What needs to be done to find the whole. Examples of solutions to typical problems involving percentages

Public lesson in mathematics in grade 5b.

Teacher: Bambutova M.I.

Topic: How to find a part of a whole and a whole from its part.

Goal: learn to solve problems of finding a part from a whole and a whole from its part.

Educational: derive the rule for finding a part from a whole and a whole from its part,

solve problems of finding a part from a whole and a whole from its part.

Educational: develop memory and mathematical speech

Educational: develop communication skills.

Lesson plan:

1).Introductory and motivational stage.

1. Org. Moment

2. Updating basic knowledge

Answer the questions (slide)

1) What does a fraction mean?

2) What does a fraction mean? ?

Formulation of the problem:

1 task:

2 tasks per slide

1) draw a rectangle with sides 2 cm and 5 cm. What is its area?

Solve the problem

1) The area of the rectangle is 10 cm 2. Parts of the rectangle's area are shaded. What is the area of the shaded part of the rectangle?

2) The shaded part of the rectangle is equal to 4 cm 2, which is part of the entire rectangle. What is the area of the rectangle?

Answer the questions: ( )

part of the whole , and in which the whole according to its parts ?

What do we find in task 1 (the whole by its part), what do we find in task 2 (part of the whole)

Task 2: Read the tasks and answer the questions:

1) Field area – 50 hectares. During the day, a team of tractor drivers plowed the fields. How many hectares did the team plow in a day?

2) During the day, the team plowed 20 hectares, which was the area of the entire field. What is the area of the field?

Answer the questions: ( distribute tasks in the form of cards)

What quantity is taken as an integer in each problem?

In which of the problems is this quantity known and in which is it not?

Which problem requires finding part of the whole , and in which the whole according to its parts ?

What are these tasks? (reciprocal)

What do these tasks have in common? What were we looking for in these problems?

-Part of the whole And whole according to its part.

So what is our topic today? ?

Topic: How to find a part of a whole and a whole from its part .(slide)

Correct solution For the last two problems, see the textbook on page 95.

So we have solved 4 problems, generalize all the problems and derive a rule for finding a part from a whole and a whole from its part.

Students try, to help them, they need to assemble word combinations randomly into a logically correct sentence, which will be the rule.

which expresses this part.

corresponding to the whole,

To find a part of the whole,

divide by the denominator

and multiply the result by the numerator of the fraction

I need a number

To find a part of a whole, you need to divide the number corresponding to the whole by the denominator and multiply the result by the numerator of the fraction that expresses this part.

and multiply the result by fraction denominator,

I need a number

divide by the numerator

which expresses this part.

To find the whole from its part,

corresponding to this part,

To find a whole from its part, you need to divide the number corresponding to this part by the numerator and multiply the result by the denominator of the fraction that expresses this part.

Collect this rule on the board.

Students recite this rule to each other.

3. Primary consolidation. Game “Sorting tasks”.

Problem solving workshop. Option 1 solves problems of finding a part of a whole, option 2 solves problems of finding a whole from its part.

1. There are 80 students in the choir, ¼ of them are boys. How many boys are there in the choir?

2. There are 20 boys in the choir, which is ¼ of all students in the choir. How many students are there in the choir?

3. A small deciduous forest purifies the air from 70 tons of dust per year. And coniferous forest is ½ of this amount. How much dust does a coniferous forest filter out per year?

4. 7/12 of the kerosene that was there was poured out of the barrel. How many liters of kerosene were in the barrel if 84 liters were poured out of it?

5. The girl skied 300 m, which was 3/8 of the entire distance. What is the distance?

6. Cleared snow from 2/5 of the skating rink, which is 200 sq.m. Find the area of the entire skating rink?

7. The girl read ¾ of the book, which is 120 pages. How many pages are in the book?

8. The squirrel prepared 600 nuts in total. In the first week she collected 20% of all nuts. How much did the squirrel collect in the first week?

9. Find the number X, 1/8 of which is equal to 1/24.

10. The girl collected 40 plums, which was 1/3 of all plums. How many plums were collected in total?

11. Mom bought 6 kg of sweets. Vitya immediately ate 2/3 of all the candies and felt sick. After how many sweets did Vitya have a stomach ache?

12. The boy collected 80 nuts, which is 2/3 of all the collected nuts. How many nuts were collected?

13. There were 40 chickens in the chicken coop. In a week, the fox carried away 3/8 of all the chickens. How many chickens did the fox take?

14. Alice fell into a fairy well and flew 90 m in 1 minute. What is the depth of the well if Alice flew ¾ of the entire distance in 1 minute?

15. Before the ball, the stepmother gave Cinderella a lot of work. It took Cinderella 6 hours to complete 3/5 of this work. How long will it take Cinderella to complete all the work?

4. Reflection. The rule is to speak it out.

5. Homework: learn the rule, make a card with tasks for finding a part of a whole and a whole from its part (3 tasks for each rule).

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

The purpose of the lesson:

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

Equipment: Multimedia projector, presentation Power 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 hand over 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.

§ 1 Rules for finding a part from a whole and a whole from its part

In this lesson, we will formulate the rules for finding a part from a whole and a whole from its part, and also consider solving problems using these rules.

Let's consider two problems:

How many kilometers did the tourists walk on the first day, if the entire tourist route is 20 km?

Find the length of the entire tourist path.

Let's compare these problems - in both, the entire path is taken as a whole. In the first problem the whole is known - 20 km, and in the second it is unknown. In the first task you need to find a part of a whole, and in the second - a whole from its part. The quantity known in the first problem, 20 km, is unknown in the second problem, and vice versa, what is known in the second problem, 8 km, must be found in the first. Such problems are called mutually inverse, since in them the known and sought quantities are swapped.

Let's consider the first problem:

The denominator 5 shows how many parts the whole was divided into, i.e. if the whole 20 is divided by 5, we find out how many kilometers one part is, 20: 5 = 4 km. Numerator 2 shows that the tourists walked 2 parts of the path, which means 4 must be multiplied by 2, the result is 8 km. On the first day, tourists walked 8 km.

The result is expression 20: 5 ∙ 2 = 8.

Let's move on to the second problem.

Therefore, one part will be equal to the quotient of 8 and 2, the result is 4, the denominator is 5, which means there are 5 parts in total.

4 multiplied by 5, you get 20. The answer is 20 km, the length of the entire path.

Let's write the expression: 8: 2 ∙ 5 = 20

Using the meaning of multiplying and dividing a number by a fraction, the rules for finding a part of a whole and a whole from its part can be formulated as follows:

To find a part of a whole, you need to multiply the number corresponding to the whole by the fraction corresponding to this part;

To find a whole from its part, you need to divide the number corresponding to this part by the fraction corresponding to the part.

Accordingly, the solution to the problems can now be written differently:

for the first problem 20 ∙ 2/5 = 8 (km),

for the second problem 8: 2/5 = 20 (km).

To avoid any difficulties, we write the solution to such problems as follows:

Whole: all the way, known - 20 km.

Answer: 8 km.

Whole: the whole path is unknown.

Answer: 20 km.

§ 2 Algorithm for solving problems of finding a whole from its part and part of the whole

Let's create an algorithm for solving such problems.

First, let's analyze the condition and question of the problem: let's find out what the whole is, whether it is known or not, then we'll find out how a part of the whole is represented and what needs to be found.

If you need to find a part of a whole, then multiply the whole by the fraction corresponding to this part; if you need to find a whole by its part, then divide the number corresponding to the part by the fraction corresponding to this part. As a result, we get the expression. Next, we will find the meaning of the expression and write down the answer, having first read the question of the problem again.

So, before solving such problems, it is necessary to answer the following questions:

What quantity is accepted as a whole?

Is this quantity known?

What do you need to find: a part of the whole or a whole from its part?

Let's summarize: in this lesson you learned about the rules for finding a part of a whole and a whole from its part, and also learned how to solve problems using these rules.

List of used literature:

Mathematics. Grade 6: lesson plans for I.I.’s textbook. Zubareva, A.G. Mordkovich //author-compiler L.A. Topilina. Mnemosyne, 2009.
Mathematics. 6th grade: textbook for students educational institutions. I.I. Zubareva, A.G. Mordkovich. - M.: Mnemosyne, 2013.
Mathematics. 6th grade: textbook for general education institutions/G.V. Dorofeev, I.F. Sharygin, S.B. Suvorov and others / edited by G.V. Dorofeeva, I.F. Sharygina; Russian Academy of Sciences, Russian Academy of Education, M.: Prosveshcheniye, 2010.
Mathematics. 6th grade: educational. for general education institutions /N.Ya. Vilenkin, V.I. Zhokhov, A.S. Chesnokov, S.I. Schwartzburd. – M.: Mnemosyne, 2013.
Mathematics. 6th grade: textbook / G.K. Muravin, O.V. Muravina. – M.: Bustard, 2014.

§ 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, we 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!

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 amount of sales.

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

Instructions

If the value of a fraction is expressed in the format of an ordinary fraction, then this means that the whole, undivided value contains the number of fractions that is indicated in the denominator of the fraction. Calculate exactly how many percent are in each fraction by dividing one hundred percent (the whole number) by the number in the denominator of the fraction (the total number of fractions). Multiply the resulting value by the number in the numerator of the common fraction - this will be the desired percentage value. For example, if a share is expressed as a fraction 4/15, then there are 15 shares in total and each of them accounts for 100% / 15? 6.67%, and the desired value corresponds to 4 * 6.67%? 26.67%. Sometimes the fraction is expressed as a decimal fraction. Most often this number is less than one, but there are exceptions when the share is more than one hundred percent. In any case, the total whole is taken to be equal to one, and to calculate the value of the fraction as a percentage, it is enough to increase the decimal fraction by a hundred times. For example, if it is expressed as 0.42, then the corresponding percentage value will be equal to 0.42*100=42%. The share can also be given in absolute units - in rubles, square meters, kilograms, etc. In this case, to calculate percentages, you also need to know the number expressed in the same units, corresponding to one hundred percent. Divide this number by a hundred to find out how many absolute units there are for each percentage, and divide the value converted to percentage by the result obtained. For example, if the fraction is 40 square meters housing with a total area of 120 m2, then each percent corresponds to 120/100 = 1.2 m2. This means that the forty-meter percentage will be equal to 40/1.2? 33.3%. How simple

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 extra do you need to pay? 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 price. 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 will 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.