Today, in the modern world can not do without interest.Even in school, starting from the 5th grade, children learn the concept and tasks of this magnitude.Interest found in every sphere of modern structures.Take, for example, banks, the size of the overpayment the loan depends on the value specified in the contract;the dimension of income is also affected by the interest rate.Therefore vital to know what percentage.
concept percent
According to one legend, the percentage appeared from behind a silly typo.Typewriting had put the number 100, but has mixed and set as follows: 010. This was the reason that the first zero bit of rose and the second dropped.The unit became a backslash.Such manipulations were the fact that there was a percent sign.Of course, there are other legends about the origin of this magnitude.
the percentage of Indians known in the V century.In Europe decimals, which is closely linked our concept emerged after a millennium.For the first time in the Old World, the judgment that this percentage has introduced a scientist from Belgium Simon Stevin.In 1584 it was first published table of values by the same researchers.
word "interest" has its origins in the Latin language as a pro centum.If we translate the phrase, you get "the hundred."So, under the percentage refers to one hundredth of a magnitude number.This value is indicated by the sign%.
Thanks interest an opportunity to compare parts of a whole without difficulty.The advent of shares greatly simplify calculations, so they have become so common.
Translation fractions to percentages
To convert a decimal to a percentage, you may need the so-called formula per cent, the fraction is multiplied by 100, the result is ascribed%.
If you want to convert to a percentage of fractions, it is necessary to start to make a decimal, and then use the above formula.
Translation percent fraction
As such, the formula percent is conditional enough.But you need to know how to translate this value into the fractional expression.To convert the share (percentage) in decimals, you must remove the% sign and share figure is 100.
formula for calculating the percentage of the number of
For Tests on chemicals assessment "excellent" received 30% of the students.Total 40 students in the class.How many students have written quiz on the "5"? This task shows how to find out the percentage of the number.
Solution:
1) 40 x 30 = 1200.
2) 1200: 100 = 12 (students).
answer quiz on the "5" written by 12 students.
You can use ready-made table that lists some fractions and percentages that correspond to them.
turns out that the number percent of the formula as follows: C = (A ∙ B) / 100 where A - the original number (in the specific example equal to 40);B - amount of interest (in this task B = 30%);C - the desired result.
formula for counting the number of percentage
next task will show what percentage, and how to find the number of percentage.
Garment factory manufactured dresses 1200, where 32% of them - dress the new style.How many dresses new style produced a garment factory?
Solution:
1. 1200: 100 = 12 (dresses) - 1% of the issued products.
2. 12 x 32 = 384 (dresses).
Answer: The factory produced 384 new style dresses.
If you want to find a number of his interest, you can use the following formula: C = (A ∙ 100) / B, where A - the total number of items (in this case A = 1200);B - amount of interest (in particular the problem of B = 32%);C - the unknown quantity.
increase, decrease the number of a predetermined amount of interest
Students need to learn what the interest is to consider them and to solve various problems.To do this you need to understand how increases or decreases in the number of N%.
often given the job, and in life it is necessary to know what will be equal to the numbers increased by a predetermined amount of interest.For example, given the number H. It is necessary to know what is the value of X if it is increased, for example, 40%.First you need to transfer 40% of Float (40/100).So, the result will be the increase in the number of X: X + 40% ∙ x = (1 + 40/100) ∙ x = 1,4 ∙ H. If instead substitute any number of X, let's take, for example, 100, then the entire expression will be equal to: 1,4 ∙ X = 1,4 ∙ 100 = 140.
Around the same principle is used when reducing the number of the specified number of percents.It is necessary to carry out the calculations: X - X ∙ 40% = A ∙ (1-40 / 100) = 0,6 ∙ H. If the value is 100, then 0.6 ∙ X = 0.6.100 = 60.
There are jobs where you need to find out the percentage increase in the number.
For example, given the task: driver was driving along one section of a journey at a speed of 80 km / h.On the other site of the train speed increased to 100 km / h.By what percentage has increased the speed of the train?
Solution:
Suppose 80 km / h - 100%.Then we make the calculations: (100% ∙ 100 km / h) / 80 km / h = 1000: 8 = 125%.It turns out that 100 km / h - this is 125%.To determine how much the speed increased, it is necessary to calculate: 125% - 100% = 25%.
Answer: 25% increased speed of the train on the second site.
proportion
are many cases where it is necessary to solve the problems of the interest, using proportion.In fact, this method of finding the result largely facilitates the task of students, teachers and not only.
So, what is the proportion?This term refers to the equality of two relations, which can be expressed as follows: A / B = C / D.
textbooks of mathematics appears this rule: the product of extreme members equal to the product averages.This is expressed by the following formula: D = A x B x C
With this formulation, we can calculate any number if the three other members of the proportions known.For example, A - unknown number.To find it, you need to
In solving problems by proportion should be understood by taking a number of interest.There are times when you need to take a share of the different variables.Compare:
1. After the sale of T-shirts in the store cost increased by 25% and amounted to 200 rubles.What was the value at the time of sale.
Solution:
In this case, you need the value of 200 rubles corresponds to 125% of the original (rasprodazhnoy) price T-shirts.Then, to find out its value at the time of sale, should be (200 x 100): 125. It will turn 160 rubles.
2. On the planet Vitsenets 200,000 inhabitants: the people and the representatives of humanoid races Naawi.Naawi accounted for 80% of the total population Vitsenets.Because 40% of people are busy servicing the mine, and the rest is produced tetanium.How many people mined tetanium?
Solution:
The first thing to find numerically the number of people and the number of Naawi.For example, 80% from 200 000 to be equal to 160 000. As many representatives of humanoid races live on Vitsenets.The number of people, respectively, is 40 000. Of these, 40%, or 16,000, serve mine.So 24,000 people are engaged in extraction tetaniuma.
Repeated changes in the number into a number of interest
When it was clear that such a percentage, it is necessary to examine the concept of the absolute and relative changes.Under the absolute transformation means increasing a specific number.So, X increased by 100. What would have substituted in place of any X would still increase this number to 100: 15 to + 100;99.9 + 100;a + 100, and so on. d.
Under the change is understood as a relative increase in the value of a certain number of percent.Suppose X increased by 20%.This means that X will be: X + ∙ 20%.The relative change is meant every time it comes to an increase of a half or one-third reduction in the quarter, increasing by 15%, and so on. D.
There is another important point: if the value of X is increased by 20%, followed by 20%, the result of a general increase of 44%, not 40%.This is evident from the following calculation:
1. X + 20% ∙ x = 1,2 ∙ X
2. 1,2 ∙ X + 20% ∙ 1,2 ∙ X = 1,2 ∙ X + 0.24∙ X = 1,44 ∙ X
This shows that X has increased by 44%.
Examples of tasks on interest
1. What percentage of the number 36 is the number 9?
Solution:
According to the formula of finding percent of the number, it is necessary to multiply 9 by 100 and divided by 36.
Answer: The number 9 is 25% of 36.
2. Calculate the number of C, which is 10% of 40.
Solution:
According to the formula for determining the number of its percentage, you multiply 40 by 10 and divide the result by 100.
Answer: The number 4 is 10% of 40.
3. FirstPartner has invested in the business 4,500 rubles, the second - 3,500 rubles, the third - 2000 rubles.They made a profit in 2400 rubles.Profits are shared equally.How ruble lost first partner, compared to how much he would have received if they were divided according to the percentage of income on investment?
Solution:
So together they invested 10,000 rubles.Earnings per share was equal to 800 rubles.To find out how much had to get the first partner, and as he thus lost, it is necessary to know the percentage of invested funds.Then you need to know how much profit in rubles of this contribution.And the last - 800 rubles deducted from the result.
Answer: The first partner lost 280 rubles, profit sharing.
little
economy today is quite popular question - a loan for a specified period.But how to choose a profitable loan, not to pay?Firstly, the need to look at the interest rate.Desirably, this rate was as low as possible.Then, to apply the formula for calculating interest on the loan.
As a rule, the size of the overpayment affects the amount of debt, interest rate and the method of repayment.There are annuity and differentiated payments.In the first case, the loan is repaid in equal installments each month.Here the same amount that overlaps the main loan increases and interest cost gradually decreases.In the second case kreditozaemschik pays a constant amount to repay the loan, which adds to the interest on the outstanding principal balance.Monthly total amount of payments will be reduced.
Now you need to consider both methods of repayment.So, if annuity option overpaid amount will be higher, and the differential - the first payment.Naturally, the terms of the loan are the same for both cases.
Conclusion
So interest.How to count them?Simple enough.However, they can sometimes be difficult.This theme was beginning to learn in school, but it catches up with all in loans, deposits, taxes and so on. D. Therefore, it is desirable to get to the core of the issue.If, however, it is impossible to carry out the calculations, there are plenty of online calculators to help you cope with the task.
