Specify which numeric expressions can accept. Rules for using numeric values

Writing the conditions of problems using the notation accepted in mathematics leads to the appearance of so-called mathematical expressions, which are simply called expressions. In this article, we will talk in detail about numeric, literal, and variable expressions: we will give definitions and give examples of expressions of each type.

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Numeric expressions - what is it?

Acquaintance with numerical expressions begins almost from the very first lessons of mathematics. But their name - numerical expressions - they officially acquire a little later. For example, if you follow the course of M. I. Moro, then this happens on the pages of a mathematics textbook for grade 2. There, the representation of numerical expressions is given as follows: 3+5, 12+1−6, 18−(4+6) , 1+1+1+1+1, etc. - this is all numeric expressions, and if we perform the indicated actions in the expression, then we will find expression value.

It can be concluded that at this stage of the study of mathematics, numerical expressions are called records that have mathematical meaning, composed of numbers, brackets and signs of addition and subtraction.

A little later, after getting acquainted with multiplication and division, the entries of numerical expressions begin to contain the signs "·" and ":". Here are some examples: 6 4 , (2+5) 2 , 6:2 , (9 3):3 etc.

And in high school, the variety of entries for numerical expressions grows like a snowball rolling down a mountain. Common and decimal fractions, mixed numbers and negative numbers, powers, roots, logarithms, sines, cosines, and so on appear in them.

Let's summarize all the information in the definition of a numeric expression:

Definition.

Numeric expression is a combination of numbers, signs of arithmetic operations, fractional strokes, root signs (radicals), logarithms, notation of trigonometric, inverse trigonometric and other functions, as well as brackets and other special mathematical symbols, compiled in accordance with the rules accepted in mathematics.

Let us explain all the constituent parts of the voiced definition.

Absolutely any numbers can participate in numerical expressions: from natural to real, and even complex. That is, in numerical expressions one can meet

Everything is clear with the signs of arithmetic operations - these are the signs of addition, subtraction, multiplication and division, respectively, having the form "+", "−", "·" and ":". In numerical expressions, one of these characters, some of them, or all at once, and more than once, can be present. Here are examples of numerical expressions with them: 3+6 , 2.2+3.3+4.4+5.5 , 41−2 4:2−5+12 3 2:2:3:12−1/12.

As for brackets, there are both numerical expressions in which there are brackets, and expressions without them. If there are brackets in a numeric expression, then they are basically

And sometimes brackets in numerical expressions have some specific, separately indicated special purpose. For example, you can find square brackets denoting the integer part of the number, so the numerical expression +2 means that the number 2 is added to the integer part of the number 1.75.

From the definition of a numeric expression, it is also clear that the expression can contain , , log , ln , lg , designations or etc. Here are examples of numerical expressions with them: tgπ , arcsin1+arccos1−π/2 and .

Division in numeric expressions can be denoted with . In this case, there are numerical expressions with fractions. Here are examples of such expressions: 1/(1+2) , 5+(2 3+1)/(7−2,2)+3 and .

As special mathematical symbols and notations that can be found in numerical expressions, we give. For example, let's show a numerical expression with a modulus .

What are literal expressions?

The concept of literal expressions is given almost immediately after getting acquainted with numerical expressions. It is entered like this. In a certain numerical expression, one of the numbers is not written down, but a circle (or a square, or something similar) is put in its place, and it is said that a certain number can be substituted for the circle. Let's take the entry as an example. If you put, for example, the number 2 instead of a square, then you get a numerical expression 3 + 2. So instead of circles, squares, etc. agreed to write letters, and such expressions with letters were called literal expressions. Let's return to our example, if in this entry instead of a square we put the letter a, then we get a literal expression of the form 3+a.

So, if we allow in a numerical expression the presence of letters that denote some numbers, then we get the so-called literal expression. Let us give an appropriate definition.

Definition.

An expression containing letters that denote some numbers is called literal expression.

From this definition it is clear that a literal expression fundamentally differs from a numeric expression in that it can contain letters. Usually, in literal expressions, small letters of the Latin alphabet are used (a, b, c, ...), and when denoting angles, small letters of the Greek alphabet (α, β, γ, ...).

So, literal expressions can be composed of numbers, letters and contain all mathematical symbols that can be found in numerical expressions, such as brackets, root signs, logarithms, trigonometric and other functions, etc. Separately, we emphasize that a literal expression contains at least one letter. But it can also contain several identical or different letters.

Now we give some examples of literal expressions. For example, a+b is a literal expression with the letters a and b . Here is another example of the literal expression 5 x 3 −3 x 2 +x−2.5. And we give an example of a literal expression of a complex form: .

Expressions with variables

If in a literal expression a letter denotes a value that does not take on any one specific value, but can take on different values, then this letter is called variable and the expression is called variable expression.

Definition.

Expression with variables is a literal expression in which the letters (all or some) denote quantities that take on different values.

For example, let in the expression x 2 −1 the letter x can take any natural values ​​from the interval from 0 to 10, then x is a variable, and the expression x 2 −1 is an expression with the variable x .

It is worth noting that there can be several variables in an expression. For example, if we consider x and y as variables, then the expression is an expression with two variables x and y .

In general, the transition from the concept of a literal expression to an expression with variables occurs in the 7th grade, when they begin to study algebra. Up to this point, literal expressions have modeled some specific tasks. In algebra, on the other hand, they begin to look at the expression more generally, without being tied to a specific task, with the understanding that this expression fits a huge number of tasks.

In conclusion of this paragraph, let us pay attention to one more point: by the appearance of a literal expression, it is impossible to know whether the letters included in it are variables or not. Therefore, nothing prevents us from considering these letters as variables. In this case, the difference between the terms "literal expression" and "expression with variables" disappears.

Bibliography.

• Maths. 2 cells Proc. for general education institutions with adj. to an electron. carrier. At 2 o'clock, Part 1 / [M. I. Moro, M. A. Bantova, G. V. Beltyukova and others] - 3rd ed. - M.: Education, 2012. - 96 p.: ill. - (School of Russia). - ISBN 978-5-09-028297-0.
• Maths: studies. for 5 cells. general education institutions / N. Ya. Vilenkin, V. I. Zhokhov, A. S. Chesnokov, S. I. Shvartsburd. - 21st ed., erased. - M.: Mnemosyne, 2007. - 280 p.: ill. ISBN 5-346-00699-0.
• Algebra: textbook for 7 cells. general education institutions / [Yu. N. Makarychev, N. G. Mindyuk, K. I. Neshkov, S. B. Suvorova]; ed. S. A. Telyakovsky. - 17th ed. - M. : Education, 2008. - 240 p. : ill. - ISBN 978-5-09-019315-3.
• Algebra: textbook for 8 cells. general education institutions / [Yu. N. Makarychev, N. G. Mindyuk, K. I. Neshkov, S. B. Suvorova]; ed. S. A. Telyakovsky. - 16th ed. - M. : Education, 2008. - 271 p. : ill. - ISBN 978-5-09-019243-9.

Each of us has his own unique word (usually the number of the full name), which corresponds to a certain number. And it has an impact on our lives.

It is known that all letters of the Russian alphabet occupy a strictly defined place and correspond to their serial number, that is:

A - 1, A - 1, B - 2, C - 3, D - 4, D - 5, E - 6, E - 7, F -8, H - 9, I - 10, J - 11, K - 12, L - 13, M -14, N - 15, O - 16, P - 17, R - 18, S - 19, T - 20, U - 21, F - 22, X - 23, C - 24, H - 25, W - 26, W - 27, L - 28, Y - 29, B - 30, E - 31, Yu - 32, Z - 33.

For example, let's define the code of the word "language" (in this case, the language is a means of communication), summing up all the serial numbers of the letters, we get the number 83.

The word "number" itself is associated with the same mathematical meaning.

Language: 33 + 9 + 29 + 12 = 83.

N and with l about: 25 + 10 + 19 + 13 + 16 = 83.

The word "numerology" and the phrase "Count all the words" also have the same code in total - 116. Numerology: 15 + 21 + 14 + 6 + 18 + 16 + 13 + 16 + 4 + 10 + 33 = 116.

With the number of words: 19 + 25 + 10 + 20 + 1 + 11 + 3 + 19 + 6 + 19 + 13 + 16 + 3 + 1 \u003d 116.

If each letter of the Russian alphabet is assigned a numerical value from 1 to 9, then any phrase - be it a first name, surname or just a phrase - is decomposed into simple numbers, adding which, we get a certain resulting number that determines the nature of the spoken.

To characterize a person in the modern Russian alphabet, the correspondence of letters to numbers (from 1 to 9) is distributed as follows:

1 - A, I, C, b.

2 - B, Y, T, Y.

3 - B, K, U, b.

4 – G, L, F, E.

5 - D, M, X, Y.

6 – E, N, C, I.

7 - E, O, C.

8 – J, P, Sh.

9 - Z, R, Shch.

Currently, there are generally accepted characteristics for numbers from 1 to 9: 1 - unity, creativity, independence;

2 - duality, appearance;

3 - power, power, producing force;

4 - solidity, hardness, dullness;

5 - sensuality, pleasure;

6 - perfection, harmony, balance;

7 - mysticism, mediumship, magic;

8 - materialism, success, justice;

9 - spirituality, mental achievements.

It is believed that people whose names correspond to the numbers 11 and 22 are very developed spiritually. These numbers are not reduced to a single digit. For example, in the name Ivan, the letters correspond to the following numbers: I=1, B=3, A=1, H=6. The sum of the numbers: 1 + 3 + 1 + 6 = 11. In accordance with the rule, the number 11 does not add up, and its value determines a highly developed and spiritual personality.

The words we don't need

Let's calculate some words and phrases that we are used to using in ordinary speech, try to determine whether they are compatible with the number of your name and your birth. For convenience, we repeat the table with which you can perform the calculation:

1 - A, I, C, b.

2 - B, Y, T, Y.

3 - B, K, U, b.

4 – G, L, F, E.

5 - D, M, X, Y.

6 – E, N, C, I.

7 - E, O, C.

8 – J, P, Sh.

9 - Z, R, Shch.

Now let's try to find the code for the word "count": 8 + 9 + 1 + 3 + 1 + 6 + 3 = 3 + 1 = 4. The number 4 - on the one hand, is controlled by Mercury, which is responsible for sociability and communication. On the other hand, it is the number of commitments made. Thus, by telling someone to “figure it out”, we are actually forcing the interlocutor to take part in the conversation and forcing him to commit himself to some action. That is, "pretending." Think for yourself, how pleasant is such a duty for a partner?

Let's break down the word "tin": 8 + 6 + 1 + 2 + 3 = 2 + 0 = 2.

In numerology, the main drawback of the deuce is that it expresses self-doubt and eternal fluctuations. Having said the word "tin", we thus express our feelings. But at the same time they are rather negative.

Numerology is an interesting science that will open the doors to the mysterious world of the mystery of the name. We all know that the name of a person has an influence on the fate and character of its bearer. Numerology by date of birth and name will be able to calculate its true value, show hidden talents and inclinations, aspirations of a person.

Table of correspondence between letters of the name and numbers:

Number	Letters

For example, let's calculate the name "Tatiana":

As a result, we will get 2+1+2+3+6+6+1= 21, we will reduce this figure to a simple number 2+1=3.

It turns out the number of the name "Tatyana" - 3.

Have you already learned your name number? Let's find out what this figure carries.

Having calculated numerology by date of birth and name, let's summarize the results of the calculation:

1. Leadership is embedded in the numerology of the name of this person. A person with such a name number is ambitious, ambitious, energetic, courageous, self-confident. Such people need to occupy leadership positions, or run their own business.

2. The person is active, but he needs the help of a partner. Number 2 people are peace-loving, they are focused on family values, such people get along well in teams. They need to find themselves in working with people, their professions are teachers, doctors, psychologists.

3. Threes are talented, well-rounded people who love to be the center of attention. They are great optimists, often the soul of the company. Their forte is the world of arts, so they will make excellent writers, singers, musicians, speakers.

4. Stability, reliability, honesty - the main feature of the fours. Such people are workaholics, prone to painstaking, responsible work, they are very punctual. Fours are excellent accountants, architects, engineers.

5. Extraordinary, independent people with their own outlook on life. Numerology speaks of such people that they are not afraid to rush into the abyss of novelty, they easily abandon outdated stereotypes. Fives constantly strive for intellectual development. Such people will be comfortable working in tourism, in jurisprudence, journalism.

6. Sixes have a heightened sense of justice, honesty, and responsibility. They are very demanding of themselves, for which they are respected by others. They can be entrusted with any business that requires trust and responsibility. The profession of the owners of names with the calculated number "1" is social workers, educators, doctors.

7. Such a person constantly strives for knowledge, he will collect, check whether the theory corresponds to practice, while he loves to share knowledge with others. Since sevens do not really like physical labor, their professions are philosophers, scientists, inventors.

8. Eights require attention and recognition. They are in constant pursuit of new victories and achievements. Such people are practical and seek profit always and everywhere, while waiting for recognition in their deeds. The ideal habitat for Eights is finance, commerce, administration, construction.

9. Man-harmony. He is kind, patient, seeks peace. Such people usually protect the rights of the disadvantaged, they are for world peace. The nine man will always come to your aid in a difficult moment. Professions of nines are teachers, nurses, social workers, writers.

We hope that we have lifted the veil of secrecy related to the calculation of the numerology of the name. Check your name and maybe you will learn something new about yourself.

The word is not a sparrow, it will fly out - you will not catch it. Before sending some phrase “in flight, make sure that you do not launch negative energy into the Universe. Often, at first glance, even harmless words possess it ...

Everything we say has a certain vibration. Backed by strong emotions, words can materialize - and bring both joy and sorrow.

Calculate the energy of the words that you often use, and think about it: is it time for you to “cleanse” your speech?

In the Russian alphabet, each letter corresponds to a specific number:

1 - A, I, C, b,

2 - B, Y, T, S,

3 - B, K, Y, b,

4 - G, L, F, E,

5 - D, M, X, Yu,

6 - E, N, C, I,

7 - Yo, O, Ch,

8 - F, P, W,

9 - 3, R, Shch.

Add up all the numbers in the word or expression whose energy you want to know, and bring the sum to a prime number. For example, the word "okay" (4+1+5+6+7=23. 2+3=5) has a five vibration.

1. The unit "shows character". It is a symbol of leadership, ambition, risk and selfishness. Words endowed with the energy of the number 1 often carry a fairly strong negative message. For example, by saying "wow", you are letting the universe know that you don't need anything. Saying the word-refusal "fire", you fill the space with negative vibrations. The word "war" and the expression "not in life" also possess "single" energy.

2. The energy of the two is unifying and entirely positive. She charges the words with enthusiasm, warmth and love: “I love”, “God has mercy”, “wealth”, “welcome”. The word “great” has the same energy - it is worth pronouncing it more often instead of the popular “cool” (number b) and “cool” (number 5).

3. The triple has a very strong energy and symbolizes the fulfillment of desires. Saying the words with the energy of the triple, you literally doom them to materialization: “thank you”, “good”, “pleasantly dear”. Be careful about negative phrases - "triples", try to pronounce them as rarely as possible (for example, "never in my life").

4. Four is a symbol of a healthy body, physical strength and beauty. Words - "fours" can affect you and your life in different ways. Everything will depend on what emotions you put into them. For example, the words "can't" and "don't" represent your physical impotence, rejection of good health and good mood. The words “glorious” and “endless” also have the energy of the four. Admiring the appearance of a person or object, say "wow" or "charming" - they carry a stronger positive charge.

5. Five is associated with home, family, human development, life planning. It is a symbol of new knowledge, travel, activity, dynamics. Negative phrases - "five" in this sense, it is better not to use: "crap", "enough", "do not like", "better not". Saying them, you will not achieve positive changes in the area of ​​\u200b\u200bresponsibility of the five.

6. Six means hard work on the path to prosperity. It symbolizes the process of achieving a goal at any cost, without regard to one's own health and state of mind. A vivid confirmation of this is the words "nightmare" or "no way." By giving them an assessment of what is happening, you send a negative impulse into your own life. Often pronouncing the word - "six" "of course", you run the risk of not achieving your dream. Replace it with an energetically more positive "definitely".

7. Seven carries the energy of good luck, success, happiness. By pronouncing the words in which the vibration of the number 7 is concentrated, you are setting up the Universe for a favorable attitude towards you. These words include "good" and "excellent". The energy of the seven is also carried by the word "money".

8. Eight as a symbol of infinity endows words with positive energy. The word "hello" is just from its ranks. When you greet someone in this way, you wish the person eternal health. By the sum of the letters, the word "money" also appears in the eight team. By saying it often, you are programming the space so that your financial source will never dry up. The figure eight is also a symbol of responsibility and duty. Agreeing to fulfill the request, instead of “yes” (six is ​​​​negative energy), say “mandatory”, and the energy of the eight will help you achieve your goal.

9. Nine is the number of strength and militancy. Words endowed with the energy of the number 9 remain in the memory of the Universe for a long time. It is difficult to come up with an expression that has a more negative charge than "only over my dead body." The word "never" also carries an extremely negative energy. Think carefully before you promise, otherwise you risk regretting what was said. It is interesting that the word "truth", which can both heal and hurt, gives a nine by the sum of the letters. If you say “truth” (three) instead of it, then your words will very soon come true.

§ 6. Numeric and letter expressions. Formula

Addition, subtraction, multiplication, division - arithmetic operations (or arithmetic operations). These arithmetic operations correspond to the signs of arithmetic operations:

+ (read " plus") - the sign of the addition operation,

- (read " minus") - the sign of the subtraction operation,

∙ (read " multiply") - the sign of the multiplication operation,

: (read " divide") is the sign of the division operation.

A record consisting of numbers interconnected by signs of arithmetic operations is called numerical expression. Parentheses can also be present in a numeric expression. For example, entry 1290 : 2 - (3 + 20 ∙ 15) is a numeric expression.

The result of performing operations on numbers in a numerical expression is called the value of a numeric expression. Performing these actions is called calculating the value of a numeric expression. Before writing the value of a numeric expression, put equal sign"=". Table 1 shows examples of numeric expressions and their meanings.

Table 1

A record consisting of numbers and small letters of the Latin alphabet, interconnected by signs of arithmetic operations is called literal expression. This entry may contain parentheses. For example, the entry a +b - 3 ∙c is a literal expression. Instead of letters in a literal expression, you can substitute various numbers. In this case, the meaning of the letters can change, so the letters in the literal expression are also called variables.

Substituting numbers instead of letters into the literal expression and calculating the value of the resulting numerical expression, they find the value of a literal expression given the values ​​of the letters(for the given values ​​of the variables). Table 2 shows examples of literal expressions.

A literal expression may not have a value if, by substituting the values ​​of the letters, a numeric expression is obtained whose value for natural numbers cannot be found. Such a numerical expression is called incorrect for natural numbers. They also say that the meaning of such an expression " undefined" for natural numbers, and the expression itself "doesn't make sense". For example, the literal expression a-b does not matter for a = 10 and b = 17. Indeed, for natural numbers, the minuend cannot be less than the subtrahend. For example, having only 10 apples (a = 10), you cannot give away 17 of them (b = 17)! Table 2 (column 2) shows an example of a literal expression. By analogy, fill in the table completely.

table 2

For natural numbers, the expression 10 -17 wrong (doesn't make sense), i.e. the difference 10 -17 cannot be expressed as a natural number. Another example: you cannot divide by zero, so for any natural number b, the quotient b:0 undefined.

Mathematical laws, properties, some rules and relationships are often written in literal form (i.e. in the form of a literal expression). In these cases, the literal expression is called formula. For example, if the sides of a heptagon are equal a,b,c,d,e,f,g, then the formula (literal expression) for calculating its perimeter p looks like:

p=a +b +c +d+e +f +g

For a = 1, b = 2, c = 4, d = 5, e = 5, f = 7, g = 9, the perimeter of the heptagon is p = a + b + c + d + e + f + g = 1 + 2 + 4 + 5 +5 + 7 + 9 = 33.

For a = 12, b = 5, c = 20, d = 35, e = 4, f = 40, g = 18, the perimeter of another heptagon is p = a + b + c + d + e + f + g = 12 + 5 + 20 + 35 + 4 + 40 + 18 = 134.

Block 6.1. Dictionary

Compile a dictionary of new terms and definitions from § 6. To do this, enter the words from the list of terms below in the empty cells. In the table (at the end of the block), indicate the numbers of terms in accordance with the numbers of the frames. It is recommended that before filling in the cells of the dictionary, carefully review § 6 again.

4. The result of performing operations on numbers in numerical terms.

1. The value of a numeric expression that results from substituting variables.into a literal expression.

1. A numeric expression whose value for natural numbers cannot be found.

10. Numerical expression, the value of which for natural numbers can be found.

1. An alphabet whose small letters are used to write literal expressions.

List of terms and definitions

Answer table

Block6 .2. Match

Match the task in the left column with the solution in the right. Write down the answer in the form: 1a, 2d, 3b ...

IN option 1

IN option 2

Block 3. Facet test. Numeric and alphabetic expressions

Faceted tests replace collections of problems in mathematics, but compare favorably with them in that they can be solved on a computer, check solutions and immediately find out the result of the work. This test contains 70 tasks. But you can solve problems by choice, for this there is an evaluation table, which lists simple tasks and more difficult ones. Below is a test.

1. Given a triangle with sides c,d,m, expressed in cm
2. Given a quadrilateral with sides b,c,d,m expressed in m
3. The speed of the car in km/h is b, travel time in hours is d
4. Distance traveled by a tourist m hours, is from km
5. The distance traveled by a tourist moving at a speed m km/h is b km
6. The sum of two numbers is greater than the second number by 15
7. The difference is less than the reduced by 7
8. A passenger liner has two decks with the same number of passenger seats. In each of the deck rows m seats, rows on deck on n more than seats in a row
9. Petya is m years old Masha is n years old, and Katya is k years younger than Petya and Masha together
10. m=8, n=10, k=5
11. m=6, n=8, k=15
12. t=121, x=1458

1. The value of this expression
2. The literal expression for the perimeter is
3. Perimeter expressed in centimeters
4. Formula for the distance s traveled by the car
5. Velocity formula v, tourist movements
6. Time formula t, tourist movements
7. Distance traveled by car in kilometers
8. Tourist speed in kilometers per hour
9. Travel time in hours
10. The first number is...
11. Subtracted equals….
12. The expression for the largest number of passengers that the liner can carry in k flights
13. The largest number of passengers that an airliner can carry in k flights
14. Letter expression for Katya's age
15. Katya's age
16. The coordinate of point B, if the coordinate of point C is t
17. The coordinate of point D, if the coordinate of point C is t
18. The coordinate of point A, if the coordinate of point C is t
19. The length of the segment BD on the number line
20. The length of the segment CA on the number line
21. The length of the segment DA on the number line

Answers (equal, has the form, undefined):

a) 1; b)s=b ∙d; at 9; d) 40; e)b +c +d+m; e) 7; g) the expression does not make sense (incorrectly) for natural numbers; h) 2 ∙m (m +n) ∙k; And) (m +n)-k; j) 6; k) 15; m) 3760; m)t - 3; o) the figure cannot be a triangle; n) 22; R) t - 3 ∙ 7; c) 0; r) 32; y) 59600; f) 6019; x) 2880; c) 10378; h) 1440; w) it is impossible to divide by zero; w) 13; s) 1800; e) 496; j) 2; i) 12; aa) 14; bb) 5; c) 35; dd) 79200; her) 1900; lj) 118; zz) 18; ii) 12800; kk) 98; ll) 1458; mm) v=c:m; nn) 100; oo) 19900; pp)t =b:m; pp) 2520; ss)c +d+m; tt)x; yy) 1579; ff)t+2; xx) 10206; cc) 135; hh)t + 2 ∙ 7; shsh) 7 ∙x; schw)x - 2; yy) 7 ∙x - 2 ∙ 7; uh)t +x ∙ 7; yuyu) 10192; ya)t +x; aaa) 123; bbb) 1456; www) 10327.

TEST INDICATORS. Number of tasks 70, execution time 2 - 3 hours, total points: 1 ∙ 22 + 2 ∙ 24 + 3 ∙ 24 = 142. The following rating scale can be used for the facet test.

Dungeon Treasure Educational Game

On the playing field is an illustration for R. Kipling's book "Mowgli". There are padlocks on five chests, on their reverse sides the number of points received by the team if it manages to “open the chest” is indicated. This number is different for each of the chests: for wood - 1 point, for tin - 2, for copper - 3, for silver - 4, for gold - 5. To open the chest, you must complete the “White Cobra task”.

The task is common to all chests

Read how the money of each of the chests was spent, and make a literal expression for this money. Then substitute the values ​​of the variables and calculate the amount of money that was in the chest at first. This number must be entered in response to the computer version of the game. Locked answers!

Wooden chest. Was bought but books for the price of 50 rubles, b paintings at a price of 250 rubles, d chairs at a price of 300 rubles. There are 250 rubles left in the chest. Variable values: a = 40, b = 8, d = 20.

Tin chest. Purchased to renovate a school d kg of paint at a price of 120 rubles, k bags of cement at a price of 200 rubles, m lamps at a price of 280 rubles. The chest still has a sum of money left, like in a wooden chest, but rounded to the nearest thousand. Values variables: d = 12, k = 16, m = 25.

Copper chest. From this chest they took the amount of money of the tin chest, rounded to hundreds. If you report 5200 rubles to it, then with this money you can buy m tables by price n rubles and 5 computers for the price R rubles. Variable values: m = 10,n= 400 (rubles), p= 6000 (rubles).

Silver chest. From the silver chest they took an amount of money equal to the amount of money in the copper chest rounded to the nearest thousand. Then they reported 12,000 rubles and bought x microscopes by price y rubles and rchemical kits by price z rubles . Variable values: x = 15, y = 8600 (rub), r = 16, z =1500 (rub).

Golden chest. For the money of this chest, the mathematics room was repaired, which took an amount of money equal to the money of the silver chest. It was planned to buy for the gym with the remaining money: mats at a price r( rubles) , balls on p( rubles), sportswear at a price z(rubles). Each of the items k things . However, the price of the ball and form increased by m rubles. Therefore, I had to take a loan of 5200 rubles. Variable values: k = 20 , r = 3200, m = 200, p = 400, z = 1200.

iʞwɐε ɐн and mıqw doɔdʎʞ ǝɯiɓǝʚɐн wɐҺɐɓɐε ʞ ıqɯǝʚɯo qɯɐнεʎ ıqƍоɯҺ

Educational game "Leopold's lessons"

In various places on the playing field, the mice Fat Man and Genius set up ambushes, they are numbered on the field. Only five ambushes. Hover over the number of the ambush and get tasks. Enter your answers into the boxes on the screen. If the answers are correct, then the ambush has been found, and the mice ask Leopold for forgiveness. In case of an error, the game must be repeated.

Trap #1

Identify each of the unshaded beats and type in the answer. Use forward slashes to write fractions. For example: 1/2, 1/3, 1/4, etc.

Trap #2

Convert to Arabic numerals and solve:

1. IX+III=?
2. VI- IV=?
3. II + X1 = ?
4. X - V = ?

Trap #3 Solve the chain Substitute the values ​​of the variables in your answer. At what value of the variable a is the literal expression 4 ?

Trap #4 Solve the chain 4 becomes invalid if all variables are natural numbers ?

Trap #5 Solve the chain Substitute the values ​​of the variables in your answer. At what value of the variable with a literal expression 4 becomes invalid if all variables are natural numbers ?

Answers to the game "Leopold's Lessons"

Trap 1: 1/2, 1/3, 2/3, 7/8.

Trap 2. 12, 2, 13 5.

Trap 3. 6

Trap 4. 15.

The numerical values ​​of the quantities in the text must be indicated with the required degree of accuracy, while in a number of quantities the alignment of the number of decimal places is mandatory. It is unacceptable to give the following series of values: 10; twenty; 16.7; 13.14. This row should look like this: 10.00; 20.00; 16.70; 13.14. The text of the work should not give values ​​in which the number of significant digits is more than three. You should not enter 86.7897. For use in the text of the work, it is better to round the value to 86.8. It is even better if the values ​​are expressed as whole numbers. Therefore, in economic calculations, percentages expressed as an integer are more often used, giving sufficient accuracy, and in describing socio-economic processes - per mille.

In the text of the work, the numerical values ​​of quantities with the designation of units of physical quantities and counting units should be written in numbers, and the number without designation of physical quantities and counting units from one to nine - in a word. For example: “Documents are sampled five times, while the total amount of monetary documents must be at least 9 rubles”, “Sampling is carried out 15 times”. It is unacceptable to separate a unit of a physical quantity from a numerical value (transfer them to different lines or pages), except for the units of physical quantities placed in tables.

If the text to characterize the indicator contains a range of numerical values ​​expressed in the same units of measurement, then the measurements of the unit are indicated after the last numerical value of the range, for example: “the number of overpayments in the amount from 100 to 500 rubles.”

If the text of the work contains a number of numerical values ​​expressed in the same units of measurement, then the units of measurement are indicated only after the last numerical value, for example: "200, 300, 4000 rubles."

Conventional letters, images or signs must comply with those adopted in the current legislation or state standards.

Rules for applying formulas

The text of the work usually uses mathematical formulas that use the designation of parameters. Before the designation of the parameter, its explanation is given, for example: “pair correlation coefficient r”. Formulas must be consecutively numbered in Arabic numerals, which are written at the formula level on the right in parentheses. One formula is designated - "(1)". The numbering of formulas within the chapter of the thesis or the question of the course work is allowed. In this case, the formula number consists of the chapter or question number and the formula number, separated by a dot, for example: "(3.1)". References in the text to the ordinal numbers of formulas are given in parentheses, for example, "... in formula (1)".

Deciphering the symbols included in the formula should be given directly below the formula. The values ​​of each character are given on a new line in the order in which they are given in the formula. The first line of the decryption must begin with the word "where" without a colon after it, for example:

where r is the pair correlation coefficient;

X Y- the average value of the product of the factor by the indicator;

* - average value of the indicator;

U - average value of the factor;

<т, - среднеквадратическое отклонение показателя; - среднеквадратическое отклонение фактора.

It is allowed to transfer the formula to the next line only on the signs of the operations performed. In this case, the applied character at the beginning of the next line is repeated. When transferring the formula on the multiplication sign, the sign "x" is used. The order of presentation in the text of the work of mathematical equations is the same as the formulas.