To find a part of the whole. Finding a part from a whole and a whole from its part

But for beginners it will be very useful. In addition, Excel allows you to find percentages, add, delete, and so on much more conveniently than with a calculator, and allows you to work immediately with big amount data. In this article you will learn how to find percentages of a number or amount, as well as what percentage a number is of another amount.

Task. There are data on employee sales, it is necessary to calculate the bonus, which currently is 5% of the sales amount. That is, we need to find 5% of the number (employee sales).

For convenience, we will put the 5% bonus amount in a separate table, so that when changing this percentage, the data changes automatically. To understand how to calculate a percentage of a number, we can create a proportion.

We solve the proportion by multiplying the values ​​diagonally from x and dividing by the opposite number diagonally from x. The formula for calculating the amount (percentage of a number) will look like this:

So, to find 5 percent of the sales amount, write the formula in cell C2

We have described in detail the principle of calculating the percentage of the amount and the algorithm of actions. In general, to calculate the percentage of a number, you can simply multiply that number by the percentage divided by 100.

That is, in our case, the formula for finding 5% of the amount could be like this:

Very short and fast. If you need to find 15%, then multiply the number by 0.15 and so on.

This is the inverse problem. We have a number and we need to calculate how much the number is as a percentage of the principal amount.

Task. We have a table with data on sales and returns by employee. We need to calculate the return percentage, that is, what percentage is the return from the total sales amount.

Let's also create a proportion. 35,682 rubles is all of Petrov’s revenue, that is, 100% of the money. 2023 rubles is a return - x% of the sales amount

We solve the proportion by multiplying the values ​​diagonally from x and dividing by the opposite number diagonally from x:

x=2023*100%/3568

Let's write this formula into cell D2 and drag the formula down.

You must apply the format to the cells of the resulting results "Percentage", since x is calculated as a percentage. To do this, select the cells, right-click on any of the selected cells and select "Format", then select the tab "Number", "Percentage". This format will automatically multiply the number by 100 and add a percent sign, which is what we need. There is no need to write the percent sign yourself - use a format specially designed for this.

In the end we will get next result. Let's find how much the number (return) of the amount (sale) is as a percentage.

In this case, you can also make everything shorter. The principle is the following, if the task is to find “What percentage is the number...”. Then this number is divided by the total amount and a percentage format is applied.

How to find 100% of a known percentage value

Let's say we have data on returns in rubles and as a percentage of sales. Knowing this data, we need to find the amount of sales for each employee, that is, 100%.

We compose and solve the proportion. We multiply the values ​​diagonally from x and divide by the opposite number diagonally from x:

We write the formula in cell D2 and extend it down to other employees:

Let's say we have sales data for 2014 and 2015. You need to find out the percentage change in sales.

To find out how much sales have changed, you need to subtract the data for 2015 from the data for 2014.

25686-35682=-9996

We find that sales decreased (minus sign) by 9996 rubles. Now you need to calculate how much it is as a percentage. Our starting point is 2014. It is with this year that we compare how much sales have changed, so 2014 is 100%

We make up a proportion and solve it: multiply the values ​​diagonally from x and divide by the opposite number diagonally from x

x=-9996*100%/35682=-28.02%

Thus, the amount of sales in 2015 decreased (minus sign) by 28.02% compared to 2014.

A share is a certain number of equal parts into which the total whole is divided. Since most areas of activity of our civilization today are dominated by decimal system In calculus, most often the whole is divided by the number of parts derived from ten. The most commonly used is one hundredth - a percentage.

Posting sponsor P&G Articles on the topic "How to find a share in a percentage" How to convert grams to percentages How to find the percentage of the difference between numbers How to find what percentage a number is

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A percentage of a number is a hundredth of that number, denoted 1%. One hundred percent (100%) is equal to the number itself, and 10% of a number is equal to a tenth of that number. Subtracting a percentage means reducing a number by some fraction. You will need a calculator, a piece of paper, a pen, skills oral counting. Sponsor

A percentage is one hundredth of some original value. This is a proportion, that is, a relative indicator that has no dimension (rubles, pieces, liters, etc.). In addition to simple operations of finding percentages, sometimes it is necessary to perform more complex ones - for example, dividing percentages by

A number that consists of one or many parts of one whole is usually called a fraction in mathematics and related sciences. The parts of a unit are called shares. The total number of shares in a unit is the denominator of the fraction, and the number of shares taken is its numerator. You will need - a sheet of paper; - pen; -

The word "percent" means a hundredth of a number, and a fraction is, accordingly, a part of something. Therefore, to determine the percentage of a number, it is necessary to find the fraction of it, given that the original number is a whole hundred. To perform this action you need to be able to solve proportions. Sponsor

A percentage is a relative unit of measurement that expresses the value of a certain fraction of a total whole compared to the number 100. A value written in fraction format also shows the ratio of the fraction (numerator) to the whole (denominator). This allows you to convert any number into a percentage, amounting to

Sometimes when solving problems it becomes necessary to express a fraction as a percentage. You can also convert to percentages decimal, and ordinary, and correct, and incorrect. Let's look at how to do this. Sponsored by P&G Articles on the topic "How to express a number" How to find a percentage of a number How

IN general case percentage is a fraction equal to one hundredth of a unit. However, more often it is used as a relative unit of measurement for the amount of something, and then one percent takes on a variety of numerical values. Measured in these units, a quantitative measure of a certain fraction of

In this lesson, you will see how to quickly calculate percentages using Excel, get acquainted with the basic formula for calculating percentages, and learn a few tricks that will make your work with percentages easier. For example, the formula for calculating percentage growth, calculating the percentage of the total amount and something else.

Knowing how to work with percentages can be useful in the most different areas life. This will help you estimate the amount of tips in a restaurant, calculate commissions, calculate the profitability of any enterprise and the degree of your personal interest in this enterprise. Tell me honestly, will you be happy if they give you a promotional code for a 25% discount to buy a new plasma? Sounds tempting, right?! Can you calculate how much you will actually have to pay?

In this tutorial, we'll show you several techniques that will help you easily calculate percentages using Excel, as well as introduce you to the basic formulas that are used to work with percentages. You'll learn some tricks and hone your skills by working out solutions to practical problems using percentages.

Basic knowledge about percentages

Term Percent(per cent) came from Latin (per centum) and was originally translated as OUT OF HUNDREDS. At school you learned that a percentage is some part of 100 shares of the whole. The percentage is calculated by dividing, where the numerator of the fraction is the desired part, and the denominator is the whole, and then the result is multiplied by 100.

The basic formula for calculating interest looks like this:

(Part/Whole)*100=Percentage

Example: You had 20 apples, 5 of which you gave to your friends. What percentage of your apples did you give away? Having made simple calculations, we get the answer:

(5/20)*100 = 25%

This is exactly how you were taught to calculate percentages in school, and you use this formula in Everyday life. Calculating percentages in Microsoft Excel is an even simpler task, since many mathematical operations are produced automatically.

Unfortunately, there is no universal formula for calculating interest for all occasions. If you ask the question: what formula to use for calculating interest to get the desired result, then the most correct answer will be: it all depends on what result you want to get.

I want to show you some interesting formulas for working with data presented as percentages. This, for example, is the formula for calculating the percentage increase, the formula for calculating the percentage of the total amount, and some other formulas that are worth paying attention to.

Basic formula for calculating percentage in Excel

The basic formula for calculating percentage in Excel looks like this:

Part/Whole = Percentage

If you compare this formula from Excel with the usual formula for percentages from a math course, you will notice that it does not multiply by 100. When calculating a percentage in Excel, you do not need to multiply the result of division by 100, since Excel will do this automatically if for the cell given Percentage format.

Now let's see how calculating percentages in Excel can help in real work with data. Let's say that in column B you have recorded a certain number of ordered products (Ordered), and in column C you have entered data on the number of delivered products (Delivered). To calculate what share of orders have already been delivered, we do the following:

• Write down the formula =C2/B2 in cell D2 and copy it down as many lines as necessary using the autofill marker.
• Click command Percent Style(Percent Format) to display division results in percent format. It's on the tab Home(Home) in the command group Number(Number).
• If necessary, adjust the number of decimal places displayed to the right of the decimal point.
• Ready!

If you use any other formula to calculate percentages in Excel, the general sequence of steps will remain the same.

In our example, column D contains values ​​that show, as a percentage, what proportion of total number orders are already delivered orders. All values ​​are rounded to whole numbers.

Calculate percentage of total amount in Excel

In fact, the example given is a special case of calculating a percentage of the total amount. To better understand this topic, let's look at a few more problems. You'll see how you can quickly calculate a percentage of a total in Excel using different data sets as examples.

Example 1. The total amount is calculated at the bottom of the table in a specific cell

Very often at the end of a large data table there is a cell labeled Total in which the total is calculated. At the same time, we are faced with the task of calculating the share of each part relative to the total amount. In this case, the formula for calculating the percentage will look the same as in the previous example, with one difference - the reference to the cell in the denominator of the fraction will be absolute (with $ signs before the row name and column name).

For example, if you have some values ​​written in column B, and their total is in cell B10, then the formula for calculating percentages will be as follows:

Clue: There are two ways to make the cell reference in the denominator absolute: either by entering a sign $ manually, or select the desired cell reference in the formula bar and press the key F4.

The figure below shows the result of calculating the percentage of the total amount. The data is displayed in Percentage format with two decimal places.

Example 2: Parts of the total amount are on multiple lines

Imagine a data table like the previous example, but here the product data is spread across multiple rows in the table. You need to calculate what portion of the total amount is made up of orders for a specific product.

In this case we use the function SUMIF(SUMIF). This function allows you to sum only those values ​​that meet a specific criterion, in our case a given product. We use the result obtained to calculate the percentage of the total amount.

SUMIF(range,criteria,sum_range)/total
=SUMMIF(range,criteria,sum_range)/total sum

In our example, column A contains the names of products (Product) - this is range. Column B contains quantity data (Ordered) - this is sum_range. In cell E1 we enter our criterion- the name of the product for which the percentage needs to be calculated. The total amount for all products is calculated in cell B10. The working formula will look like this:

SUMIF(A2:A9,E1,B2:B9)/$B$10
=SUMIF(A2:A9,E1,B2:B9)/$B$10

By the way, the name of the product can be entered directly into the formula:

SUMIF(A2:A9,"cherries",B2:B9)/$B$10
=SUMIF(A2:A9,"cherries";B2:B9)/$B$10

If you need to calculate how much of the total amount comes from several different products, you can add up the results for each of them and then divide by the total amount. For example, this is what the formula would look like if we wanted to calculate the result for cherries And apples:

=(SUMIF(A2:A9,"cherries",B2:B9)+SUMIF(A2:A9,"apples",B2:B9))/$B$10
=(SUMIF(A2:A9,"cherries";B2:B9)+SUMIF(A2:A9,"apples";B2:B9))/$B$10

How to Calculate Percentage Change in Excel

One of the most popular tasks that can be performed using Excel is calculating the percentage change in data.

Excel formula that calculates percentage change (increase/decrease)

(B-A)/A = Percentage change

When using this formula when working with real data, it is very important to correctly determine which value to put in place A, and which one - in place B.

Example: Yesterday you had 80 apples, and today you have 100 apples. This means that today you have 20 more apples than you had yesterday, that is, your result is an increase of 25%. If yesterday there were 100 apples, and today there are 80, then this is a decrease of 20%.

So, our formula in Excel will work as follows:

(New value - Old value) / Old value = Percentage change

Now let's see how this formula works in Excel in practice.

Example 1: Calculate percentage change between two columns

Let's assume that column B contains the prices of the last month (Last month), and column C contains the current prices for this month (This month). In column D, enter the following formula to calculate the change in price from last month to the current month as a percentage.

This formula calculates the percentage change (increase or decrease) in price this month (column C) compared to the previous month (column B).

After you write the formula in the first cell and copy it to all the necessary rows, by dragging the autofill marker, do not forget to set Percentage format for cells with a formula. As a result, you should get a table similar to the one shown in the figure below. In our example, positive data that shows an increase is displayed in standard black, and negative values ​​(percentage decrease) are highlighted in red. For details on how to configure this formatting, read this article.

Example 2: Calculate percentage change between rows

In the case where your data is located in one column, which reflects information about sales for a week or month, the percentage change can be calculated using the following formula:

Here C2 is the first value and C3 is the next value.

Comment: Please note that with this arrangement of data in the table, you must skip the first row of data and write the formula from the second row. In our example, this will be cell D3.

After you write down the formula and copy it to all the necessary rows in your table, you should end up with something similar to this:

For example, this is what the formula would look like to calculate the percentage change for each month compared to the indicator January(January):

When you copy your formula from one cell to all the others, the absolute reference will remain the same, while the relative reference (C3) will change to C4, C5, C6 and so on.

Calculation of value and total amount based on a known percentage

As you can see, calculating percentages in Excel is easy! It’s just as easy to calculate the value and total amount by known percentage.

Example 1: Calculating a value based on a known percentage and total amount

Let's say you buy a new computer for $950, but you need to add VAT of 11% to this price. Question - how much do you need to pay extra? In other words, 11% of the indicated cost is how much in foreign currency?

The following formula will help us:

Total * Percentage = Amount
Total * Percentage = Value

Let's pretend that total amount(Total) is written in cell A2, and Interest(Percent) – in cell B2. In this case, our formula will look quite simple =A2*B2 and will give results $104.50 :

Important to remember: When you manually enter a numeric value into a table cell followed by a % sign, Excel understands this as hundredths of the entered number. That is, if you enter 11% from the keyboard, then the cell will actually store the value 0.11 - this is the value Excel will use when performing calculations.

In other words, the formula =A2*11% is equivalent to the formula =A2*0.11. Those. in formulas you can use either decimal values ​​or values ​​with a percent sign - whichever is more convenient for you.

Example 2: Calculating the total amount using a known percentage and value

Let's say your friend offered to buy his old computer for $400 and said that it was 30% cheaper than its full cost. Do you want to know how much this computer originally cost?

Since 30% is a reduction in price, the first thing we do is subtract this value from 100% to calculate what fraction of the original price you need to pay:

Now we need a formula that will calculate the initial price, that is, find the number 70% of which is equal to $400. The formula will look like this:

Amount/Percentage = Total
Value/Percentage = Total Amount

To solve our problem we get the following form:

A2/B2 or =A2/0.7 or =A2/70%

How to increase/decrease a value by a percentage

With the onset of the holiday season, you notice certain changes in your usual weekly expenses. You may want to make some additional adjustments to the calculation of your spending limits.

To increase the value by a percentage, use this formula:

Value*(1+%)

For example, the formula =A1*(1+20%) takes the value contained in cell A1 and increases it by 20%.

To decrease the value by a percentage, use this formula:

Value*(1-%)

For example, the formula =A1*(1-20%) takes the value contained in cell A1 and decreases it by 20%.

In our example, if A2 is yours running costs, and B2 is the percentage by which you want to increase or decrease their value, then in cell C2 you need to write the following formula:

Increase by percentage: =A2*(1+B2)
Decrease by percentage: =A2*(1-B2)

How to increase/decrease all values ​​in a column by a percentage

Let's assume that you have an entire column filled with data that needs to be increased or decreased by some percentage. In this case, you do not want to create another column with a formula and new data, but change the values ​​in the same column.

§ 20. Finding a part of a whole and a whole but its part - Textbook on Mathematics, grade 5 (Zubareva, Mordkovich)

Short description:

It happens that we need to find some part of a number, for example, with a certain number Peel only a third of the potatoes. Or vice versa, when we are told that only a quarter of the class came on an excursion, we need to find out what the total number of students in the class is. Knowing the whole, you can find some given part of it, and in the same way, knowing the part, you can determine what the whole was like. You will learn about this today from this paragraph of the textbook.
The definition of a part from the whole, and vice versa, is directly related to simple fractions that you have already studied. In this case, actions occur not with two numbers, which are denoted by a fraction, but with one fraction and one integer. For example, finding 1/2 of 16 would mean multiplying 16 by 1/2, in which case the denominator of 16 = 1 and the expression can be written as: 1/2 16/1 = 16/2 = 8.
To find a whole number from its part, use the reverse method and multiply known number by an inverted fraction (that is, divide by it). In another way, this can be explained as follows: in order to find a whole from its part, you need to divide the known number that corresponds to its part by the numerator and multiply by the denominator of the fraction that denotes this part (which is the action of dividing a fraction, or multiplying to an inverted fraction - you can remember the most convenient way for you to solve such problems). Thus, to find an integer whose 3/4 is equal to 12, you need 12: 3/4 = 12 4/3 = 48/3 = 16. Or method No. 2, which removes unnecessary mathematical operations - number x, 2/5 from which they are equal to 20: x = 20: 2 5 = 50.
Test yourself when completing tasks from the textbook and do not forget to review the material to better master and remember it!

§ 20. Finding a part of a whole and a whole but its part - Textbook on Mathematics, grade 5 (Zubareva, Mordkovich)

Short description:

Lesson topic:“Finding a part of a whole and a whole by its part.”

The purpose of the lesson:

1. Learn to find a fraction from a number and a number from its fraction.
2. Generalize the concept of a common fraction and operations with common fractions.

Equipment: Multimedia projector, Power presentation Point ( Application ).

DURING THE CLASSES

I. Organizational moment

Students are seated in groups (5-6 people). You can suggest diagnosing your mood at the stages of the lesson. Each student is given a card on which he identifies the “character” of his mood.

II. Updating knowledge

We are already familiar with the concept of a common fraction.
– What does the numerator of a fraction show? (How many parts is the whole divided into?)
– What does the denominator of a fraction show? (How many parts did they take).

– Look at the picture and answer the questions:

Students are asked to reproduce it.

III. Verbal counting. (Best counter)

Each team is given a task on the screen. Teams take turns completing the task.

1st team

2nd team

3rd team

4th team

The bottom line is which team is the best counter.

IV. Dictation

The dictation is carried out followed by self-test. It is possible to make a carbon copy; students submit one copy to the teacher for checking.

1. Instead of x, insert the missing number:

2. Reduce a fraction:

3. Arrange the fractions in descending order:

4. Follow these steps:

5. On the islands Pacific Ocean giant turtles live. They are so big that children can ride while sitting on their shell. The following task will help us find out the name of the largest turtle in the world.

After submitting the solution, students check their answers.

V. New material

The teacher offers to solve problems (5 – 7 minutes are given to think about them)

1. 12 birds were sitting on a branch. Then it flew away from them. How many birds flew away?

2. In your math class, 6 people received a grade of “5” in the third quarter. This is the number of all students in the class. How many students are in the class?

Then the solution is checked and shown on the slide.

Method 1: 12: 3 2 = 8 (birds)

Method 2: 12 = 8 (birds)

Task 2. 6: = 6 = 34 (persons)

The teacher draws attention to the fact that two types of tasks can be distinguished:

1. To find part of the number, expressed as a fraction, you need this number multiply for this fraction.
2. To find number according to its frequency and, expressed as a fraction, you need divide for this fraction the number corresponding to it.

Students are asked to memorize this rule in class and retell it to each other in pairs.

The teacher focuses on the following: for those who find it difficult to determine the type of task, I advise you to pay attention to prepositions What , This . These prepositions are found in problems of finding numbers by their fraction.

VI. Consolidating new material

On the slide there are six problems and students are asked to sort them into two columns by type.

1. The store accepted 156 kg of fish for sale. 1/3 of all fish were carp. How many kg of carp did the store receive?
2. We carried out 18 experiments, this amounted to 2/9 of the entire series of experiments. How many experiments should be carried out?
3. The teacher checked 20 notebooks. This amounted to 4/5 of all notebooks. How many notebooks does a teacher need to check?
4. Of the 72 fifth-graders, 3/8 are involved in athletics. How many students play this sport?
5. 30 paintings were selected for the exhibition. This amounted to 2/3 of the paintings available in the museum. How many paintings were taken to the exhibition?
6. From a rope 18 m long, 3/4 of its length was cut off. How many meters of rope are left?

VII. Lesson Summary

The teacher returns students to the purpose of the lesson and suggests identifying two types of fraction problems and algorithms for solving them. Leaflets with mood diagnostics are collected.

VIII. Homework: P. 9.6, No. 1050, 1058, 1060.