Money and the millionaire mindset. Game "Mathematical matrices"

Extracting the quadrant root of a number is not the only operation that can be performed with this mathematical phenomenon. Just like regular numbers, square roots add and subtract.

Yandex.RTB R-A-339285-1

Rules for adding and subtracting square roots

Operations such as addition and subtraction of square roots are only possible if the radical expression is the same.

Example 1

You can add or subtract expressions 2 3 and 6 3, but not 5 6 And 9 4. If it is possible to simplify the expression and reduce it to roots with the same radical, then simplify and then add or subtract.

Actions with roots: basics

6 50 - 2 8 + 5 12

Action algorithm:

1. Simplify the radical expression. To do this, it is necessary to decompose the radical expression into 2 factors, one of which is a square number (the number from which an integer is extracted Square root, for example, 25 or 9).
2. Then you need to extract the root from square number and write the resulting value before the root sign. Please note that the second factor is entered under the sign of the root.
3. After the simplification process, it is necessary to emphasize the roots with the same radical expressions - only they can be added and subtracted.
4. For roots with the same radical expressions, it is necessary to add or subtract the factors that appear before the root sign. The radical expression remains unchanged. You cannot add or subtract radical numbers!

Tip 1

If you have an example with big amount identical radical expressions, then underline such expressions with single, double and triple lines to facilitate the calculation process.

Example 3

Let's try to solve this example:

6 50 = 6 (25 × 2) = (6 × 5) 2 = 30 2. First you need to decompose 50 into 2 factors 25 and 2, then take the root of 25, which is equal to 5, and take 5 out from under the root. After this, you need to multiply 5 by 6 (the multiplier at the root) and get 30 2.

2 8 = 2 (4 × 2) = (2 × 2) 2 = 4 2. First you need to decompose 8 into 2 factors: 4 and 2. Then take the root from 4, which is equal to 2, and take 2 out from under the root. After this, you need to multiply 2 by 2 (the factor at the root) and get 4 2.

5 12 = 5 (4 × 3) = (5 × 2) 3 = 10 3. First you need to decompose 12 into 2 factors: 4 and 3. Then extract the root of 4, which is equal to 2, and remove it from under the root. After this, you need to multiply 2 by 5 (the factor at the root) and get 10 3.

Simplification result: 30 2 - 4 2 + 10 3

30 2 - 4 2 + 10 3 = (30 - 4) 2 + 10 3 = 26 2 + 10 3 .

As a result, we saw how many identical radical expressions are contained in in this example. Now let's practice with other examples.

Example 4

• Let's simplify (45). Factor 45: (45) = (9 × 5) ;
• We take 3 out from under the root (9 = 3): 45 = 3 5;
• Add the factors at the roots: 3 5 + 4 5 = 7 5.

Example 5

6 40 - 3 10 + 5:

• Let's simplify 6 40. We factor 40: 6 40 = 6 (4 × 10) ;
• We take 2 out from under the root (4 = 2): 6 40 = 6 (4 × 10) = (6 × 2) 10 ;
• We multiply the factors that appear in front of the root: 12 10 ;
• We write the expression in a simplified form: 12 10 - 3 10 + 5 ;
• Since the first two terms have the same radical numbers, we can subtract them: (12 - 3) 10 = 9 10 + 5.

Example 6

As we can see, it is not possible to simplify radical numbers, so we look for terms with the same radical numbers in the example, carry out mathematical operations (add, subtract, etc.) and write the result:

(9 - 4) 5 - 2 3 = 5 5 - 2 3 .

Adviсe:

• Before adding or subtracting, it is necessary to simplify (if possible) the radical expressions.
• Adding and subtracting roots with different radical expressions is strictly prohibited.
• You should not add or subtract a whole number or root: 3 + (2 x) 1 / 2 .
• When performing operations with fractions, you need to find a number that is divisible by each denominator, then reduce the fractions to common denominator, then add the numerators and leave the denominators unchanged.

If you notice an error in the text, please highlight it and press Ctrl+Enter

Instructions

There are four types of mathematical operations: addition, subtraction, multiplication and division. Therefore, there will be four types of examples. Negative numbers within the example are highlighted so as not to confuse the mathematical operation. For example, 6-(-7), 5+(-9), -4*(-3) or 34:(-17).

Addition. This action can look like: 1) 3+(-6)=3-6=-3. Replacement action: first, the parentheses are opened, the “+” sign is changed to the opposite, then from the larger (modulo) number “6” the smaller one, “3,” is subtracted, after which the answer is assigned the larger sign, that is, “-”.
2) -3+6=3. This can be written according to the principle ("6-3") or according to the principle "subtract the smaller from the larger and assign the sign of the larger to the answer."
3) -3+(-6)=-3-6=-9. When opening, the action of addition is replaced by subtraction, then the modules are summed up and the result is given a minus sign.

Subtraction.1) 8-(-5)=8+5=13. The parentheses are opened, the sign of the action is reversed, and an example of addition is obtained.
2) -9-3=-12. The elements of the example are added and get general sign "-".
3) -10-(-5)=-10+5=-5. When opening the brackets, the sign changes again to “+”, then the smaller number is subtracted from the larger number and the sign of the larger number is taken away from the answer.

Multiplication and division: When performing multiplication or division, the sign does not affect the operation itself. When multiplying or dividing numbers with the answer, a “minus” sign is assigned; if the numbers have the same signs, the result always has a “plus” sign. 1) -4*9=-36; -6:2=-3.
2)6*(-5)=-30; 45:(-5)=-9.
3)-7*(-8)=56; -44:(-11)=4.

Sources:

• table with cons

How to decide examples? Children often turn to their parents with this question if homework needs to be done at home. How to correctly explain to a child the solution to examples of adding and subtracting multi-digit numbers? Let's try to figure this out.

You will need

• 1. Textbook on mathematics.
• 2. Paper.
• 3. Handle.

Instructions

Read the example. To do this, divide each multivalued into classes. Starting from the end of the number, count three digits at a time and put a dot (23.867.567). Let us remind you that the first three digits from the end of the number are to units, the next three are to class, then millions come. We read the number: twenty-three eight hundred sixty-seven thousand sixty-seven.

Write down an example. Please note that the units of each digit are written strictly below each other: units under units, tens under tens, hundreds under hundreds, etc.

Perform addition or subtraction. Start performing the action with units. Write down the result under the category with which you performed the action. If the result is number(), then we write the units in place of the answer, and add the number of tens to the units of the digit. If the number of units of any digit in the minuend is less than in the subtrahend, we take 10 units of the next digit and perform the action.

Read the answer.

Video on the topic

note

Prohibit your child from using a calculator even to check the solution to an example. Addition is tested by subtraction, and subtraction is tested by addition.

Helpful advice

If a child has a good grasp of the techniques of written calculations within 1000, then operations with multi-digit numbers, performed in an analogous manner, will not cause any difficulties.
Give your child a competition to see how many examples he can solve in 10 minutes. Such training will help automate computational techniques.

Multiplication is one of the four basic mathematical operations, which underlies many more complex functions. Moreover, in fact, multiplication is based on the operation of addition: knowledge of this allows you to correctly solve any example.

To understand the essence of the multiplication operation, it is necessary to take into account that there are three main components involved in it. One of them is called the first factor and is a number that is subject to the multiplication operation. For this reason, it has a second, somewhat less common name - “multiplicable”. The second component of the multiplication operation is usually called the second factor: it represents the number by which the multiplicand is multiplied. Thus, both of these components are called multipliers, which emphasizes their equal status, as well as the fact that they can be swapped: the result of the multiplication will not change. Finally, the third component of the multiplication operation, resulting from its result, is called the product.

Order of multiplication operation

Solving multiplication examples

Video on the topic

Sources:

• Multiplication in 2019

Multiplication is one of the four basic arithmetic operations, which is often encountered both in school and in Everyday life. How can you quickly multiply two numbers?

The basis of the most complex mathematical calculations are the four basic arithmetic operations: subtraction, addition, multiplication and division. Moreover, despite their independence, these operations, upon closer examination, turn out to be interconnected. Such a connection exists, for example, between addition and multiplication.

Number multiplication operation

It should be remembered that the essence of the multiplication operation is actually based on addition: to carry it out, it is necessary to add together a certain number of the first factors, and the number of terms of this sum must be equal to the second factor. In addition to calculating the product of the two factors in question, this algorithm can also be used to check the resulting result.

An example of solving a multiplication problem

In addition, it must be remembered that the so-called commutative law applies to the multiplication operation, which establishes that changing the places of the factors in the original example will not change its result. Thus, you can add the number 4 8 times, resulting in the same product - 32.

Multiplication table

Video on the topic

In this lesson, you will learn various useful formulas for adding and subtracting dates in Excel. For example, you will learn how to subtract another from one date, how to add several days, months or years to a date, etc.

If you have already taken lessons on working with dates in Excel (ours or any other lessons), then you should know the formulas for calculating units of time, such as days, weeks, months, years.

When analyzing dates in any data, you often need to perform arithmetic operations on these dates. This article will explain some formulas for adding and subtracting dates that you may find useful.

How to subtract dates in Excel

Let's assume that in your cells A2 And B2 contains dates, and you need to subtract one date from another to find out how many days there are between them. As is often the case in Excel, this result can be obtained in several ways.

Example 1. Directly subtract one date from another

I think you know that Excel stores dates as integers starting at 1, which corresponds to January 1, 1900. So you can simply arithmetically subtract one number from another:

Example 2: Subtracting dates using the DATEDAT function

If the previous formula seems too simple to you, the same result can be obtained more in a sophisticated way using the function RAZNDAT(DATEDIF).

RAZNDAT(A2;B2,"d")
=DATEDIF(A2,B2,"d")

The following figure shows that both formulas return the same result, except for row 4, where the function RAZNDAT(DATEDIF) returns an error #NUMBER!(#NUM!). Let's see why this happens.

When you subtract a later date (May 6, 2015) from an earlier date (May 1, 2015), the subtraction operation returns a negative number. However, the function syntax RAZNDAT(DATEDIF) does not allow start date was more end date and, of course, returns an error.

Example 3. Subtract the date from the current date

To subtract a specific date from the current date, you can use any of the previously described formulas. Just use the function instead of today's date TODAY(TODAY):

TODAY()-A2
=TODAY()-A2

RAZNDAT(A2;TODAY();"d")
=DATEDIF(A2,TODAY(),"d")

As in the previous example, the formulas work great when the current date is greater than the subtracted date. Otherwise the function RAZNDAT(DATEDIF) returns an error.

Example 4: Subtracting Dates Using the DATE Function

If you prefer to enter dates directly into the formula, specify them using the function DATE(DATE) and then subtract one date from the other.

Function DATE has the following syntax: DATE OF( year; month; day) .

For example, the following formula subtracts May 15, 2015 from May 20, 2015 and returns the difference - 5 days.

DATE(2015,5,20)-DATE(2015,5,15)
=DATE(2015,5,20)-DATE(2015,5,15)

If needed count the number of months or years between two dates, then the function RAZNDAT(DATEDIF) is the only possible solution. In the continuation of the article you will find several examples of formulas that reveal this function in detail.

Now that you know how to subtract one date from another, let's see how you can add or subtract a certain number of days, months or years from a date. There are several for this Excel functions. Which one to choose depends on what units of time need to be added or subtracted.

How to add (subtract) days to a date in Excel

If you have a date in a cell or a list of dates in a column, you can add (or subtract) a certain number of days to them using the appropriate arithmetic operation.

Example 1: Adding days to a date in Excel

The general formula for adding a certain number of days to a date is:

= date + N days

The date can be set in several ways:

• Cell reference:
• Calling a function DATE(DATE):

  DATE(2015;5;6)+10
  =DATE(2015,5,6)+10

• Calling another function. For example, to add several days to the current date, use the function TODAY(TODAY):

  TODAY()+10
  =TODAY()+10

The following figure shows the operation of these formulas. At the time of writing, the current date was May 6, 2015.

Note: The result of these formulas is an integer representing a date. To show it as a date, you need to select the cell (or cells) and click Ctrl+1. A dialog box will open Cell Format(Format Cells). On the tab Number(Number) in the list of number formats, select date(Date) and then specify the format you need. More detailed description You will find it in the article.

Example 2: Subtracting days from a date in Excel

To subtract a certain number of days from a date, you again need to use the normal arithmetic operation. The only difference from the previous example is minus instead of plus

= date - N days

Here are some examples of formulas:

A2-10
=DATE(2015,5,6)-10
=TODAY()-10

How to add (subtract) several weeks to a date

When you need to add (subtract) several weeks to a certain date, you can use the same formulas as before. You just need to multiply the number of weeks by 7:

• Add N weeks to date in Excel:

  A2+ N weeks * 7

  For example, to add 3 weeks to a date in a cell A2, use the following formula:

• Subtract N weeks from date in Excel:

  A2 - N weeks * 7

  To subtract 2 weeks from today's date, use this formula:

  TODAY()-2*7
  =TODAY()-2*7

How to add (subtract) several months to a date in Excel

To add (or subtract) a certain number of months to a date, you need to use the function DATE(DATE) or DATAMES(EDATE) as shown below.

Example 1: Adding several months to a date using the DATE function

If the list of dates is, for example, in the column A, indicate the number of months that you want to add (positive number) or subtract (negative number) in some cell, say, in C2.

Type in cell B2 formula below, click on the highlighted corner of the cell and drag it down the column with the mouse B to the last filled cell in the column A. Formula from cell B2 will be copied to all cells of the column B.

DATE(YEAR(A2),MONTH(A2)+$C$2,DAY(A2))
=DATE(YEAR(A2),MONTH(A2)+$C$2,DAY(A2))

Let's see what this formula does. The logic of the formula is clear and obvious. Function DATE OF( year; month; day) receives the following arguments:

• Year from date in cell A2;
• Month from date in cell A2+ number of months indicated in the cell C2;
• Day from date in cell A2;

It's simple! If you enter in C2 negative number, the formula will subtract months rather than add.

Naturally, nothing prevents you from entering a minus directly in the formula to subtract months:

DATE(YEAR(A2),MONTH(A2)-$C$2,DAY(A2))
=DATE(YEAR(A2),MONTH(A2)-$C$2,DAY(A2))

And, of course, you can specify the number of months to add or subtract directly in the formula without cell reference. The finished formulas will look something like this:

• Add months to date:

  DATE(YEAR(A2),MONTH(A2)+2,DAY(A2))
  =DATE(YEAR(A2),MONTH(A2)+2,DAY(A2))

• Subtract months from date:

  DATE(YEAR(A2),MONTH(A2)-2,DAY(A2))
  =DATE(YEAR(A2),MONTH(A2)-2,DAY(A2))

Example 2: Adding or subtracting months from a date using the DATAMES function

Excel provides a special function that returns a date that is a certain number of months ago or forward from a given date - this is the function DATAMES(EDATE). It is available in latest versions Excel 2007, 2010, 2013 and the new Excel 2016.

Using DATAMES(EDATE) You provide the following two arguments:

• Start date – the date from which the number of months is counted.
• Months – the number of months to be added (positive number) or subtracted (negative number).

These formulas will give the same result as formulas with the function DATE(DATE) in the previous example:

When using the function DATAMES(EDATE) the start date and number of months can be specified directly in the formula. Dates can be set using the function DATE(DATE) or as a result of executing other formulas. For example:

• This formula adds 10 months to May 7, 2015

  DATAMES(DATE(2015,5,7),10)
  =EDATE(DATE(2015,5,7),10)

• This formula subtracts 10 months from today's date

  DATAMES(TODAY();-10)
  =EDATE(TODAY(),-10)

Note: Function DATAMES(EDATE) returns just an integer. To represent it as a date, you need to apply a date format to the cell. How to do this is indicated in the article How to change date format in Excel.

How to add (subtract) years to a date in Excel

Adding years to dates in Excel is the same as adding months. You need to use the function again DATE(DATE), but this time you need to specify the number of years you want to add:

DATE(YEAR( date) + N years; MONTH( date); DAY( date))
= DATE(YEAR( date) + N years,MONTH( date), DAY( date))

On an Excel worksheet, the formulas might look like this:

• Add 5 years to the date specified in the cell A2:

  DATE(YEAR(A2)+5,MONTH(A2),DAY(A2))
  =DATE(YEAR(A2)+5,MONTH(A2),DAY(A2))

• Subtract 5 years from the date specified in the cell A2:

  DATE(YEAR(A2)-5,MONTH(A2),DAY(A2))
  =DATE(YEAR(A2)-5,MONTH(A2),DAY(A2))

To get a universal formula, you can enter the number of years in a cell, and then refer to that cell in the formula. Positive number will allow you to add years to the date, and subtract negative ones.

Adding (subtracting) days, months and years to a date

If you carefully read the two previous examples, then I think you figured out how to add (or subtract) years, months and days to a date in one formula. Yes, using the good old function DATE(DATA)!

• For additions X years, Y months and Z days:

  DATE(YEAR( date) + X years; MONTH( date) + Y months; DAY( date) + Z days)
  = DATE(YEAR( date) + X years,MONTH( date) + Y months, DAY( date) + Z days)

• For subtraction X years, Y months and Z days:

  DATE(YEAR( date) - X years; MONTH( date) - Y months; DAY( date) - Z days)
  = DATE(YEAR( date) - X years,MONTH( date) - Y months, DAY( date) - Z days)

For example, the following formula adds 2 years and 3 months, and subtracts 15 days from the date in the cell A2:

DATE(YEAR(A2)+2;MONTH(A2)+3;DAY(A2)-15)
=DATE(YEAR(A2)+2,MONTH(A2)+3,DAY(A2)-15)

When applied to our date column, the formula takes the following form:

DATE(YEAR(A2)+$C$2,MONTH(A2)+$D$2,DAY(A2)+$E$2)
=DATE(YEAR(A2)+$C$2,MONTH(A2)+$D$2,DAY(A2)+$E$2)

How to Add and Subtract Time in Excel

IN Microsoft Excel You can add and subtract time using the function TIME(TIME). It allows you to handle units of time (hours, minutes and seconds) in the same way as years, months and days in the function DATE(DATE).

• Add time in Excel:

  A2 + TIME( watch; minutes; seconds)
  = A2 + TIME( watch, minutes, seconds)

• Subtract time in Excel:

  A2 - TIME( watch; minutes; seconds)
  = A2 - TIME( watch, minutes, seconds)

  Where A2– this is a cell with the time that needs to be changed.

For example, to add 2 hours 30 minutes and 15 seconds to the time in a cell A2 you need to use the following formula:

A2+TIME(2;30;15)
=A2+TIME(2,30,15)

A2+TIME(2;30;-15)
=A2+TIME(2.30,-15)

You can also enter required values into worksheet cells and refer to them in the formula:

A2+TIME($C$2,$D$2,$E$2)
=A2+TIME($C$2,$D$2,$E$2)

It is quite important even in everyday life. Subtraction can often come in handy when counting change at the store. For example, you have one thousand (1000) rubles with you, and your purchases amount to 870. Before you have paid, you will ask: “How much change will I have left?” So, 1000-870 will be 130. And there are many different types of calculations, and without mastering this topic, it will be difficult in real life. Subtraction is an arithmetic operation in which the second number is subtracted from the first number, and the result is the third.

The addition formula is expressed as follows: a - b = c

a– Vasya had apples initially.

b– the number of apples given to Petya.

c– Vasya has apples after the transfer.

Let's put it into the formula:

Subtracting numbers

Subtraction of numbers is easy for any first grader to learn. For example, from 6 you need to subtract 5. 6-5=1.6 more number 5 per one, which means the answer will be one. To check, you can add 1+5=6. If you are not familiar with addition, you can read ours.

Big number is divided into parts, take the number 1234, and in it: 4-units, 3-tens, 2-hundreds, 1-thousands. If you subtract the units, then everything is easy and simple. But let's take an example: 14-7. In the number 14: 1 is tens, and 4 is ones. 1 ten – 10 units. Then we get 10+4-7, let’s do this: 10-7+4, 10 – 7 =3, and 3+4=7. The answer was found correctly!

Consider example 23 -16. The first number is 2 tens and 3 ones, and the second is 1 ten and 6 ones. Let's imagine the number 23 as 10+10+3, and 16 as 10+6, then imagine 23-16 as 10+10+3-10-6. Then 10-10=0, what remains is 10+3-6, 10-6=4, then 4+3=7. The answer has been found!

The same is done with hundreds and thousands.

Column subtraction

Answer: 3411.

Subtracting Fractions

Let's imagine a watermelon. A watermelon is one whole, and if we cut it in half, we get something less than one, right? Half a unit. How to write this down?

½, this is how we designate half of one whole watermelon, and if we divide the watermelon into 4 equal parts, then each of them will be designated ¼. And so on…

subtracting fractions, how is it?

It's simple. Subtract ¼ from 2/4. When subtracting, it is important that the denominator (4) of one fraction coincides with the denominator of the second. (1) and (2) are called numerators.

So, let's subtract. We made sure that the denominators were the same. Then we subtract the numerators (2-1)/4, so we get 1/4.

Subtracting limits

Subtracting limits is not difficult. A simple formula is enough here, which says that if the limit of the difference of functions tends to the number a, then this is equivalent to the difference of these functions, the limit of each of which tends to the number a.

Subtracting Mixed Numbers

A mixed number is a whole number with a fractional part. That is, if the numerator is less than the denominator, then the fraction is less than one, and if the numerator is greater than the denominator, then the fraction is greater than one. A mixed number is a fraction that is greater than one and whose integer part is highlighted; let’s illustrate it with an example:

To perform a subtraction mixed numbers, need to:

Reduce fractions to a common denominator.

Add the whole part to the numerator

Perform calculation

Subtraction lesson

Subtraction is an arithmetic operation in which the difference between two numbers is sought and the answer is the third. The addition formula is expressed as follows: a - b = c.

You can find examples and tasks below.

At subtracting fractions it should be remembered that:

Given the fraction 7/4, we find that 7 is greater than 4, which means 7/4 is greater than 1. How to select the whole part? (4+3)/4, then we get the sum of fractions 4/4 + 3/4, 4:4 + 3/4=1 + 3/4. Result: one whole, three quarters.

Subtraction 1st grade

First grade is the beginning of the journey, the beginning of teaching and learning the basics, including subtraction. Training should be carried out in game form. In first grade, calculations always begin with simple examples on apples, candies, and pears. This method is used not in vain, but because children are much more interested when they are played with. And this is not the only reason. Children have seen apples, candies and the like very often in their lives and have dealt with transfer and quantity, so teaching the addition of such things will not be difficult.

You can come up with a whole bunch of subtraction problems for first graders, for example:

Task 1. In the morning, while walking through the forest, the hedgehog found 4 mushrooms, and in the evening, when he came home, the hedgehog ate 2 mushrooms for dinner. How many mushrooms are left?

Task 2. Masha went to the store to buy bread. Mom gave Masha 10 rubles, and bread costs 7 rubles. How much money should Masha bring home?

Task 3. In the store in the morning there were 7 kilograms of cheese on the counter. Before lunch, visitors bought 5 kilograms. How many kilograms are left?

Task 4. Roma took the candy his dad gave him into the yard. Roma had 9 candies, and he gave his friend Nikita 4. How many candies does Roma have left?

First graders mostly solve problems in which the answer is a number from 1 to 10.

Subtraction 2nd grade

The second class is already higher than the first, and accordingly, the examples for the solution are also higher. So let's get started:

Numerical tasks:

Single digit numbers:

1. 10 - 5 =
2. 7 - 2 =
3. 8 - 6 =
4. 9 - 1 =
5. 9 - 3 - 4 =
6. 8 - 2 - 3 =
7. 9 - 9 - 0 =
8. 4 - 1 - 3 =

Double figures:

1. 10 - 10 =
2. 17 - 12 =
3. 19 - 7 =
4. 15 - 8 =
5. 13 - 7 =
6. 64 - 37 =
7. 55 - 53 =
8. 43 - 12 =
9. 34 - 25 =
10. 51 - 17 - 18 =
11. 47 - 12 - 19 =
12. 31 - 19 - 2 =
13. 99 - 55 - 33 =

Word problems

Subtraction grade 3-4

The essence of subtraction in grades 3-4 is columnar subtraction of large numbers.

Let's look at the example 4312-901. First, let's write the numbers one below the other, so that out of the number 901, one is under 2, 0 is under 1, 9 is under 3.

Then we subtract from right to left, that is, from the number 2 the number 1. We get one:

Subtracting nine from three, you need to borrow 1 ten. That is, subtract 1 ten from 4. 10+3-9=4.

And since 4 took 1, then 4-1=3

Answer: 3411.

Subtraction 5th grade

Fifth grade is the time to work on complex fractions With different denominators. Let's repeat the rules: 1. Numerators are subtracted, not denominators.

So, let's subtract. We made sure that the denominators were the same. Then we subtract the numerators (2-1)/4, so we get 1/4. When adding fractions, only the numerators are subtracted!

2. To perform subtraction, make sure the denominators are equal.

If you come across a difference between fractions, for example, 1/2 and 1/3, then you will have to multiply not one fraction, but both, in order to bring it to a common denominator. The easiest way to do this is to multiply the first fraction by the denominator of the second, and the second fraction by the denominator of the first, we get: 3/6 and 2/6. Add (3-2)/6 and get 1/6.

3. Reducing a fraction is done by dividing the numerator and denominator by the same number.

The fraction 2/4 can be converted to the form ½. Why? What is a fraction? ½ = 1:2, and if you divide 2 by 4, then this is the same as dividing 1 by 2. Therefore, the fraction 2/4 = 1/2.

4. If the fraction is greater than one, then the whole part can be selected.

Given the fraction 7/4, we find that 7 is greater than 4, which means 7/4 is greater than 1. How to select the whole part? (4+3)/4, then we get the sum of fractions 4/4 + 3/4, 4:4 + 3/4=1 + 3/4. Result: one whole, three quarters.

Subtraction presentation

The link to the presentation is below. The presentation examines the basic questions of sixth grade subtraction: Download presentation

Presentation of addition and subtraction

Examples for addition and subtraction

Games for developing mental arithmetic

Special educational games developed with the participation of Russian scientists from Skolkovo will help improve mental arithmetic skills in an interesting game form.

Game "Quick Count"

The game "quick count" will help you improve your thinking. The essence of the game is that in the picture presented to you, you will need to choose the answer “yes” or “no” to the question “are there 5 identical fruits?” Follow your goal, and this game will help you with this.

Game "Mathematical matrices"

"Mathematical Matrices" is great brain exercise for kids which will help you develop his mental work, mental calculation, quick search necessary components, care. The essence of the game is that the player has to find a pair from the proposed 16 numbers that in total will give given number, for example, in the picture below, the given number is “29”, and the desired pair is “5” and “24”.

Game "Number Span"

The number span game will challenge your memory while practicing this exercise.

The essence of the game is to remember the number, which takes about three seconds to remember. Then you need to play it back. As you progress through the stages of the game, the number of numbers increases, starting with two and further.

Game "Mathematical Comparisons"

A great game with which you can relax your body and tense your brain. The screenshot shows an example of this game, in which there will be a question related to the picture, and you will need to answer. Time is limited. How much time will you have to answer?

Game "Guess the operation"

The game “Guess the Operation” develops thinking and memory. The main point game, you need to choose a mathematical sign for the equality to be true. There are examples on the screen, look carefully and put the right sign"+" or "-" so that the equality is true. The “+” and “-” signs are located at the bottom of the picture, select the desired sign and click on the desired button. If you answered correctly, you score points and continue playing.

Game "Simplification"

The game “Simplification” develops thinking and memory. The main essence of the game is to quickly perform a mathematical operation. A student is drawn on the screen at the blackboard, and a mathematical operation is given; the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need using the mouse. If you answered correctly, you score points and continue playing.

Visual Geometry Game

The game "Visual Geometry" develops thinking and memory. The main essence of the game is to quickly count the number of shaded objects and select it from the list of answers. In this game, blue squares are shown on the screen for a few seconds, you need to quickly count them, then they close. Below the table there are four numbers written, you need to select one correct number and click on it with the mouse. If you answered correctly, you score points and continue playing.

Game "Piggy Bank"

The Piggy Bank game develops thinking and memory. The main point of the game is to choose which piggy bank to use more money.In this game there are four piggy banks, you need to count which piggy bank has the most money and show this piggy bank with the mouse. If you answered correctly, then you score points and continue playing.

Development of phenomenal mental arithmetic

We have looked at only the tip of the iceberg, to understand mathematics better - sign up for our course: Accelerating mental arithmetic - NOT mental arithmetic.

From the course you will not only learn dozens of techniques for simplified and quick multiplication, addition, multiplication, division, and calculating percentages, but you will also practice them in special tasks and educational games! Mental arithmetic also requires a lot of attention and concentration, which are actively trained when solving interesting problems.

Speed ​​reading in 30 days

Increase your reading speed by 2-3 times in 30 days. From 150-200 to 300-600 words per minute or from 400 to 800-1200 words per minute. The course uses traditional exercises for the development of speed reading, techniques that speed up brain function, methods for progressively increasing reading speed, the psychology of speed reading and questions from course participants. Suitable for children and adults reading up to 5000 words per minute.

Development of memory and attention in a child 5-10 years old

The course includes 30 lessons with useful tips and exercises for children's development. In every lesson helpful advice, some interesting exercises, an assignment for the lesson and an additional bonus at the end: an educational mini-game from our partner. Course duration: 30 days. The course is useful not only for children, but also for their parents.

Super memory in 30 days

Remember the necessary information quickly and for a long time. Wondering how to open a door or wash your hair? I’m sure not, because this is part of our life. Light and simple exercises To train your memory, you can make it a part of your life and do it a little during the day. If eaten daily norm meals at a time, or you can eat in portions throughout the day.

Secrets of brain fitness, training memory, attention, thinking, counting

The brain, like the body, needs fitness. Physical exercise strengthen the body, mentally develop the brain. 30 days of useful exercises and educational games to develop memory, concentration, intelligence and speed reading will strengthen the brain, turning it into a tough nut to crack.

Money and the Millionaire Mindset

Why are there problems with money? In this course we will answer this question in detail, look deep into the problem, and consider our relationship with money from psychological, economic and emotional points of view. From the course you will learn what you need to do to solve all your financial problems, start saving money and invest it in the future.

Knowledge of the psychology of money and how to work with it makes a person a millionaire. 80% of people take out more loans as their income increases, becoming even poorer. On the other hand, self-made millionaires will earn millions again in 3-5 years if they start from scratch. This course teaches you how to properly distribute income and reduce expenses, motivates you to study and achieve goals, teaches you how to invest money and recognize a scam.

One of the frequently performed tasks in Excel is subtracting or adding percentages to a value. For example, when the price of goods increases, the original price usually increases by a certain percentage. When providing customers with a discount, the price is reduced by several percent.

How to add a number and a percentage in Excel

The figure below clearly shows an example: how to add or subtract a percentage in Excel. For this purpose it is used simple formula. In cell D2, 10% interest is added to the price of item 1. And in cell D5, Client A is given a 20% discount.

To add a specified percentage to a value, simply multiply the same value by 1 + the specified % in a cell with a percentage format for display. For example, in the figure the price of product 1 is increased by 10%. To do this, first add the number 1+10% and the result is 110%. Then we multiply the original price of $100 by 110%. The calculated price this way is $110. In order for the operation of adding a unit with a percentage to be performed first, it should be placed in parentheses.

Excel always follows the rules for the order of mathematical operations - the multiplication action is always first! The presence of parentheses increases the priority of the addition operation over the multiplication operation.

How to subtract a percentage from a number in Excel

To decrease the value by a given percentage, you must again multiply the original value by the number 1, only this time -20%. In the example in the figure, customer A is given a -20% discount. First we subtract 20% from one and the result is 80%. Then you should multiply the original price of $1000 (before the discount) by 80%. Calculated using this method new price the share amounted to $800. As in the previous example, in order for the operation of subtracting the percentage from one to be performed first, it should be placed in parentheses.