we see quite often in Everyday life. Let's take a bar of chocolate, a pack of ice cream on which it says “56% cocoa”, “100% ice cream”. What is a percentage?
Percentage called one hundredth part. Write it down briefly 1 % . Sign % replaces the word "percentage".
Whatever number or value we take, its hundredth part is one percent given number or magnitude. For example, for the number 400 (0.01 of the number 400) is the number 4, so 4 is 1% of the number 400; 1 hryvnia (0.01 hryvnia) is 1 kopeck, so 1 kopeck is 1% of the hryvnia.
For example:
The puzzle contains 500 elements. How many elements are there in 1 percent of it? Let 500 puzzle pieces be 100%. Then 1% contains 100 times less of its elements. Hence 500: 100 = 5 (el.). So, 1% is 5 pieces of the puzzle.
Please note: to find 1% of a number A, you need to divide this number by 100. Knowing what number or value is 1%, you can find the number or value that is a few percent.
For example:
Marina needs to sew on a braid, 3 cm of which is 1% of her length. Marina sewed 50% of the braid. How many centimeters of braid did she sew? Since 50% is 50 times greater than 1%, Marina sewed braids 50 times larger than 3 cm. Hence 3.50 = 150 (cm). So, Marina sewed 150 cm of braid.
In practice, it often happens that both of the above problems must be solved together - first find what number or value is in 1%, and then in several percent. Such tasks are called problems to find the percentage of a number.
For example:
Sweet pears contain 15% sugar. How much sugar is in 3 kg of pears?
Let's make a short record of the task data.
Pears: 3 kg – 100%
Sugar: ? - 15%
1. How many kilograms corresponds to 1%?
Percentage of two numbers is their ratio expressed as a percentage. A percentage shows what percentage one number is of another.
Interest— a convenient relative measure that allows you to operate with numbers in a format familiar to humans, regardless of the size of the numbers themselves. This is a kind of scale to which any number can be reduced. One percent is one hundredth. The word itself percent comes from the Latin "pro centum", meaning "hundredth part".
Interest is irreplaceable in insurance, financial sector, in economic calculations. Tax rates, return on investment, fees for borrowed funds are expressed as percentages. cash(for example, bank loans), economic growth rates and much more.
1. Formula for calculating the percentage share.
Let two numbers be given: A 1 and A 2. It is necessary to determine what share in percentage is the number A 1 from A 2.
P = A 1 / A 2 * 100.
In financial calculations it is often written
P = A 1 / A 2 * 100%.
Example. What percentage is 10 of 200?P = 10 / 200 * 100 = 5 (percent).
2. Formula for calculating percentage of a number.
Let the number A 2 be given. We need to calculate the number A 1, which is specified percentage P from A 2 .
A 1 = A 2 * P / 100.
Example. Bank loan 10,000 rubles at 5 percent interest. The interest amount will be.
P = 10000 * 5 / 100 = 500.
3. Formula for increasing a number by a given percentage. Value with VAT.
Let the number A 1 be given. We need to calculate the number A 2, which more number A 1 by a given percentage P. Using the formula for calculating the percentage of a number, we get:
A 2 = A 1 + A 1 * P / 100.
A 2 = A 1 * (1 + P / 100).
Example 1. Bank loan 10,000 rubles at 5 percent interest. The total amount of debt will be.
A 2 = 10000 * (1 + 5 / 100) = 10000 * 1.05 = 10500.
Example 2. The amount excluding VAT is 1000 rubles, VAT 18 percent. The amount including VAT is:
A 2 = 1000 * (1 + 18 / 100) = 1000 * 1.18 = 1180.
style="center">4. Formula for reducing a number by a given percentage.
Let the number A 1 be given. We need to calculate the number A 2, which less number A 1 by a given percentage P. Using the formula for calculating the percentage of a number, we get:
A 2 = A 1 - A 1 * P / 100.
A 2 = A 1 * (1 - P / 100).
Example. The amount of money to be issued minus income tax (13 percent). Let the salary be 10,000 rubles. Then the amount to be issued is:
A 2 = 10000 * (1 - 13 / 100) = 10000 * 0.87 = 8700.
5. Formula for calculating the initial amount. Price without VAT.
Let a number A 1 be given, equal to some initial number A 2 with an added percentage P. We need to calculate the number A 2 . In other words: we know the monetary amount including VAT, we need to calculate the amount excluding VAT.
Let us denote p = P / 100, then:
A 1 = A 2 + p * A 2 .
A 1 = A 2 * (1 + p).
Then
A 2 = A 1 / (1 + p).
Example. The amount including VAT is 1180 rubles, VAT 18 percent. Cost without VAT is:
A 2 = 1180 / (1 + 0.18) = 1000.
style="center">6. Calculation of interest on a bank deposit. Formula for calculating simple interest.
If interest on a deposit is accrued once at the end of the deposit term, then the amount of interest is calculated using the simple interest formula.
S = K + (K*P*d/D)/100
Sp = (K*P*d/D)/100
Where:
S is the amount of the bank deposit with interest,
Sp - amount of interest (income),
K - initial amount (capital),
d — number of days of accrual of interest on the attracted deposit,
D — number of days in calendar year(365 or 366).
Example 1. The bank accepted a deposit in the amount of 100 thousand rubles for a period of 1 year at a rate of 20 percent.
S = 100000 + 100000*20*365/365/100 = 120000
Sp = 100000 * 20*365/365/100 = 20000
Example 2. The bank accepted a deposit in the amount of 100 thousand rubles for a period of 30 days at a rate of 20 percent.
S = 100000 + 100000*20*30/365/100 = 101643.84
Sp = 100000 * 20*30/365/100 = 1643.84
7. Calculation of interest on a bank deposit when calculating interest on interest. Formula for calculating compound interest.
If interest on a deposit is accrued several times at equal intervals and is credited to the deposit, then the amount of the deposit with interest is calculated using the formula compound interest.
S = K * (1 + P*d/D/100) N
Where:
P—annual interest rate,
When calculating compound interest, it is easier to calculate total amount with interest, and then calculate the amount of interest (income):
Sp = S - K = K * (1 + P*d/D/100) N - K
Sp = K * ((1 + P*d/D/100) N - 1)
Example 1. A deposit of 100 thousand rubles was accepted for a period of 90 days at a rate of 20 percent per annum with interest accrued every 30 days.
S = 100000 * (1 + 20*30/365/100) 3 = 105 013.02
Sp = 100000 * ((1 + 20*30/365/100) N - 1) = 5 013.02
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Example 2. Let's check the formula for calculating compound interest for the case from the previous example.
Let's divide the deposit period into 3 periods and calculate the interest accrual for each period using the simple interest formula.
S 1 = 100000 + 100000*20*30/365/100 = 101643.84
Sp 1 = 100000 * 20*30/365/100 = 1643.84
S 2 = 101643.84 + 101643.84*20*30/365/100 = 103314.70
Sp 2 = 101643.84 * 20*30/365/100 = 1670.86
S 3 = 103314.70 + 103314.70*20*30/365/100 = 105013.02
Sp 3 = 103314.70 * 20*30/365/100 = 1698.32
The total amount of interest, taking into account the calculation of interest on interest (compound interest)
Sp = Sp 1 + Sp 2 + Sp 3 = 5013.02
Thus, the formula for calculating compound interest is correct.
8. Another compound interest formula.
If the interest rate is not given on an annual basis, but directly for the accrual period, then the compound interest formula looks like this.
S = K * (1 + P/100) N
Where:
S—deposit amount with interest,
K - deposit amount (capital),
P - interest rate,
N is the number of interest periods.
Example. A deposit of 100 thousand rubles was accepted for a period of 3 months with monthly interest accrual at a rate of 1.5 percent per month.
S = 100000 * (1 + 1.5/100) 3 = 104,567.84
Sp = 100000 * ((1 + 1.5/100) 3 - 1) = 4,567.84
Good day!
Interest, I tell you, is not only something “boring” in mathematics lessons at school, but also an extremely necessary and practical thing in life (found everywhere: when you take out a loan, open a deposit, calculate profits, etc. ). And in my opinion, when studying the topic of “percentages” in the same school, extremely little time is devoted to this ().
Perhaps because of this, some people find themselves in not very pleasant situations (many of which could have been avoided if they had figured out what was there and how in time...).
Actually, in this article I want to look at the most popular problems with percentages that occur in life (of course, I will consider this as much as possible in simple language with examples). Well, forewarned means forearmed (I think that knowledge of this topic will allow many to save both time and money).
And so, closer to the topic...
Option 1: calculate prime numbers in your head in 2-3 seconds.
In the vast majority of cases in life, you need to quickly estimate in your mind how much a 10% discount on a certain number (for example) will be. Agree, in order to make a purchasing decision, you don’t need to calculate everything down to the penny (it’s important to figure out the order).
The most common variants of numbers with percentages are given in the list below, as well as what you need to divide the number by to find out the desired value.
Simple examples:
- 1% of the number = divide the number by 100 (1% of 200 = 200/100 = 2);
- 10% of a number = divide the number by 10 (10% of 200 = 200/10 = 20);
- 25% of a number = divide the number by 4 or twice by 2 (25% of 200 = 200/4 = 50);
- 33% of the number ≈ divide the number by 3;
- 50% of a number = divide the number by 2.
Problem! For example, you want to buy equipment for 197 thousand rubles. The store offers a 10.99% discount if you meet certain conditions. How can you quickly figure out if it’s worth it?
Example solution. Yes, just round these pair of numbers: instead of 197, take the amount of 200, instead of 10.99%, take 10% (conditionally). In total, you need to divide 200 by 10 - i.e. we estimated the size of the discount at approximately 20 thousand rubles. (with some experience, the calculation is done almost automatically in 2-3 seconds).
Exact calculation: 197 * 10.99/100 = 21.65 thousand rubles.
Option 2: use the Android phone calculator
When you need a more accurate result, you can use a calculator on your phone (in the article below I will give screenshots from Android). It's quite simple to use.
For example, you need to find 30% of the number 900. How to do this?
Yes, quite simple:
- open the calculator;
- write 30%900 (of course, the percentage and number can be different);
- Please note that below your written “equation” you will see the number 270 - this is 30% of 900.
Below are more complex example. We found 17.39% of the number 393,675 (result 68460, 08).
If you need, for example, to subtract 10% from 30,000 and find out how much it will be, then you can write it like this (by the way, 10% of 30,000 is 3000). Thus, if you subtract 3000 from 30,000, you will get 27,000 (which is what the calculator showed).
In general, it is a very convenient tool when you need to calculate 2-3 numbers and get accurate results, down to tenths/hundredths.
Option 3: count the percentage of the number (the essence of the calculation + the golden rule)
It is not always and not everywhere possible to round numbers and calculate percentages in your head. Moreover, sometimes it is necessary not only to obtain some exact result, but also to understand the very “essence of the calculation” (for example, to calculate a hundred/thousand different problems in Excel).
Let's say we need to find 17.39% of the number 393,675. Let's solve this simple problem...
To remove all the points on "Y", I will consider inverse problem. For example, what percentage is the number 30,000 of the number 393,675.
Option 4: calculate percentages in Excel
Excel is good because it allows you to make fairly voluminous calculations: you can simultaneously calculate dozens of different tables by linking them together. And in general, is it possible to manually calculate percentages for dozens of items of goods, for example.
Below I will show a couple of examples that you most often encounter.
Problem one. There are two numbers, for example, the purchase and sale price. You need to find out the difference between these two numbers as a percentage (how much more/less one is than the other).
For a more precise understanding, I will give one more example. Another problem: there is a purchase price and the desired percentage of profit (let's say 10%). How to find out the selling price. Everything seems to be simple, but many people “stumble”...
Additions on the topic are always welcome...
That's all, good luck!
Good day, dear guests! Did you do well at school? I’m doing great, but I also have situations when I need to refresh my memory school knowledge.
Unfortunately, among the entire volume of information, it is very difficult to identify the information that may actually be needed.
Let's remember today how to find out the percentage of a number.
Mathematics is necessary in everyday life, because it teaches you to think outside the box and develops logic. Knowledge of computational manipulation makes life easier financially.
Here are examples of using %:
- This ratio allows you to improve the perception of information in order to compare certain parameters. For example, the human body consists of 70% water, and jellyfish - 98%.
- Such calculations are also used in economics. This is necessary, for example, for profit calculations.
- Knowledge is also necessary for analyzing specific quantities. For example, the difference between salaries in different months.
Interest concept
Interestingly, the Hindus used percentages in calculations back in the 5th century. In Europe, they learned about decimal fractions only after a millennium.
This concept was introduced by a Belgian scientist Simon Stevin. In the 16th century, a table with values was published.
The word itself is of Latin origin. The word is translated as “from a hundred.” This means one hundredth of any value.
% provide the opportunity to compare the components of one whole without difficulty. The emergence of shares made calculations easier and they became standard.
Calculation methods
In the 5th grade mathematics textbook you can find out that % is a hundredth of a number. To find out what % of certain value, you can use proportion and create a cross rule.
For example, you need to find 500 from 1000. In this case, the data that is located opposite each other must be multiplied and then divided by the third number.
In this case, numbers are written under the numbers, and percentages under the same indicators.
It turns out:
1000 – 100%;
500 – x%.
We get: X=(500*100)/1000.
X=50%.
You can also use Excel.
For example, you need to find the amount that is 15% of the whole number 8500.
First, create an Excel sheet on your desktop.
Then open the document and in the highlighted line enter:
- = (equal);
- then 8500;
- after that press * (multiply);
- then 15;
- Then press the % and Enter keys.
How to calculate percentage on a calculator
Then you need to enter the requested data in the fields and get the result. In this case, you can find out how % of total number, and what percentage the value of one number is from another.
To summarize, we can say that the calculator allows you to decide on the following questions:
- Calculate a specific % from a specific value. Or, if % is known, then add it to some number.
- What % is of the given indicator.
- How many % does one value contain from another.
A regular calculator also has a function for determining %. If there is an option, then there should be a key where %.
To do this, find the percentage (%) button on his keyboard.
For example, let's find out how much 12 is from 125.
To do this, we will carry out the following manipulations:
Enter 125 on the calculator.
Click multiply (*).
Press 12.
Then click the percentage button.
In this case, the result will be displayed on the screen - 9.6%.
This way you can find any other values with two numbers. You can also use the calculator on your mobile phone.
In a laptop or computer, you can find useful programs through the start menu.
Calculation using formulas
So, let's look at some formulas for calculation.
Formula for calculating percentage of a certain value.
If the number A and the percentage component B are known, then the percentage of A is found like this:
B=A*P/100%.
There is a special formula for calculating percentages. In this case, you need to find out from what value %.
If B is known, which is P percent of the number A, then the quantity A is found like this.
A=B*100%/R.
You can also calculate the percentage of one number from another. If two values A and B are known, then you can find out what % B contains of A. The following formula is used. P=B/A*100%.
To find out how much the number has increased compared to the original, there is also a certain formula.
If you know the number A and you need to find B, which is a certain percentage greater than the number A, then the following formula is applied: B=A(1+P/100%).
There is also a formula for calculating which is less than the original by a certain percentage.
If we know the number A and it is necessary to find B, which is P% less than A, then the following calculation is used: B=A(1-P/100%).
I hope you find the information in my article useful. If you want to add to it, write in the comments.
Remember your school knowledge and use it in everyday life. Mathematical calculations make life a lot easier.
That's all I have for today. Goodbye, dear fans of my blog!
The rules for writing numbers with a fractional part provide for several formats, the main ones being “decimal” and “ordinary”. Common fractions, in turn, can be written in formats called “irregular” and “mixed”. To select an entire part from fractional number For each of these recording options, it is more convenient to use different methods.
Instructions
Discard the fractional part if you need to separate from positive fraction, recorded in a mixed format. In such a fraction there is an integer part before the fractional part - for example, 12 ⅔. In this fraction whole part will be the number 12. If mixed fraction has a sign, then reduce the number obtained in this way by one. The necessity of this action follows from the definition of the integer part of a number, according to which it cannot be greater value original fraction. For example, the integer part of the fraction -12 ⅔ is the number -13.
Divide the numerator of the original fraction without a remainder by its denominator if it is written in the wrong ordinary format. If the original number has a positive sign, then the resulting result will be an integer part. For example, the whole part of the fraction 716/51 is equal to 14. If the original number is negative, then one should be subtracted from the result - for example, calculating the whole part of the fraction -716/51 should give the number -15.
Consider zero to be the whole part of a positive fraction, written in ordinary format and not a mixed or improper fraction. For example, this is for the fraction 48/51. If the original fraction is less than zero, then, as in previous cases, the result should be one. For example, the integer part of the fraction -48/51 should be considered the number -1.
Drop all signs after decimal point, if you need to select from positive number, written in the format decimal. In this case, it is the separation