How is proportion calculated with percentages? Calculating the percentage of a number

§ 125. The concept of proportion.

Proportion is the equality of two ratios. Here are examples of equalities called proportions:

Note. The names of the quantities in the proportions are not indicated.

Proportions are usually read as follows: 2 is to 1 (unit) as 10 is to 5 (the first proportion). You can read it differently, for example: 2 is as many times more than 1, how many times is 10 more than 5. The third proportion can be read like this: - 0.5 is as many times less than 2, how many times 0.75 is less than 3.

The numbers included in the proportion are called members of the proportion. This means that the proportion consists of four terms. The first and last members, i.e. the members standing at the edges, are called extreme, and the terms of the proportion located in the middle are called average members. This means that in the first proportion the numbers 2 and 5 will be the extreme terms, and the numbers 1 and 10 will be the middle terms of the proportion.

§ 126. The main property of proportion.

Consider the proportion:

Let us multiply its extreme and middle terms separately. The product of the extremes is 6 4 = 24, the product of the middle ones is 3 8 = 24.

Let's consider another proportion: 10: 5 = 12: 6. Let's multiply the extreme and middle terms separately here too.

The product of the extremes is 10 6 = 60, the product of the middle ones is 5 12 = 60.

The main property of proportion: the product of the extreme terms of a proportion is equal to the product of its middle terms.

In general, the main property of proportion is written as follows: ad = bc .

Let's check it on several proportions:

1) 12: 4 = 30: 10.

This proportion is correct, since the ratios from which it is composed are equal. At the same time, taking the product of the extreme terms of the proportion (12 10) and the product of its middle terms (4 30), we will see that they are equal to each other, i.e.

12 10 = 4 30.

2) 1 / 2: 1 / 48 = 20: 5 / 6

The proportion is correct, which is easy to verify by simplifying the first and second ratios. The main property of proportion will take the form:

1 / 2 5 / 6 = 1 / 48 20

It is not difficult to verify that if we write an equality in which on the left side there is the product of two numbers, and on the right side the product of two other numbers, then a proportion can be made from these four numbers.

Let us have an equality that includes four numbers multiplied in pairs:

these four numbers can be terms of a proportion, which is not difficult to write if we take the first product as the product of the extreme terms, and the second as the product of the middle terms. The published equality can be compiled, for example, into the following proportion:

In general, from equality ad = bc the following proportions can be obtained:

Do the following exercise yourself. Given the product of two pairs of numbers, write the proportion corresponding to each equality:

a) 1 6 = 2 3;

b) 2 15 = b 5.

§ 127. Calculation of unknown terms of proportion.

The basic property of proportion allows you to calculate any of the terms of the proportion if it is unknown. Let's take the proportion:

X : 4 = 15: 3.

In this proportion one extreme member is unknown. We know that in any proportion the product of the extreme terms is equal to the product of the middle terms. On this basis we can write:

x 3 = 4 15.

After multiplying 4 by 15, we can rewrite this equation as follows:

X 3 = 60.

Let's consider this equality. In it, the first factor is unknown, the second factor is known, and the product is known. We know that to find an unknown factor, it is enough to divide the product by another (known) factor. Then it will turn out:

X = 60:3, or X = 20.

Let's check the result found by substituting the number 20 instead of X in this proportion:

The proportion is correct.

Let's think about what actions we had to perform to calculate the unknown extreme term of the proportion. Of the four terms of the proportion, only the extreme one was unknown to us; the middle two and the second extreme were known. To find the extreme term of the proportion, we first multiplied the middle terms (4 and 15), and then divided the found product by the known extreme term. Now we will show that the actions would not change if the desired extreme term of the proportion were not in the first place, but in the last. Let's take the proportion:

70: 10 = 21: X .

Let's write down the main property of proportion: 70 X = 10 21.

Multiplying the numbers 10 and 21, we rewrite the equality as follows:

70 X = 210.

Here one factor is unknown; to calculate it, it is enough to divide the product (210) by another factor (70),

X = 210: 70; X = 3.

So we can say that each extreme term of the proportion is equal to the product of the averages divided by the other extreme.

Let us now move on to calculating the unknown average term. Let's take the proportion:

30: X = 27: 9.

Let's write the main property of proportion:

30 9 = X 27.

Let's calculate the product of 30 by 9 and rearrange the parts of the last equality:

X 27 = 270.

Let's find the unknown factor:

X = 270:27, or X = 10.

Let's check with substitution:

30:10 = 27:9. The proportion is correct.

Let's take another proportion:

12: b = X : 8. Let's write the main property of proportion:

12 . 8 = 6 X . Multiplying 12 and 8 and rearranging the parts of the equality, we get:

6 X = 96. Find the unknown factor:

X = 96:6, or X = 16.

Thus, each middle term of the proportion is equal to the product of the extremes divided by the other middle.

Find the unknown terms of the following proportions:

1) A : 3= 10:5; 3) 2: 1 / 2 = x : 5;

2) 8: b = 16: 4; 4) 4: 1 / 3 = 24: X .

The last two rules can be written in general form as follows:

1) If the proportion looks like:

x: a = b: c , That

2) If the proportion looks like:

a: x = b: c , That

§ 128. Simplification of proportion and rearrangement of its terms.

In this section we will derive rules that allow us to simplify the proportion in the case when it includes large numbers or fractional terms. The transformations that do not violate the proportion include the following:

1. Simultaneous increase or decrease of both terms of any ratio by the same number of times.

EXAMPLE 40:10 = 60:15.

Multiplying both terms of the first ratio by 3 times, we get:

120:30 = 60: 15.

The proportion was not violated.

Reducing both terms of the second relation by 5 times, we get:

We got the correct proportion again.

2. Simultaneous increase or decrease of both previous or both subsequent terms by the same number of times.

Example. 16:8 = 40:20.

Let us double the previous terms of both relations:

We got the correct proportion.

Let us decrease the subsequent terms of both relations by 4 times:

The proportion was not violated.

The two conclusions obtained can be briefly stated as follows: The proportion will not be violated if we simultaneously increase or decrease by the same number of times any extreme term of the proportion and any middle one.

For example, reducing by 4 times the 1st extreme and 2nd middle terms of the proportion 16:8 = 40:20, we get:

3. Simultaneous increase or decrease of all terms of the proportion by the same number of times. Example. 36:12 = 60:20. Let's increase all four numbers by 2 times:

The proportion was not violated. Let's decrease all four numbers by 4 times:

The proportion is correct.

The listed transformations make it possible, firstly, to simplify proportions, and secondly, to free them from fractional terms. Let's give examples.

1) Let there be a proportion:

200: 25 = 56: x .

In it, the members of the first ratio are relatively large numbers, and if we wanted to find the value X , then we would have to perform calculations on these numbers; but we know that the proportion will not be violated if both terms of the ratio are divided by the same number. Let's divide each of them by 25. The proportion will take the form:

8:1 = 56: x .

We have thus obtained a more convenient proportion, from which X can be found in the mind:

2) Let's take the proportion:

2: 1 / 2 = 20: 5.

In this proportion there is a fractional term (1/2), from which you can get rid of. To do this, you will have to multiply this term, for example, by 2. But we do not have the right to increase one middle term of the proportion; it is necessary to increase one of the extreme members along with it; then the proportion will not be violated (based on the first two points). Let's increase the first of the extreme terms

(2 2) : (2 1/2) = 20:5, or 4:1 = 20:5.

Let's increase the second extreme member:

2: (2 1/2) = 20: (2 5), or 2: 1 = 20: 10.

Let's look at three more examples of freeing proportions from fractional terms.

Example 1. 1 / 4: 3 / 8 = 20:30.

Let's bring the fractions to a common denominator:

2 / 8: 3 / 8 = 20: 30.

Multiplying both terms of the first ratio by 8, we get:

Example 2. 12: 15 / 14 = 16: 10 / 7. Let's bring the fractions to a common denominator:

12: 15 / 14 = 16: 20 / 14

Let's multiply both subsequent terms by 14, we get: 12:15 = 16:20.

Example 3. 1 / 2: 1 / 48 = 20: 5 / 6.

Let's multiply all terms of the proportion by 48:

24: 1 = 960: 40.

When solving problems in which some proportions occur, it is often necessary to rearrange the terms of the proportion for different purposes. Let's consider which permutations are legal, i.e., do not violate the proportions. Let's take the proportion:

3: 5 = 12: 20. (1)

Rearranging the extreme terms in it, we get:

20: 5 = 12:3. (2)

Let us now rearrange the middle terms:

3:12 = 5: 20. (3)

Let us rearrange both the extreme and middle terms at the same time:

20: 12 = 5: 3. (4)

All these proportions are correct. Now let's put the first relation in the place of the second, and the second in the place of the first. You get the proportion:

12: 20 = 3: 5. (5)

In this proportion we will make the same rearrangements as we did before, that is, we will first rearrange the extreme terms, then the middle ones, and finally, both the extremes and the middle ones at the same time. You will get three more proportions, which will also be fair:

5: 20 = 3: 12. (6)

12: 3 = 20: 5. (7)

5: 3 = 20: 12. (8)

So, from one given proportion, by rearranging, you can get 7 more proportions, which together with this one makes 8 proportions.

The validity of all these proportions is especially easy to discover when writing in letters. The 8 proportions obtained above take the form:

a: b = c: d; c: d = a: b ;

d: b = c: a; b:d = a:c;

a: c = b: d; c: a = d: b;

d: c = b: a; b: a = d: c.

It is easy to see that in each of these proportions the main property takes the form:

ad = bc.

Thus, these permutations do not violate the fairness of the proportion and can be used if necessary.

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

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A simple example when you need to apply knowledge about solving proportions: how to calculate 13% of your salary - the same percentage 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 the total number of employees: X (persons) = 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

A cube is a special case of 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, thirteen percent must be subtracted from the total monetary amount. How to do it? After all, it is impossible to subtract different types of numbers without a certain

Everything is relative. The ratio of some quantities to each other can be expressed as a percentage. For example, by calculating what percentage of liquid from the bulk 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

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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

The need for complex mathematical calculations makes the average person's head spin. Try to calculate the amount of income tax on 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, “more 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

Solving most problems in high school mathematics requires knowledge of formulating 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.

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 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.

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 the total. 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 make a script to calculate the cost of a stretch ceiling. NMitra But what about bank interest, say, on a loan or 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 that has to do with numbers and calculations. And oddly enough, I’m studying to be a financier, but I don’t know the most basic arithmetic operations. 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 diluted) continue to calculate the percentages. And how many drops per ml depends on many factors (state of thickness, pipette size, etc.) Anonymous Hi, how can you find out the difference between 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?

* to pay 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 an infinitesimal function. Anonymous So how to solve the example? It seems like a simple problem from elementary school, but it blew the minds of all my friends who are around thirty))) NMitra The question would make sense if it sounded like this: “How many more apples does he have in his right hand than in his left?”

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, 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's 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 interest on the loan

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. Different months have different numbers of days.

IF I COUNT CORRECTLY THEN IT WORKS: 344*100/30984 = 1.11 NMitra You think right. Anonymous The level of population seeking medical care in 2013 was 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% by how much% it was 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, which results in 16,200 €. Question:

How to find out the bank's interest rate, 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 €,

Thank you 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 meanings; 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 :) Arthur Nechipuruk Yesterday I figured it out, read the explanations :) Anonymous it was 165 now 230 by what % did the sales volume increase? NMitra 230-165=65

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

Interest calculator: 7 basic operations with percentages

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One percent is a hundredth of a number. This concept is used when it is necessary to denote the relationship of a share to the whole. In addition, several values can be compared as percentages, but be sure to indicate relative to which integer 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.

Interest as a financial concept is a payment from a borrower to a 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 household chemicals department - 55. What percentage of customers 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 is taught as part of the school mathematics course. It will look like this.

Let us have A - the main 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 known numbers into the formula - and you can make the calculation.

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

Finally, you can use a simpler method. 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 from an already known amount, which is a certain amount of percent, 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 amount of 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.

A proportion is a mathematical expression that compares two or more numbers to each other. Proportions can compare absolute values and quantities or parts of a larger whole. Proportions can be written and calculated in several different ways, but the basic principle is the same.

Steps

Part 1

What is proportion

Find out what proportions are for. Proportions are used both in scientific research and in everyday life to compare different quantities and quantities. In the simplest case, two numbers are compared, but a proportion can include any number of quantities. When comparing two or more quantities, you can always use proportion. Knowing how quantities relate to each other allows, for example, to write down chemical formulas or recipes for various dishes. Proportions will be useful to you for a variety of purposes.

Learn what proportion means. As noted above, proportions allow us to determine the relationship between two or more quantities. For example, if you need 2 cups of flour and 1 cup of sugar to make cookies, we say that there is a 2 to 1 ratio between the amount of flour and sugar.
- Proportions can be used to show how different quantities relate to each other, even if they are not directly related (unlike a recipe). For example, if there are five girls and ten boys in a class, the ratio of girls to boys is 5 to 10. In this case, one number is not dependent on or directly related to the other: the proportion may change if someone leaves the class or vice versa , new students will come to it. A proportion simply allows you to compare two quantities.
Notice the different ways of expressing proportions. Proportions can be written in words or using mathematical symbols.
- In everyday life, proportions are more often expressed in words (as above). Proportions are used in a variety of fields, and unless your profession is related to mathematics or other science, this is the way you will most often come across this way of writing proportions.
- Proportions are often written using a colon. When comparing two numbers using a proportion, they can be written with a colon, for example 7:13. If more than two numbers are being compared, a colon is placed consecutively between each two numbers, for example 10:2:23. In the above example for a class, we are comparing the number of girls and boys, with 5 girls: 10 boys. Thus, in this case the proportion can be written as 5:10.
- Sometimes a fraction sign is used when writing proportions. In our class example, the ratio of 5 girls to 10 boys would be written as 5/10. In this case, you should not read the “divide” sign and you must remember that this is not a fraction, but a ratio of two different numbers.
Part 2
Operations with proportions
1. Reduce the proportion to its simplest form. Proportions can be simplified, like fractions, by reducing their members by a common divisor. To simplify a proportion, divide all numbers included in it by common divisors. However, we should not forget about the initial values that led to this proportion.
  - In the example above with a class of 5 girls and 10 boys (5:10), both sides of the proportion have a common factor of 5. Dividing both quantities by 5 (the greatest common factor) gives a ratio of 1 girl to 2 boys (i.e. 1:2) . However, when using a simplified proportion, you should remember the original numbers: there are not 3 students in the class, but 15. The reduced proportion only shows the ratio between the number of girls and boys. For every girl there are two boys, but this does not mean that there is 1 girl and 2 boys in the class.
  - Some proportions cannot be simplified. For example, the ratio 3:56 cannot be reduced, since the quantities included in the proportion do not have a common divisor: 3 is a prime number, and 56 is not divisible by 3.
2. To “scale” proportions can be multiplied or divided. Proportions are often used to increase or decrease numbers in proportion to each other. Multiplying or dividing all quantities included in a proportion by the same number keeps the relationship between them unchanged. Thus, the proportions can be multiplied or divided by the “scale” factor.
  - Let's say a baker needs to triple the amount of cookies he bakes. If flour and sugar are taken in a ratio of 2 to 1 (2:1), to triple the amount of cookies, this proportion should be multiplied by 3. The result will be 6 cups of flour to 3 cups of sugar (6:3).
  - You can do the opposite. If the baker needs to reduce the amount of cookies by half, both parts of the proportion should be divided by 2 (or multiplied by 1/2). The result is 1 cup of flour per half cup (1/2, or 0.5 cup) of sugar.
3. Learn to find an unknown quantity using two equivalent proportions. Another common problem for which proportions are widely used is finding an unknown quantity in one of the proportions if a second proportion similar to it is given. The rule for multiplying fractions greatly simplifies this task. Write each proportion as a fraction, then equate these fractions to each other and find the required quantity.
  - Let's say we have a small group of students consisting of 2 boys and 5 girls. If we want to maintain the ratio between boys and girls, how many boys should there be in a class of 20 girls? First, let's create both proportions, one of which contains the unknown quantity: 2 boys: 5 girls = x boys: 20 girls. If we write the proportions as fractions, we get 2/5 and x/20. After multiplying both sides of the equality by the denominators, we obtain the equation 5x=40; divide 40 by 5 and ultimately find x=8.
Part 3
Troubleshooting
1. When operating with proportions, avoid addition and subtraction. Many problems with proportions sound like the following: “To prepare a dish you need 4 potatoes and 5 carrots. If you want to use 8 potatoes, how many carrots will you need?” Many people make the mistake of trying to simply add up the corresponding values. However, to maintain the same proportion, you should multiply rather than add. Here is the wrong and correct solution to this problem:
  - Incorrect method: “8 - 4 = 4, that is, 4 potatoes were added to the recipe. This means that you need to take the previous 5 carrots and add 4 to them so that... something is wrong! Proportions work differently. Let's try again".
  - Correct method: “8/4 = 2, that is, the number of potatoes has doubled. This means that the number of carrots should be multiplied by 2. 5 x 2 = 10, that is, 10 carrots must be used in the new recipe.”
2. Convert all values to the same units. Sometimes the problem occurs because quantities have different units. Before writing down the proportion, convert all quantities into the same units. For example:
  - The dragon has 500 grams of gold and 10 kilograms of silver. What is the ratio of gold to silver in dragon hoards?
  - Grams and kilograms are different units of measurement, so they should be unified. 1 kilogram = 1,000 grams, that is, 10 kilograms = 10 kilograms x 1,000 grams/1 kilogram = 10 x 1,000 grams = 10,000 grams.
  - So the dragon has 500 grams of gold and 10,000 grams of silver.
  - The ratio of the mass of gold to the mass of silver is 500 grams of gold/10,000 grams of silver = 5/100 = 1/20.
3. Write down the units of measurement in the solution to the problem. In problems with proportions, it is much easier to find an error if you write down its units of measurement after each value. Remember that if the numerator and denominator have the same units, they cancel. After all possible abbreviations, your answer should have the correct units of measurement.
  - For example: given 6 boxes, and in every three boxes there are 9 balls; how many balls are there in total?
  - Incorrect method: 6 boxes x 3 boxes/9 marbles = ... Hmm, nothing is reduced, and the answer comes out to be “boxes x boxes / marbles“. It does not make sense.
  - Correct method: 6 boxes x 9 balls/3 boxes = 6 boxes x 3 balls/1 box = 6 x 3 balls/1= 18 balls.

The ability to calculate a percentage of a number when you need to find out a late fee, the amount of an overpayment on a loan, or a company’s profit if its turnover and markup are known.

How to find a number by its percentage?

Rule. To find a number by its specified percentage, you need to divide the given number by the given percentage value, and multiply the result by 100.

With this calculation, we first determine how many units of this number are contained in 1%, and then in the whole number (100%).

For example:
A number whose 23% is 52 is found like this:
52: 23 * 100 = 226.1

This means that if the number 226.1 is equal to 100%, then the number 52 is equal to 23% of this number.

We find a number whose 125% is 240 as follows:
240: 125 * 100 = 192.

When determining a number by its percentage, remember that:

- if the percentage is less than 100%, then the number obtained as a result of calculations is greater than the specified number (if 23%< 100%, то 226,1 > 52);
— if the percentage is greater than 100%, then the number obtained as a result of the calculation is less than the specified number (if 125% > 100%, then 192< 240).

Therefore, when calculating a number by its percentage, for self-control you need to check:

— the percentage specified in the condition is greater or less than 100%;
— the result of a calculation is greater or less than a given number.

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?

To do this, you will have to use knowledge about the method of proportions, which is taught as part of the school mathematics course. It will look like this:

Let A be the principal amount equal to 100%, and B be the amount whose relationship with A as a percentage we need to know. 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:

X = 100 * V / A

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:

B = 100 * X / A

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

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

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.

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

If you need to subtract an unknown number from an already known amount, which is a certain amount of percent, 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 an amount with a calculator in hand?

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?

Online interest calculator:

calculator.ru - allows you to perform various calculations when working with percentages;

mirurokov.ru - interest calculator;

A source of information:

nsovetnik.ru - article on how to calculate the percentage of the amount;

In the last video lesson we looked at solving problems involving percentages using proportions. Then, according to the conditions of the problem, we needed to find the value of one or another quantity.

This time the initial and final values have already been given to us. Therefore, the problems will require you to find percentages. More precisely, by how many percent has this or that value changed. Let's try.

Task. The sneakers cost 3,200 rubles. After the price increase, they began to cost 4,000 rubles. By what percentage was the price of sneakers increased?

So, we solve through proportion. The first step - the original price was 3,200 rubles. Therefore, 3200 rubles is 100%.

In addition, we were given the final price - 4000 rubles. This is an unknown percentage, so let's call it x. We get the following construction:

3200 — 100%
4000 - x%

Well, the condition of the problem is written down. Let's make a proportion:

The fraction on the left cancels perfectly by 100: 3200: 100 = 32; 4000: 100 = 40. Alternatively, you can shorten it by 4: 32: 4 = 8; 40: 4 = 10. We get the following proportion:

Let's use the basic property of proportion: the product of the extreme terms is equal to the product of the middle terms. We get:

8 x = 100 10;
8x = 1000.

This is an ordinary linear equation. From here we find x:

x = 1000: 8 = 125

So, we got the final percentage x = 125. But is the number 125 a solution to the problem? No way! Because the task requires finding out by how many percent the price of sneakers was increased.

By what percentage - this means that we need to find the change:

∆ = 125 − 100 = 25

We received 25% - that’s how much the original price was increased. This is the answer: 25.

Problem B2 on percentages No. 2

Let's move on to the second task.

Task. The shirt cost 1800 rubles. After the price was reduced, it began to cost 1,530 rubles. By what percentage was the price of the shirt reduced?

Let's translate the condition into mathematical language. The original price is 1800 rubles - this is 100%. And the final price is 1,530 rubles - we know it, but we don’t know what percentage it is of the original value. Therefore, we denote it by x. We get the following construction:

1800 — 100%
1530 - x%

Based on the received record, we create a proportion:

To simplify further calculations, let's divide both sides of this equation by 100. In other words, we will cross out two zeros from the numerator of the left and right fractions. We get:

Now let's use the basic property of proportion again: the product of the extreme terms is equal to the product of the middle terms.

18 x = 1530 1;
18x = 1530.

All that remains is to find x:

x = 1530: 18 = (765 2) : (9 2) = 765: 9 = (720 + 45) : 9 = 720: 9 + 45: 9 = 80 + 5 = 85

We got that x = 85. But, as in the previous problem, this number in itself is not the answer. Let's go back to our condition. Now we know that the new price obtained after the reduction is 85% of the old one. And in order to find changes, you need from the old price, i.e. 100%, subtract the new price, i.e. 85%. We get:

∆ = 100 − 85 = 15

This number will be the answer: Please note: exactly 15, and in no case 85. That's all! The problem is solved.

Attentive students will probably ask: why in the first problem, when finding the difference, did we subtract the initial number from the final number, and in the second problem did exactly the opposite: from the initial 100% we subtracted the final 85%?

Let's be clear on this point. Formally, in mathematics, a change in a quantity is always the difference between the final value and the initial value. In other words, in the second problem we should have gotten not 15, but −15.

However, this minus should under no circumstances be included in the answer, because it is already taken into account in the conditions of the original problem. It says directly about the price reduction. And a price reduction of 15% is the same as a price increase of −15%. That is why in the solution and answer to the problem it is enough to simply write 15 - without any minuses.

That's it, I hope we have sorted this out. This concludes our lesson for today. See you again!