Action rule 7 letters last p. Arithmetic action
Indeed, the division itself is spoken of in many ways: there is a division of the genus into species, then - a division in which the whole is broken into its own parts, another division - when polysemantic word allows division into eigenvalues.
It is easy to see that all cyclic numbers are in direct relationship with the geometric division of the circle: for example, 4320 = 360x12; however, there is nothing accidental or conventional about this division, since, for reasons concerning the correspondence between arithmetic and geometry, it is normal that this division be carried out according to multiples of 3, 9, and 12, while the decimal division directly corresponds to a straight line.
Thus, if we combine the zero division of the vernier with the zero division of the main scale, then the first division of the vernier will “lag behind” the first division of the main scale by the difference in the intervals of the scales, i.e.
Meanwhile, however, for a correct definition, division of species is necessary, and perhaps this is precisely the rule of division and definition: after all, definition is formed along with division.
In addition, it should be emphasized that the division into quarters was superimposed by the division into "tribes"; as can be seen from the etymology of the word itself, it was a tripartite division.
6. The post-industrial society is characterized by: 1) class division of society; 2) the natural nature of the economy; 3) the prevailing ...
This division is traditional, typical for all branches of law, not only Russian, but also foreign, as well as international law. The division of criminal law into two parts has the following premises: 1. This division is a manifestation of the legislative technique and allows not to indicate in each article of the Special Part all the signs of the subject of the crime, to formulate provisions on an unfinished crime, complicity and other features of the objective and subjective sides, as well as to disclose the content of punishment, etc.
Bisection of a string (1/2) gives an octave, further division into three parts (2/3) gives a fifth, division into four (3/4) a fourth, etc.
of the last century, is associated with the formation of a global economy based on the creation of a global computer network and the transcontinental financial system. Question 3 International division of labor Answer The international division of labor (MRT) is a process of specialization of workers from different countries in the performance of specific types of labor operations. There are 3 main forms of the international division of labor: 1) general (division of countries into industrial, agricultural, raw ); 2) private (associated with the export of certain goods and services); 3) single (production of individual components and parts at enterprises dependent on TNCs). According to another classification, the international division of labor manifests itself in 2 forms of international specialization of production (Fig.
A word of 7 letters, the first letter is "E", the second letter is "K", the third letter is "C", the fourth letter is "T", the fifth letter is "R", the sixth letter is "I", the seventh letter is "M", the word for the letter "E", the last "M". If you do not know a word from a crossword puzzle or a crossword puzzle, then our site will help you find the most difficult and unfamiliar words.
Guess the riddle:
Once upon a time there was one orphan girl in the thicket, she had only two kittens, two puppies, three parrots, a turtle and a hamster with a hamster that was supposed to give birth to 7 hamsters. The girl went for food. She goes through the forest, field, forest, field, field, forest, forest, field. She came to the store, but there was no food there. Goes on, forest, forest, field, field, forest, field, forest, field, forest, field, field, forest. And the girl fell into the hole. If she gets out, dad will die. If she stays there, her mother will die. The tunnel cannot be dug. What should she do? Show answer>>
Three friends lived in the forest: Deaf, Mute, and Blind. All was good. But somehow the Deaf One died. How now will the Mute tell the Blind that their Deaf friend is dead? Show answer>>
Husband and wife lived. The husband had his own room in the house, which he forbade his wife to enter. The key to the room was in the bedroom dresser. So they lived for 10 years. And so the husband went on a business trip, and the wife decided to go into this room. She took the key, opened the room, turned on the light. The wife walked around the room, then saw a book on the table. She opened it and heard someone open the door. She closed the book, turned off the light and closed the room, putting the key in the chest of drawers. This is the husband. He took the key, opened the room, did something in it and asked his wife: “Why did you go there?” How did the husband guess?
When we work with various expressions, including numbers, letters and variables, we have to perform a large number of arithmetic operations. When we do a transformation or calculate a value, it is very important to follow the correct order of these actions. In other words, arithmetic operations have their own special execution order.
In this article, we will tell you what actions should be done first and which after. First, let's look at a few simple expressions in which there are only variables or numerical values, as well as division, multiplication, subtraction, and addition signs. Then we will take examples with brackets and consider in what order they should be evaluated. In the third part, we will give the correct order of transformations and calculations in those examples that include the signs of roots, powers, and other functions.
Definition 1In the case of expressions without brackets, the order of actions is determined unambiguously:
- All actions are performed from left to right.
- First of all, we perform division and multiplication, and secondly, subtraction and addition.
The meaning of these rules is easy to understand. Traditional order writing from left to right determines the basic sequence of calculations, and the need to first multiply or divide is explained by the very essence of these operations.
Let's take a few tasks for clarity. We have used only the simplest numerical expressions so that all calculations can be done mentally. So you can quickly remember the desired order and quickly check the results.
Example 1
Condition: calculate how much 7 − 3 + 6 .
Solution
There are no brackets in our expression, multiplication and division are also absent, so we perform all the actions in the specified order. First, subtract three from seven, then add six to the remainder, and as a result we get ten. Here is a record of the entire solution:
7 − 3 + 6 = 4 + 6 = 10
Answer: 7 − 3 + 6 = 10 .
Example 2
Condition: in what order should the calculations be performed in the expression 6:2 8:3?
Solution
To answer this question, we reread the rule for expressions without parentheses, which we formulated earlier. We only have multiplication and division here, which means we keep the written order of calculations and count sequentially from left to right.
Answer: first, we divide six by two, multiply the result by eight, and divide the resulting number by three.
Example 3
Condition: calculate how much will be 17 − 5 6: 3 − 2 + 4: 2.
Solution
First, let's determine the correct order of operations, since we have here all the basic types of arithmetic operations - addition, subtraction, multiplication, division. The first thing we need to do is divide and multiply. These actions do not have priority over each other, so we perform them in the written order from right to left. That is, 5 must be multiplied by 6 and get 30, then 30 divided by 3 and get 10. After that we divide 4 by 2 , that's 2 . Substitute the found values into the original expression:
17 - 5 6: 3 - 2 + 4: 2 = 17 - 10 - 2 + 2
There is no division or multiplication here, so we do the remaining calculations in order and get the answer:
17 − 10 − 2 + 2 = 7 − 2 + 2 = 5 + 2 = 7
Answer:17 - 5 6: 3 - 2 + 4: 2 = 7.
Until the order of performing actions is firmly learned, you can put numbers over the signs of arithmetic operations, indicating the order of calculation. For example, for the problem above, we could write it like this:
If we have literal expressions, then we do the same with them: first we multiply and divide, then we add and subtract.
What are steps one and two
Sometimes in reference books all arithmetic operations are divided into operations of the first and second stages. Let us formulate the required definition.
The operations of the first stage include subtraction and addition, the second - multiplication and division.
Knowing these names, we can write the rule given earlier regarding the order of actions as follows:
Definition 2
In an expression that doesn't have parentheses, you must first perform the actions of the second step in the direction from left to right, then the actions of the first step (in the same direction).
Order of evaluation in expressions with brackets
Parentheses themselves are a sign that tells us the desired order in which to perform actions. In this case right rule can be written like this:
Definition 3
If there are parentheses in the expression, then the action in them is performed first, after which we multiply and divide, and then add and subtract in the direction from left to right.
As for the parenthesized expression itself, it can be considered as a component of the main expression. When calculating the value of the expression in brackets, we keep the same procedure known to us. Let's illustrate our idea with an example.
Example 4
Condition: calculate how much 5 + (7 − 2 3) (6 − 4) : 2.
Solution
This expression has parentheses, so let's start with them. First of all, let's calculate how much 7 − 2 · 3 will be. Here we need to multiply 2 by 3 and subtract the result from 7:
7 − 2 3 = 7 − 6 = 1
We consider the result in the second brackets. There we have only one action: 6 − 4 = 2 .
Now we need to substitute the resulting values into the original expression:
5 + (7 − 2 3) (6 − 4) : 2 = 5 + 1 2: 2
Let's start with multiplication and division, then subtract and get:
5 + 1 2:2 = 5 + 2:2 = 5 + 1 = 6
This completes the calculations.
Answer: 5 + (7 − 2 3) (6 − 4) : 2 = 6.
Do not be alarmed if the condition contains an expression in which some brackets enclose others. We only need to apply the rule above consistently to all parenthesized expressions. Let's take this task.
Example 5
Condition: calculate how much 4 + (3 + 1 + 4 (2 + 3)).
Solution
We have brackets within brackets. We start with 3 + 1 + 4 (2 + 3) , namely 2 + 3 . It will be 5 . The value will need to be substituted into the expression and calculate that 3 + 1 + 4 5 . We remember that we must first multiply, and then add: 3 + 1 + 4 5 = 3 + 1 + 20 = 24. Substituting the found values into the original expression, we calculate the answer: 4 + 24 = 28 .
Answer: 4 + (3 + 1 + 4 (2 + 3)) = 28.
In other words, when evaluating the value of an expression involving parentheses within parentheses, we start with the inner parentheses and work our way to the outer ones.
Let's say we need to find how much will be (4 + (4 + (4 - 6: 2)) - 1) - 1. We start with the expression in the inner brackets. Since 4 − 6: 2 = 4 − 3 = 1 , the original expression can be written as (4 + (4 + 1) − 1) − 1 . Again we turn to the inner brackets: 4 + 1 = 5 . We have come to the expression (4 + 5 − 1) − 1 . We believe 4 + 5 − 1 = 8 and as a result we get the difference 8 - 1, the result of which will be 7.
The order of calculation in expressions with powers, roots, logarithms and other functions
If we have an expression in the condition with a degree, root, logarithm or trigonometric function(sine, cosine, tangent and cotangent) or other functions, then the first thing we do is calculate the value of the function. After that, we act according to the rules specified in the previous paragraphs. In other words, functions are equal in importance to the expression enclosed in brackets.
Let's look at an example of such a calculation.
Example 6
Condition: find how much will be (3 + 1) 2 + 6 2: 3 - 7 .
Solution
We have an expression with a degree, the value of which must be found first. We consider: 6 2 \u003d 36. Now we substitute the result into the expression, after which it will take the form (3 + 1) 2 + 36: 3 − 7 .
(3 + 1) 2 + 36: 3 - 7 = 4 2 + 36: 3 - 7 = 8 + 12 - 7 = 13
Answer: (3 + 1) 2 + 6 2: 3 − 7 = 13.
In a separate article devoted to calculating the values of expressions, we present other, more complex examples calculations in the case of expressions with roots, degrees, etc. We recommend that you familiarize yourself with it.
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