take a look. 5 liters of gasoline is 150 rubles. As in the first example, we write down 5l - 150r. Now let's find the third number. Of course, this is 30 liters. Agree that a pair of 30 l - x rubles is appropriate in this situation. Let's move on to mathematical language.

5 liters - 150 rubles;

30 liters - x rubles;

Let's solve this proportion:

So we decided. In your task, do not forget to check the adequacy of the answer. It happens that with the wrong decision, cars reach unrealistic speeds of 5000 kilometers per hour and so on. Now you know how to make a proportion. You can also solve it. As you can see, there is nothing complicated about this.

How to find the percentage of a number

To find the percentage of a number, for example, 35% of 1000 rubles, you need the same Where does the number 100 come from? From the very definition. A percentage is a hundredth of a number.

On a calculator you can multiply 1000 by 35 and press the % button

How to find 100 percent

For example, we know that 350 rubles is 35%. How much will 100% be?

Percentage between two numbers

What part one number is of another. For example, what percentage of the plan was fulfilled if the expected income was 800 rubles, but in the end they received 1040 rubles.

Online interest calculator

It is not necessary to take 100% into account. For example, traffic from Yandex, Google, VKontakte, etc. is 100%. 800 visitors come to the site from Yandex, which is 67% of total number. And from Google - 55 visitors. What percentage of visitors come from Google?

How to calculate how many percent one number is less than another

The salary dropped from 1040 rubles to 800 rubles. By what percentage did the salary decrease? What percent is 800 less than 1040? Unknown 800.

How to find out what percentage one number is greater than another

The salary increased from 800 to 1040 rubles. By what percentage did the salary increase? What percentage is 1040 greater than 800? Unknown 1040.

We write the proportion, we can derive the formula

Increase a number by a specified percentage

The number b is greater than 800 by 30%. We need to calculate the number b.

We write the proportion, we can derive the formula

Example: the amount excluding VAT is 1000 rubles. How much will the total amount be including VAT 18%

Decrease a number by a specified percentage

The number a is 23% less than 1040. What is a equal to?

We write the proportion, we can derive the formula

Script for web developers

JavaScript is very simple (highlighted mathematical actions in the form tag): input - field where we enter values

output - area with the result

parseFloat(g3.value) or g3.valueAsNumber - converts a string to a number

235 comments:

You don’t need anything (you have a calculator on your phone), but sometimes it may happen that you have to create a cost calculation script stretch ceiling. NMitra What about bank interest, say, for a loan or a deposit? Or the percentage of conversions from search? Or taxes for individual entrepreneurs?

Total: 20% Anonymous I need 20% propolis tincture. I bought a tincture at the pharmacy, but the instructions and the bottle say: tincture - 1:10 == How to make 20%? NMitra I don’t presume to give you advice. I have no medical education. Anonymous Since school, I can’t stand everything related to numbers and calculations. And oddly enough, I’m studying to be a financier, but the most basic arithmetic operations I don’t know. And when I hear the word “tasks,” I feel uneasy. NMitra:)) Anonymous UNS UNS UNS UNS! Anonymous is still not clear. Either I'm stupid or... I don’t know:(A(bear)***xD*** I can’t solve the problem:((Anonymous 1:10 is part of the adult dose for children. If the bottle contains 25 ml, then multiply 1 ml - that’s 25 drops - 25*25 (if it’s liquefied) continue to calculate the percentages. And how many drops per ml depends on (the state of the density, the size of the pipette, etc.) Anonymous Hi, how can you find out the difference between the two numbers in %? How much is one number greater than the second?

for example 950000 from 87000

take more for 100%? then the figure turns out to be 91.58, which is 8.42%. Am I right? Thanks Anonymous Damn, I wrote 95000 and 87000 NMitra incorrectly. Although, no, I didn’t understand the question correctly.

NMitra It's nice to hear that your work is appreciated, please Nasiba What to do if the amount of the percentage is known but the percentage itself is not. For example, 3000 principal amount is 1400 what percentage of this amount is? NMitra 3000 - 100%

NMitra It happens. An anonymous investor contributed 3,500 rubles at 15% per annum, what amount will he receive in 3 years? NMitra Is interest accrued or accrued? If counted, then in what period (once every three months, once every six months)?

525*3=1575 (for three) Anonymous I take out a loan for 5,000,000 rubles at 20% for 12 months, how much should I pay per month? Please write a calculation. Thank you. NMitra Interest annual or monthly?

* on payment of interest,

* write-off of the principal debt.

* annuity payment in which the amount of monthly payments is the same (in your case, about 463,172.53 rubles),

* differentiated payment in which the same amount of the principal debt is written off (in your case 5,000,000 / 12 = 416,666.67):

365 - number of days in a year

Interest: 5,000,000 * 0.2 * 30 / 365 = 82,191.78

Payment: 416,666.67 + 82,191.78 = 498,858.45

Percentage: 4,583,333.33 * 0.2 * 31 / 365 = 77,853.88

Payment: 416,666.67 + 77,853.88 = 494,520.55

Interest: 5,000,000 * 0.2 = 1,000,000

Payment: 416,666.67 + 1,000,000 = 1,416,666.67

Balance: 5,000,000 - 416,666.67 = 4,583,333.33

Interest: 4,583,333.33 * 0.2 = 916,666.66

Payment: 416,666.67 + 916,666.66 = 1,333,333.33

Balance: 4,583,333.33 - 416,666.67 = 4,166,666.66

Thanks a lot! Anonymous, please tell me how to subtract a percentage of revenue. Using what formula? NMitra Revenue 1000 rubles, percentage to be deducted 35%

1000*0.35=350 rubles (this is a percentage of revenue, see first form)

1000 - 350 = 650 rubles (650 rubles left in revenue) Anonymous Air humidity 97%. Reduce by 1%. How much air humidity will there be after this? NMitra 96% as far as I understand. Anonymous amount 3395 of this 0.33% per day NMitra 3395*0.33=11.2035 Anonymous instead of 1600 1200 remained by what percentage NMitra decreased Proportion:

C = 2.2*B = 2.2 * A / 0.44 = 5

x% is 1000

x = 100000/4600 = 21.73913 (the one who gave 1000€)

21.73913 is x

x = 14500*21.73913/100 = 3152.17 (the one who gave 1000€)

3600*100:9900=37%, but this is a percentage of 1000

100%-37%=63%, this is a percentage of 3600

your amount = 63% (this is 6237 euros) + invested 3600 = 9837

mine = 37% (this is 3663 euros) + 1000 = 4663 euros. Anonymous How to prove to them... that they are wrong... it turns out that their amount has increased by 4.5 times... although the total amount is more than three times. I don't want to fight over money. NMitra You subtract the initial capital from the final amount. Let's assume.

And she (see comment 64):

21.73913% (the one who gave 1000€)

78.26087% (the one who gave 3600€)

1000 out of 4600 is 1/4.6 of the amount (4600/4.6=1000).

1/4 is 25%, 1/4.6 is (100/4.6=21.73913%)

In theory, you need to solve using the proportion 7*100/0; you cannot divide by 0. This baffles me! NMitra I agree with you, the question is not posed correctly, you cannot divide by zero, you can only divide by infinity small function. Anonymous So how to solve the example? Seems like a simple problem from primary school, but blew the minds of all my friends who are around thirty))) NMitra The question would make sense if it sounded like this: “How much in right hand does it have more apples than the left one?

7 - 0 = 7 Answer: for 7 apples. Maybe a typo? Anonymous Okay. I'm telling it like it is. My husband monitors violations at work. There were none in the first quarter. In the second, 7 were recorded. The data must be submitted in the form of a percentage: by what percentage were there more violations in the second quarter. If there were 4 and 5, respectively, then it would not be difficult to solve.

NMitra Nothing works, infinity ((

in the second there are 7 violations, which corresponds to x

or 1000 * 1.12 = 1120

91 years old - 20129.03 thousand rubles

92 year - 39686.42 thousand rubles

absolute change - 19557.39 thousand rubles

NMitra What were you looking for? Even by eye it is clear that 20 is less than 40 by half (50%), namely

x=19557.39*100/39686.42=49.28 Anonymous How is the amount calculated if: 1000*1.2^12=8916. NMitra ^ is the degree symbol https://ru.wikipedia.org/wiki/%C2%EE%E7%E2%E5%E4%E5%ED%E8%E5_%E2_%F1%F2%E5%EF%E5 %ED%FC#.D0.97.D0.BD.D0.B0.D1.87.D0.BE.D0.BA_.D1.81.D1.82.D0.B5.D0.BF.D0.B5. D0.BD.D0.B8

8,916100448 * 1000 = 8916,100448

In the first case, we will have 1000*1.2^3=1728 on deposit, i.e. almost 73% growth in three months.

What will happen to the second deposit, and here is the same formula: 1000 * 1.2^12 = 8916 rubles.

We get almost 800% profit or deposit growth almost 9 times in one year.

Specifically, I am interested in this formula, how it works in general or how the percentage of profit grows.

That is, interest is added to the total amount. Anonymous Hello,

Thanks for the great site and for the percentage calculations. Only I couldn't find "reverse calculation" here. For example, there is a number: 1045, from which I want to take 600 (for further actions). Question: this 600 is what percentage of 1045? And where is the magic calculator that can calculate this? 1045/100=10.45 is one percent. Then 10.45*at 600? It turns out to be nonsense! =6270. What is this? What kind of bullshit is this?

Thank you. NMitra Anonymous,

x = 100000*5/100 = 5000 Anonymous Hello NMitra.

Please tell me how the cost of 4.3 million rubles was calculated, otherwise nothing seems to fit:

turnover is 6 million rubles per month, the average markup is 39%, therefore the cost of production is 4.3 million.

NMitra 4.3 + 4.3 * 39 / 100 = 6

Cost = O/(1 + N/100) = 6 / (1 + 39 / 100)

I thought the markup was calculated in this way:

Is this wrong? Then what could I calculate in this way? NMitra 6*39/100 is 39 percent of 6

6 - 2.34 is 61 percent of 6

Anonymous Yes, I needed to subtract 39% of the markup from turnover in order to get the cost price without markup.

Thank you very much again! Anonymous Please explain how much less if 2800 goods were exported in 2013, and 2400 goods were exported in 2014, always take 2014 as 100%.

14.3% less exported in 2014? NMitra I can do it too. Anonymous Thank you Anonymous And in case of an increase, if the amounts are the same, then it will be the same - 14.3% NMitra No, the figure will be different Anonymous Why? NMitra To figure it out, formulate the problem and offer its solution. It’s harder to explain without examples, but now you yourself will understand the difference. Anonymous Please tell me how to calculate interest according to the French and German interest systems,

if the loan issuance date is April 22, 2014, and the repayment date is September 16, the loan rate is 16% per annum.

S = s * (1 + P/100 * d/D)

Interest rate (P) = 16

Number of days in a year (D) = 365 days or 366 ( leap year) days

Number of days (d) = 8 April + 31 May + 30 June + 31 July + 31 August + 16 September = 147 days

Number of days in a year (D) = 360 days

Number of days (d) = April 8 + May 30 + June 30 + July 30 + August 30 + September 16 = 144 days Anonymous NMitra! Thank you, you helped me out. Anonymous Hello! help me calculate the loan interest

We want to take out a loan from the bank, they give 440,000 / payment 11,722 per month for 60 months

NMitra Hello, is the payment constant throughout the entire term or does it decrease as the principal debt decreases? Is the interest monthly or annual? I would focus not on the percentage (some number, for example 20%), but on the final amount that you will give to the bank in addition to the principal debt with all additional commissions, including one-time ones:

703320 - 440000 = 263320 (of which percent)

263320/5 = 52664 (percent per year)

Anonymous Hello! 40,000 at 9.20%, how much interest will accrue after a month? NMitra 40000*0.092=3680

But! Your interest is most likely annual, so you will receive this amount after a year.

And this amount is for a month. But not exactly, since it is usually not the number of months that is counted, but the number of days during which the deposit will remain. IN different months different quantities days.

IF I COUNT CORRECTLY THEN IT WORKS: 344*100/30984 = 1.11 NMitra You think right. Anonymous Level of appeal of the population for medical care in 2013 there were 121,681 requests, in 2014 - 118,480

Based on the data, how to find the percentage reduction in the number of calls?

The following solution will be correct: 121681-118480=3201*100/121681= NMitra 121681 - 100%

x = 118480*100/121681 = 97.37%

Anonymous 65651651 Anonymous help

in 2001, revenue increased compared to 2000 by 2 percent, although it was planned to be 2 times by what percentage did not exceed the NMitra plan 2 times is 200%

200% - 2% = 198% (198% underfulfilled plan) Anonymous help

in the 2nd half of the year, parts were produced by 0.5% compared to the first half of the year, the production plan was not completed by 16.5%, how much % were planned to change the production decrease or increase Anonymous help answer the question. Watermelon contains 99% humidity, but after drying (put it in the sun for several days) its humidity is 98%. HOW MUCH % WILL THE WEIGHT OF A WATERMELON CHANGE AFTER DRYING? many thanks to NMitra About production: the task was formulated incorrectly

“in the 2nd half of the year, parts were produced by 0.5% compared to the first half of the year” - more or less?

x = 40% Anonymous My head is bursting, but in reality he cannot lose half the weight. This means that the mathematical calculation does not coincide with reality. In the summer I will conduct an experiment with watermelon :)))))) Thanks NMitra The ratio of humidity and weight can follow a hyperbole (see graphs of elementary functions) Sergey Ryskin Help me solve the problem of what number we subtracted 20% from to get 600

Sergey Ryskin Using the selection method, I realized that this is 750, do I need it to count like that in Excel? for this you need a formula, the question is in the formula, how is it written

NMitra 20% = 20/100 = 0.2

total amount: 12901.00 or

Explain to me if possible. NMitra The total amount was calculated incorrectly :)

And if 11740.4 is multiplied by 130%, what do we get? NMitra Formulate questions correctly:

Okay, I still don't understand.

(Example: There is a price list - three price columns

wholesale-(1006.00), retail+35% to wholesale (1358.00), internet+25% to wholesale (1258.00).

There is a retail price - 16772.00

we want to give a discount of -30% of the amount

Why can't NMitra 1006 (wholesale) be divided by 130%?

1006 + 352.1 = 1358.1 (different 35%)

1358,1 * 0,35 = 475.335

1358,1 - 475,335 = 882,765

Wholesale = Retail/(1 + percent/100) = 1358.1/(1 + 35/100) = 1358.1 / 1.35 = 1006

x = 50*100/1100 = 4.55% (percentage of discount from retail in terms of wholesale) Anonymous Thank you very much! russYliusha Hello everyone. I really need help. Let's say my friend took out a loan from a bank for 15,000 € for five years (60 months), he pays 270 € per month for five years, resulting in 16,200 €. Question:

How to find out Interest rate bank, that is, how much interest the bank takes.

THANK YOU. NMitra 16200 - 15000 = 1200 (over 5 years)

1200 / 5 = 240 (per year)

x% = 240*100/15000 = 1.6% (annual rate)

15000 / 60 = 250 (principal debt per month)

Could you tell me the formula in Excel? Or how to calculate all this in Excel!! Thank you very much!! NMitra I have no more knowledge than was taught at school in my time. Substitute known

Guys, how do I find out how much I get paid per hour?

Worked 80 hours and received 1000 €,

Thanks in advance!! NMitra 1 - x

x = 1000 / 80 = 12.5 € (per hour) maksimovgenya Good day.

4 of them are damaged books.

x = 100*4/113 = 3.54% Anonymous We need to find what percentage is 500,000 of 32,000,000, thank you in advance Anonymous There are 2,500 euros in the account, which were deposited for 3 months at 4%. After 3 months, there were 2570 euros in the account. Am I correct in thinking that 4% of 2500 is 100 euros, i.e. the final amount at the end of the period should be 2600 euros. But the operator said that the percentages cannot be calculated so “stupidly”. How is the calculation done in this case? NMitra 32,000,000 - 100%

x = 500,000 * 100 / 32,000,000 = 50 / 32 = 1.5625% (one and a half percent) NMitra Comment 158: Interest is calculated the same in all cases. The operator is obliged to explain to you exactly how the calculation occurs (how many days, what commissions are taken, etc.)!

I am missing the information you provided:

1) as a rule, the percentage is indicated annually (this way the percentage looks more impressive), but for you it’s for three months at once?

2) has a full three months passed since the account was opened?

3) the bank does not charge one-time commissions when opening/closing an account?

The concept of "margin" has different meaning, ask your colleagues in the shop what exactly they mean. NMitra Margin in % - the ratio of the difference between price and cost to price = (Price - Cost) * 100 / Price

Total cost = 900

x - 600 = 400 / 100 * 600 = 2400

x = 2400 + 600 = 3000

0.5 cu. cameras ___ X ?? watt

1.0 cu. cameras ___ 2948 watt NMitra 0.5 is half, but there is some other pattern in the problem, not percentages

2552,18 + 382.827 = 2935

z1 - end value of the range

x = (37-22)*100/(63-22) = 1500 / 41 = 37%

2 3 4 5 6 7 8 9 10 11 12 Evgeniya Nikolskaya Please help) 15% was added to the purchase price to obtain the selling price. How much percentage to subtract from the sales price to get the purchase price? NMitra See comment 95

NMitra 500 * 0.05 = 25 Anonymous, please tell me the total transport expense is 3700, two goods were brought in one car, costing one product 2200 and the second 27800, how to calculate their transport expense NMitra total 2200+27800=30000 (this is 100%)

x = 2200*3700/30000 = 271

x = 27800*3700/30000 = 3429 Anonymous NMitra

But what about bank interest, say, on a loan or deposit? Or the percentage of conversions from search? Or taxes for individual entrepreneurs?

x = (568 - 1.2y)/0.8 = 710 - 1.5y

y = 650 - 710 + 1.5y = -60 + 1.5y

x = 42*23/94 = 10 Artur Nechipuruk Oh, you've already unsubscribed.

Fortunately, my head was not yet so dull that I couldn’t solve it on my own, I remembered, took out a notebook and independently worked out the proportion needed here.. (you need to practice at least occasionally)

NMitra Multiply the number by 10101:) Artur Nechipuruk Yesterday I figured it out, read the explanations:) Anonymous it was 165 now 230 by what % did sales volume increase? NMitra 230-165=65

x = 65*100/165=39 (by 39%) Anonymous Question in the parking lot there were cars and trucks passenger cars are 1.15 times larger, what percentage of passenger cars are more than trucks

Interest calculator: 7 basic operations with percentages

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One percent is a hundredth of a number. This concept used when you need to indicate the ratio of a part to the whole. In addition, several values can be compared as percentages, but be sure to indicate relative to which whole the percentages are calculated. For example, expenses are 10% higher than income or the price of train tickets has increased by 15% compared to last year's tariffs. A percent number above 100 means that the proportion is greater than the whole, as is often the case in statistical calculations.

Percentage as financial concept- payment from the borrower to the lender for providing money for temporary use. In business, the expression “work for interest” is common. In this case, it is understood that the amount of remuneration depends on profit or turnover (commissions). It is impossible to do without calculating percentages in accounting, business, and banking. To simplify calculations, an online interest calculator has been developed.

The calculator allows you to calculate:

Percentage of the set value.
Percentage of the amount (tax on actual salary).
Percentage of the difference (VAT from the amount including VAT).

When solving problems using a percentage calculator, you need to operate with three values, one of which is unknown (a variable is calculated using the given parameters). The calculation scenario should be selected based on the specified conditions.

Examples of calculations

1. Calculating the percentage of a number

To find a number that is 25% of 1,000 rubles, you need:

To calculate using a regular calculator, you need to multiply 1,000 by 25 and press the % button.

2. Definition of an integer (100%)

We know that 250 rub. is 25% of a certain number. How to calculate it?

Let's make a simple proportion:

3. Percentage between two numbers

Let's say a profit of 800 rubles was expected, but we received 1,040 rubles. What is the percentage of excess?

The proportion will be like this:

Exceeding the profit plan is 30%, that is, fulfillment is 130%.

4. Calculation is not based on 100%

For example, a store consisting of three departments receives 100% of customers. In the grocery department - 800 people (67%), in the department household chemicals- 55. What percentage of buyers come to the household chemicals department?

5. By what percentage is one number less than another?

The price of the product dropped from 2,000 to 1,200 rubles. By what percentage did the price of the product fall or by what percentage did 1,200 less than 2,000?

2 000 - 100 %
1,200 – Y%
Y = 1,200 × 100 / 2,000 = 60% (60% to the figure 1,200 from 2,000)
100% − 60% = 40% (the number 1,200 is 40% less than 2,000)

6. By what percentage is one number greater than another?

The salary increased from 5,000 to 7,500 rubles. By what percentage did the salary increase? What percentage is 7,500 greater than 5,000?

5,000 rub. - 100%
7,500 rub. - Y%
Y = 7,500 × 100 / 5,000 = 150% (in numbers 7,500 is 150% of 5,000)
150% − 100% = 50% (the number 7,500 is 50% greater than 5,000)

7. Increase the number by a certain percentage

The price of product S is above 1,000 rubles. by 27%. What is the price of the product?

The online calculator makes calculations much simpler: you need to select the type of calculation, enter the number and percentage (in the case of calculating a percentage, the second number), indicate the accuracy of the calculation and give the command to begin the action.

How to calculate (calculate) the percentage of the amount?

How to calculate the percentage of the amount , you need to know in many cases (when calculating state duties, loans, etc.). We'll tell you how to calculate percentage of amount using a calculator, proportions and known relationships.

How to find out the percentage of the amount in the general case?

After this there are two options:

If you want to find out what percentage another amount is from the original, you just need to divide it by the 1% amount obtained earlier.
If you need an amount that is, say, 27.5% of the original, you need to multiply the amount of 1% by the required amount of interest.

How to calculate a percentage of an amount using a proportion?

But you can do it differently. To do this, you will have to use knowledge about the method of proportions, which takes place within the framework school course mathematics. It will look like this.

Let us have A - the principal amount equal to 100%, and B - the amount whose relationship with A as a percentage we need to find out. We write down the proportion:

(X in this case is the number of percent).

According to the rules for calculating proportions, we obtain the following formula:

If you need to find out how much the amount B will be if the number of percentages of the amount A is already known, the formula will look different:

Now all that remains is to substitute it into the formula known numbers- and you can make the calculation.

How to calculate the percentage of an amount using known ratios?

Finally, you can use more in a simple way. To do this, just remember that 1% as a decimal is 0.01. Accordingly, 20% is 0.2; 48% - 0.48; 37.5% is 0.375, etc. It is enough to multiply the original amount by the corresponding number - and the result will indicate the amount of interest.

In addition, sometimes you can use simple fractions. For example, 10% is 0.1, that is, 1/10; therefore, finding out how much 10% is is simple: you just need to divide the original amount by 10.

Other examples of such relationships would be:

12.5% - 1/8, that is, you need to divide by 8;
20% - 1/5, that is, you need to divide by 5;
25% - 1/4, that is, divide by 4;
50% - 1/2, that is, it needs to be divided in half;
75% is 3/4, that is, you need to divide by 4 and multiply by 3.

True, not all simple fractions are convenient for calculating percentages. For example, 1/3 is close in size to 33%, but not exactly equal: 1/3 is 33.(3)% (that is, a fraction with infinite threes after the decimal point).

How to subtract a percentage from an amount without using a calculator

If you need to subtract an unknown number, which is a certain amount of percent, from an already known amount, you can use the following methods:

Calculate the unknown number using one of the above methods, and then subtract it from the original one.
Immediately calculate the remaining amount. To do this, subtract from 100% the number of percentages that need to be subtracted, and convert the resulting result from percentage to number using any of the methods described above.

The second example is more convenient, so let’s illustrate it. Let's say we need to find out how much is left if we subtract 16% from 4779. The calculation will be like this:

We subtract 16 from 100 (the total number of percent). We get 84.
We calculate how much 84% of 4779 is. We get 4014.36.

How to calculate (subtract) a percentage from a sum with a calculator in hand

All of the above calculations are easier to do using a calculator. It can be either in the form of a separate device or in the form of a special program on a computer, smartphone or regular mobile phone (even the oldest devices currently in use usually have this function). With their help, the question how to calculate percentage from amount, The solution is very simple:

The initial amount is collected.
The “-” sign is pressed.
Enter the number of percentages you want to subtract.
The “%” sign is pressed.
The “=” sign is pressed.

As a result, the required number is displayed on the screen.

How to subtract a percentage from an amount using an online calculator

Finally, there are now quite a few sites on the Internet that implement the online calculator function. In this case, you don’t even need to know how to calculate percentage of amount: all user operations are reduced to entering the required numbers into the windows (or moving the sliders to obtain them), after which the result is immediately displayed on the screen.

This function is especially convenient for those who calculate not just an abstract percentage, but a specific size tax deduction or the amount of state duty. The fact is that in this case the calculations are more complicated: you not only need to find the percentages, but also add a constant part of the amount to them. An online calculator allows you to avoid such additional calculations. The main thing is to choose a site that uses data that complies with the current law.

Make up a proportion. In this article I want to talk to you about proportion. Understanding what proportion is and being able to compose it is very important, it really saves you. This seems to be a small and insignificant “letter” in the large alphabet of mathematics, but without it mathematics is doomed to be lame and incomplete.First, let me remind you what proportion is. This is an equality of the form:

which is the same (this is different shape records).

Example:

They say that one is to two as four is to eight. That is, this is the equality of two relations (in in this example relations are numerical).

Basic rule of proportion:

a:b=c:d

the product of the extreme terms is equal to the product of the middle terms

that is

a∙d=b∙c

*If any value in a proportion is unknown, it can always be found.

If we consider a recording form like:

then you can use the following rule, it is called the “rule of the cross”: the equality of the products of elements (numbers or expressions) standing on the diagonal is written down

a∙d=b∙c

As you can see the result is the same.

If the three elements of proportion are known, thenwe can always find a fourth.

This is precisely the essence of the benefit and necessityproportions when solving problems.

Let's look at all the options where the unknown quantity x is located “anywhere” in the proportion, where a, b, c are numbers:

The quantity standing diagonally from x is written in the denominator of the fraction, and known quantities standing diagonally are written in the numerator as a product. It is not necessary to memorize it; you will already calculate everything correctly if you have learned the basic rule of proportion.

Now the main question related to the title of the article. When does proportion save and where is it used? For example:

1. First of all, these are problems involving percentages. We looked at them in the articles "" and "".

2. Many formulas are given in the form of proportions:

>theorem of sines

> relationship of elements in a triangle

> tangent theorem

> Thales' theorem and others.

3. In geometry problems, the condition often specifies the ratio of sides (other elements) or areas, for example 1:2, 2:3 and others.

4. Conversion of units of measurement, and the proportion is used to convert units both in one measure and to convert from one measure to another:

- hours to minutes (and vice versa).

- units of volume, area.

— lengths, for example miles to kilometers (and vice versa).

— degrees to radians (and vice versa).

here you can’t do without drawing up proportions.

The key point is that you need to correctly establish the correspondence, let's look at simple examples:

You need to determine a number that is 35% of 700.

In problems involving percentages, the value with which we are comparing is taken as 100%. We denote the unknown number as x. Let's establish correspondence:

We can say that seven hundred thirty-five corresponds to 100 percent.

X corresponds to 35 percent. Means,

700 – 100%

x – 35%

Let's decide

Answer: 245

Let's convert 50 minutes to hours.

We know that one hour equals 60 minutes. Let us denote the correspondence -x hours is 50 minutes. Means

1 – 60

x – 50

We decide:

That is, 50 minutes is five-sixths of an hour.

Answer: 5/6

Nikolai Petrovich drove 3 kilometers. How much will it be in miles (consider that 1 mile is 1.6 km)?

It is known that 1 mile is 1.6 kilometers. Let’s take the number of miles that Nikolai Petrovich has traveled as x. We can match:

One mile corresponds to 1.6 kilometers.

X miles is three kilometers.

1 – 1,6

x – 3

Answer: 1,875 miles

You know that there are formulas for converting degrees to radians (and vice versa). I don’t write them down, because I think it’s unnecessary to memorize them, and so you have to keep a lot of information in your memory. You can always convert degrees to radians (and vice versa) if you use a proportion.

Let's convert 65 degrees to radian units.

The main thing to remember is that 180 degrees is Pi radians.

Let us denote the desired quantity as x. We establish correspondence.

One hundred and eighty degrees corresponds to Pi radians.

Sixty-five degrees corresponds to x radians. study the article on this topic on the blog. The material in it is presented somewhat differently, but the principle is the same. I'll finish with this. There will definitely be something more interesting, don’t miss it!

If we recall the very definition of mathematics, then it contains the following words: mathematics studies quantitative RELATIONS (RELATIONS- Here keyword). As you can see, the very definition of mathematics contains proportion. In general, mathematics without proportion is not mathematics!!!

All the best!

Best regards, Alexander

P.S: I would be grateful if you tell me about the site on social networks.

Solving most problems in high school mathematics requires knowledge of proportions. This simple skill will help you not only perform complex exercises from the textbook, but also delve into the very essence of mathematical science. How to make a proportion? Let's figure it out now.

The simplest example is a problem where three parameters are known, and the fourth needs to be found. The proportions are, of course, different, but often you need to find some number using percentages. For example, the boy had ten apples in total. He gave the fourth part to his mother. How many apples does the boy have left? This is the simplest example that will allow you to create a proportion. The main thing is to do this. Initially there were ten apples. Let it be 100%. We marked all his apples. He gave one-fourth. 1/4=25/100. This means he has left: 100% (it was originally) - 25% (he gave) = 75%. This figure shows the percentage of the amount of fruit remaining compared to the amount initially available. Now we have three numbers by which we can already solve the proportion. 10 apples - 100%, X apples - 75%, where x is the required amount of fruit. How to make a proportion? You need to understand what it is. Mathematically it looks like this. The equal sign is placed for your understanding.

10 apples = 100%;

x apples = 75%.

Solving a proportion often comes down to simple multiplication and then division. Schools do not explain to children why this is so. Although it is important to understand that proportional relationships are mathematical classics, the very essence of science. To solve proportions, you need to be able to handle fractions. For example, you often need to convert percentages to fractions. That is, recording 95% will not work. And if you immediately write 95/100, then you can make significant reductions without starting the main calculation. It’s worth saying right away that if your proportion turns out to be with two unknowns, then it cannot be solved. No professor will help you here. And your task most likely has a more complex algorithm for correct actions.

5 liters - 150 rubles;

30 liters - x rubles;

Let's solve this proportion:

x = 900 rubles.

From a mathematical point of view, a proportion is the equality of two ratios. Interdependence is characteristic of all parts of the proportion, as well as their unchanging result. You can understand how to create a proportion by familiarizing yourself with the properties and formula of proportion. To understand the principle of solving proportions, it will be enough to consider one example. Only by directly solving proportions can you quickly and easily learn these skills. And this article will help the reader with this.

Properties of proportion and formula

Reversal of proportion. In the case when the given equality looks like 1a: 2b = 3c: 4d, write 2b: 1a = 4d: 3c. (And 1a, 2b, 3c and 4d are prime numbers, different from 0).
Multiplying the given terms of the proportion crosswise. IN literal expression it looks like this: 1a: 2b = 3c: 4d, and writing 1a4d = 2b3c will be equivalent to it. Thus, the product of the extreme parts of any proportion (the numbers at the edges of the equality) is always equal to the product middle parts (numbers located in the middle of the equality).
When drawing up a proportion, its property of rearranging the extreme and middle terms can also be useful. The formula of equality 1a: 2b = 3c: 4d can be displayed in the following ways:
- 1a: 3c = 2b: 4d (when the middle terms of the proportion are rearranged).
- 4d: 2b = 3c: 1a (when the extreme terms of the proportion are rearranged).
Its property of increasing and decreasing helps perfectly in solving proportions. When 1a: 2b = 3c: 4d, write:
- (1a + 2b) : 2b = (3c + 4d) : 4d (equality by increasing proportion).
- (1a – 2b) : 2b = (3c – 4d) : 4d (equality by decreasing proportion).
You can create a proportion by adding and subtracting. When the proportion is written as 1a:2b = 3c:4d, then:
- (1a + 3c) : (2b + 4d) = 1a: 2b = 3c: 4d (the proportion is made by addition).
- (1a – 3c) : (2b – 4d) = 1a: 2b = 3c: 4d (the proportion is calculated by subtraction).
Also, when solving a proportion containing fractional or big numbers, you can divide or multiply both of its terms by the same number. For example, the components of the proportion 70:40=320:60 can be written as follows: 10*(7:4=32:6).
An option for solving proportions with percentages looks like this. For example, write down 30=100%, 12=x. Now you should multiply the middle terms (12*100) and divide by the known extreme (30). Thus, the answer is: x=40%. In a similar way, if necessary, you can multiply the known extreme terms and divide them by a given average number, obtaining the desired result.

If you are interested in a specific proportion formula, then in the simplest and most common version, the proportion is the following equality (formula): a/b = c/d, in which a, b, c and d are four non-zero numbers.

But not everything is as complicated and incomprehensible as it seems at first glance. Why is all this needed? Here is the most common example.

Let's say we have an image upload on our website, and we want that after loading we create a miniature copy, a preview of the image. This is often necessary to announce news, for example. And the script requires that you specify at least the approximate dimensions of the miniature image - its width and height.

Let's also say that you have already outlined its width, but what about the height? How to calculate it so that the picture seems more or less proportional to the original one.

Calculation formula

Everything is done in two stages:

1 - Divide the original width by the required width;
2 - We obtain the required height by dividing the original height by the result of dividing the two widths (step 1).

Example. Let’s take the image sizes already known to everyone: 1024x768 and 800x600. Let's imagine that we don't know the height of the second picture. The formula gives the following: 768/(1024/800) = 600 . This is the height we require.

If we know the height, but we need to get the width, then we need to do everything as in the first formula, only in reverse.

To get the required width you need:

1 - Divide the original height by the required height;
2 - We obtain the required width by dividing the original width by the result of dividing the two heights (step 1).

That is, 1024/(768/600) = 800 .