And the calculated value of the expressions is based on the song’s callousness, in other words, it is necessary to adjust Order of Vikonannya.

From this article we will figure out which steps to follow and which ones follow them. Let’s start with the simplest calculations, when you put in more numbers and change them, connected by plus and minus signs, multiply and divide. Below we will explain the order in which the following lines should be drawn on the lines with bows. Determine, let's look at what sequence the actions take place in order to replace the stage, root and other functions.

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Initially multiplied and divided, then added and removed

The school gives this the rule that means the order of the viconn of actions in virazas without arches:

• they are arranged in order from left to right,
• Moreover, from the beginning the multiplication and division are completed, and then the addition and division are added.

The stated rule is to take it naturally. The order of actions from left to right is explained by the fact that we usually keep records of evil to the right. And those that are multiplied and divided are concluded before the folds and are explained by the place that these actions carry.

Let's take a look at a number of examples of this established rule. For applications, the simplest numerical calculations are simplistic, so we don’t focus on calculations, but focus on the order of actions.

butt.

Vikonite dii 7-3+6.

Decision.

The final look should not be mixed with the bow, and also the hem should not be mixed. Therefore, we need to finish all the actions in order from left to right, so that from the beginning we add 3 from 7, subtract 4, then add 6 to the removed difference 4, subtract 10.

Briefly, the solution can be written as follows: 7−3+6=4+6=10.

Subject:

7−3+6=10 .

butt.

Indicate the order of actions in the formula 6:2 · 8:3.

Decision.

To answer the nutritional task, let’s look at the rule that indicates the order of execution in the form without arches. In the output, the expressions are located only half and half, and therefore, as a rule, they need to be arranged in order from left to right.

Subject:

From now on 6 is divided by 2, which is privately multiplied by 8, solve, and the result is divided by 3.

butt.

Calculate the value of the formula 17−5·6:3−2+4:2.

Decision.

It is important to begin with that the order of the following is taken into account in the output expression. It is possible to replace and multiply from the bottom, and add from the extracts. The beginning of the evil to the right needs to be multiplied and divided. So 5 is multiplied by 6, subtracted by 30, this number is divided by 3, subtracted by 10. Now 4 is divided by 2, subtracted by 2. Substituting the substitution 5 6:3 for the output formula, the value 10 is found, and the substitution 4:2 is the value 2 May 17−5·6:3−2+4:2=17−10−2+2.

In the removed expression there is no longer a multiplication and a subdivision, so in order of evil to the right the viconties that were lost are lost: 17−10−2+2=7−2+2=5+2=7.

Subject:

17−5·6:3−2+4:2=7.

First, in order not to confuse the order of the actions when calculating the value of the virus, manually place numbers above the action signs that indicate the order of their actions. For the front butt it would be like this: .

What is the order of the action - first multiplying and dividing, then adding and removing - should be followed when working with lethal viruses.

Dii of the first and the other stage

Some mathematics students have a limited range of arithmetic operations at the first and second levels. Let's figure it out.

Viznachennya.

Activities of the first stage they call addition and appearance, and multiplication and subdivision are called activities of another level.

In these terms, the rule from the first point, which indicates the order of succession of actions, is written as follows: if you do not place the bows, then in the order of the left to the right, the steps of the other step (multiplication and division) are concluded, then the steps of the first step ena (folding and lifting).

The order of arithmetic operations in forms with bows

Virazis often move the bows to indicate the order of their actions. In this case the rule that determines the order of viconic actions in verses with bows, is formulated as follows: first, the action is drawn in the arms, in which case, in the same order from the left to the right, the multiplication and hem are drawn, then the addition and the last.

Also, the storage in the arches is seen as a warehouse for the output virus, and the order of execution that is already familiar to us is preserved in them. Let's take a look at the solutions of the butts for greater clarity.

butt.

Enter the following values: 5+(7−2·3)·(6−4):2.

Decision.

If you place the arms, then you will see the action in the places where the arms are placed. Let’s finish with virus 7-2·3. You need to multiply first, and then only 7−2·3=7−6=1. We move on to another viraza in arms 6-4. There’s only one action here – vydnіannya, which means 6−4=2.

It is possible to extract the values ​​from the output expression: 5+(7−2·3)·(6−4):2=5+1·2:2. In the removed form, the right side is converted to the right by multiplying and dividing, then – by removing 5+1·2:2=5+2:2=5+1=6. In this case, all the vykonans, we have reached the following order: 5+(7−2·3)·(6−4):2.

Let’s write down the solution briefly: 5+(7−2·3)·(6−4):2=5+1·2:2=5+1=6.

Subject:

5+(7−2·3)·(6−4):2=6.

It turns out that the temples have to be removed from the temples. There is no need to be afraid of anything, it is necessary to consistently state the stated rule for vikonannya actions in forms with arches. Let's show the solution to the butt.

butt.

Vikonate dii u virazi 4+(3+1+4·(2+3)) .

Decision.

This is from the arms, which means that the final step must be started from the arch in the arms, so 3+1+4·(2+3) . This way you can also place the arms, so you need to start viconting them. Zrobimo tse: 2+3=5. Having substituted the found value, we subtract 3+1+4·5. In this case, the whole expression is initially multiplied, then added, perhaps 3+1+4·5=3+1+20=24. The output value, after substituting this value, looks like 4+24, and it is impossible to complete the calculation: 4+24=28.

Subject:

4+(3+1+4·(2+3))=28.

However, if the virus has bows at the arms, then it is often necessary to manually start from the inner arms and work through to the outer ones.

For example, let us not need to viconate dii in the viraz (4+(4+(4−6:2))−1)−1 . Firstly, the action at the inner bows is reduced, since 4−6:2=4−3=1, then the final expression will look like (4+(4+1)−1)−1. Once again, we conclude the action at the inner arches, since 4 + 1 = 5, then we come to the next step (4 +5-1)-1. Again, the action in the arms is calculated: 4+5−1=8, which brings us to a difference of 8−1, which is equal to 7.

To correctly calculate expressions that require more work, it is necessary to know the order of calculation of arithmetic processes. Arithmetic operations without arches were arranged in this order:

1. If the direction is located at the steps, then the whole action is in the order of straightness, then from the left to the right.
2. Then (as evidenced by the virus) these multiplications and divisions are arranged in the order of their directness.
3. The remaining ones (as is obvious from the virus) are added and published in the order of their directness.

Let's look at the butt like this:

From the beginning you need to count the numbers at the steps (number 4 for the square and number 2 for the cube):

3 16 - 8: 2 + 20

Then multiply and subdivide (3 multiplied by 16 and 8 divided by 2):

And at the very end, the final addition is concluded (from 48 to 4 and to the result of addition 20):

48 - 4 + 20 = 44 + 20 = 64

Dii of the first and the other stage

Arithmetic operations are divided into operations of the first and second levels. Additions and updates are called activities of the first stage, multiply and hem - activities of another level.

If it is possible to place the action in just one step and there are no arms in it, then the action will follow the order of its right direction.

butt 1.

15 + 17 - 20 + 8 - 12

Decision. This will only apply to one step - the first (additional and additional). It is necessary to determine the order of actions and actions.

Subject: 42.

If you want to combine the steps of both steps, then the steps of the other step come first, in the order of their straightness (from left to right), and then the steps of the first step.

butt. Calculate the value of the virus:

24: 3 + 5 2 - 17

Decision. This means that there are four steps: the first two steps and the other two. The order of their order is significant: as a rule, the first step will be the bottom, the second will be the multiplication, the third will be the addition, and the fourth will be the addition.

Now let's get started with the calculations.

Today we'll talk about Viconnanny order mathematical diy. What kind of things do you have to finish first? Added and revealed, or multiplied and subdivided. It’s amazing that our children still have problems with, for example, elementary expressions.

Well, let’s guess about those who are initially counted with virazis at the temples

38 – (10 + 6) = 22 ;

Order of action:

1) at the temples: 10 + 6 = 16;

2) day: 38 – 16 = 22.

If a form without arches can only be added and removed, or only multiplied and divided, then the items are arranged in order from left to right.

10 ÷ 2 × 4 = 20;

Order of action:

1) from the left to the right, the side is divided: 10 ÷ 2 = 5;

2) multiplication: 5 × 4 = 20;

10 + 4 - 3 = 11, then:

1) 10 + 4 = 14 ;

2) 14 – 3 = 11 .

Since the expression without arms has not only the added value, but also the multiplied or hem, then they are added in order from left to the right, and if the multiplication and hem prevails, they are added to the front, and after them the addition from the bottom I love it.

18 ÷ 2 – 2 × 3 + 12 ÷ 3 = 7

Order of actions:

1) 18 ÷ 2 = 9;

2) 2 × 3 = 6;

3) 12 ÷ 3 = 4;

4) 9 - 6 = 3; tobto. left to the right – the result of the first day minus the result of the other;

5) 3 + 4 = 7; tobto. the result of the fourth day plus the result of the third;

If the virus has arches, then the virus is formed in the arms, then multiplied and divided, and then added to the arms.

30 + 6 × (13 - 9) = 54, then:

1) viraz at the temples: 13 - 9 = 4;

2) multiplication: 6 × 4 = 24;

3) added: 30 + 24 = 54;

Well, let's get the pouch. First of all, before calculating, you need to analyze the expression: what is in the bows and what they do. After this, proceed to the calculation in this order:

1) action, placed at the arms;

2) multiplication and division;

3) additional information.

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The first division of numbers is the activities of another level.
The order in which the value of the expressions is determined is determined by the following rules:

1. Since the vyraza does not have bows, it is necessary to place only one step, they are lined up in order from left to right.
2. If you want to place the steps of the first and the other step and there are no arms in the first one, then start with the steps of the other step, then the steps of the first step.
3. If the infection has arches, then place the steps in the arms (in this case, rules 1 and 2).

butt 1. We know the meaning of the virus

a) x + 20 = 37;
b) y + 37 = 20;
c) a – 37 = 20;
d) 20 – m = 37;
e) 37 - h = 20;
e) 20 + k = 0.

636. Given any natural numbers, can you get 12? How many pairs of such numbers are there? Give feedback on the same nutrition for reproduction and for subculture.

637. Three numbers are given: the first is three-digit, the other is the significant part of the division of a six-digit number into ten, and the third is 5921. How many of these numbers can you indicate?

638. Forgive Viraz:

a) 2a + 612 + 1a + 324;
b) 12у + 29у + 781 + 219;

639. Unleash jealousy:

a) 8x – 7x + 10 = 12;
b) 13y + 15y-24 = 60;
c) Зz – 2z + 15 = 32;
d) 6t + 5t – 33 = 0;
e) (x + 59): 42 = 86;
e) 528: k - 24 = 64;
g) p: 38 – 76 = 38;
h) 43m-215 = 473;
i) 89n + 68 = 9057;
j) 5905 – 21 v = 316;
l) 34s – 68 = 68;
m) 54b – 28 = 26.

640. The animal farm will ensure a yield increase of 750 g per animal per harvest. What kind of growth does the complex produce in 30 days for 800 animals?

641. Two large and five small cans have 130 liters of milk. How much milk does a small can contain, since its capacity is much less than that of a larger one?

642. The dog, having beaten the ruler, when it appears at a distance of 450 m, and runs to a new speed of 15 m/s. How to stand between the ruler and the dog in 4 s; after 10; via t?

643. Unleash the military for help:

1) Mikhail has 2 times more peas, less than Mikoli, and Petya has 3 times more, less than Mikoli. How many peas does each person have, since everyone has 72 peas at once?

2) Three girls collected 35 turtles on the sea birch. Galya knew 4 times more than Masha, and Olena knew 2 times more than Masha. How many mushels has this girl known?

644. Add up the calculation program for the virus

8217 + 2138 (6906 - 6841) : 5 - 7064.

Write down this program as a diagram. Find out the meaning of the expression.

645. Write the following for the upcoming calculation program:

1. Multiply 271 by 49.
2. Divide 1001 by 13.
3. The result of Vikonannya command 2 multiplied by 24.
4. Combine the results of teams 1 and 3.

Find out the meaning of this expression.

646. Write a sentence after the diagram (Fig. 60). Create a program for your calculation and find your value.

647. Unleash jealousy:

a) Zx + bx + 96 = 1568;
b) 357z - 1492 - 1843 - 11469;
c) 2y + 7y + 78 = 1581;
d) 256m - 147m - 1871 - 63747;
e) 88880: 110 + x = 809;
f) 6871 + p: 121 = 7000;
g) 3810 + 1206: y = 3877;
h) up to + 12705: 121 = 105.

648. Find privately:

a) 1989680: 187; c) 9018009: 1001;
b) 572163: 709; d) 533368000: 83600.

649. Motor ship 3 years ago by the lake with a wind speed of 23 km/year, and 4 years by the river. How many kilometers have the motor ships traveled in 7 years, since the river of Vine Yshov is 3 km/year lower than the lake?

650. Stand 30 m between the dog and the gut. After how many seconds does the dog need the gut, since the dog’s speed is 10 m/s, and the gut’s speed is 7 m/s?

651. Find in the table (Fig. 61) all the numbers in order from 2 to 50. You have the right to count a number of times; You can ask a friend: who knows all the numbers?

N.Ya. VILENKIN, V. I. ZHOKHOV, A. S. CHESNOKOV, S. I. SHVARTZBURD, Mathematics 5th grade, Handbook for lighting installations

Download lesson plans for mathematics lessons for 5th grade, handbooks and books free of charge, lesson plans for mathematics online

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The rules for the order of vykonannya actions in folding vyslovlyuvannya follow in the 2nd class, and the actions from them are performed by children in the 1st class.

You can immediately see the rule about the order of the verses without arches, if you vibrate over the numbers either only the addition and the subsection. The need to introduce expressions that combine two or more arithmetic operations of one level arises from the students’ familiarity with calculation techniques, which are added in between 10, and itself:

Similar: 6 – 1 – 1, 6 – 2 – 1, 6 – 2 – 2.

Since, in order to find the meaning of these expressions, schoolchildren are reduced to objective actions that are arranged in a simple order, they can easily grasp the fact that arithmetic actions (added and presented), which take place in the expressions, are arranged sequentially angry to the right.

With numerical expressions, which are related to the operation and execution, as well as the arches, scientists are first focused on the topic “Folding and presentation between 10”. If children study with such types in 1st grade, for example: 7 – 2 + 4, 9 – 3 – 1, 4 +3 – 2; in class 2, for example: 70 – 36 +10, 80 – 10 – 15, 32+18 – 17; 4*10:5, 60:10*3, 36:9*3, the reader shows how to read and write such expressions and how to find their meanings (for example, 4*10:5 read: 4 multiply by 10 and subtract the result and divide at 5). At the time of training in the 2nd class of the “Order of Actions” object, students will understand the meaning of this type of expression. Meta-works at this stage - focusing on the practical meaning of the students, increase their respect for the order of their actions in such expressions and formulate a similar rule. Learn to act independently when choosing a teacher and explain in what order they were completed; for skin butts. Then they formulate themselves and read after the guide: if the expression without arches has only one addition and the same (or only the same), then they are ordered in the order in which they are recorded (then evil iva to the right).

Regardless of those that have forms like a+b+c, a+(b+c) and (a+c)+c, the obviousness of the arms does not add up to the order of origin due to the law of folding, at which stage scientists focus more on those that start at the temples. Therefore, with expressions like a - (b + c) and a - (c - c) such formalization is unpleasant and for students at the initial stage it will be difficult to navigate the designated arms of different numerical expressions. The twist of the bows in numerical expressions, which replaces the action of the folded and visible, further removes its development, which is related to the development of such rules as adding a sum to a number, a number to a sum, adding a sum from a number and a number to a sum. When first getting acquainted with the arms, it is important to focus on what you are learning about the arms.

The teacher earns the children’s respect for the fact that it is important to adhere to this rule when making calculations, otherwise incorrect jealousy can be rejected. For example, learn to explain how the values ​​of the expressions are removed: 70 - 36 +10 = 24, 60:10 - 3 = 2, why they are incorrect, and what the meanings of the expressions really are. The order of actions in verses with bows is similar: 65 – (26 – 14), 50: (30 – 20), 90: (2 * 5). Scientists are also familiar with such statements and can read them, write them down, and calculate their meanings. Having explained the order of actions in a number of such numbers, the children formulate a formula: in the lines from the bows, the first number is written on the numbers written in the arms. Looking at the words, it is not important to show that they follow the order in which they are written down; to show the different order of their viconics and viconics of the arms.

Let us now introduce a rule for the order of the verses without arches, if they contain the first and the other steps. Since the rules of procedure are accepted for housekeeping, the teacher informs them to the children or the students to familiarize themselves with them. In order for the students to understand the rules, they have the necessary rights to include solutions to applications from the explained procedure for completing their actions. Effective also have the right to explain the amends on the order of execution of actions. For example, from the given pairs of applications, it is necessary to write down the same ones, where the calculation is done according to the rules of procedure:

After explaining the pardons, you can set the dates: vikoryst arms, change the order of actions so that the given value is not specified. For example, in order for the first of the expressions to be of little significance, which is more than 10, you need to write it like this: (20+30):5=10.

Children especially have the right to calculate the value of the calculation if the student has to comply with all the rules. For example, on the doshtsi and zoshitas the viraz 36:6+3*2 is written. Learn to calculate this value. Then, according to the teacher’s instructions, the children change the order of the expression for the help of each other:

• 36:6+3-2
• 36:(6+3-2)
• 36:(6+3)-2
• (36:6+3)-2

What’s important, and what’s more important, is the turn to the right: arrange the arms so that the given value is aligned:

• 72-24:6+2=66
• 72-24:6+2=6
• 72-24:6+2=10
• 72-24:6+2=69

Also useful are rights of this type:

• 1. Separate the arms so that the evenness is correct:
• 25-17:4=2 3*6-4=6
• 24:8-2=4
• 2. Place the “+” and “-” signs instead of the star so that the correct values ​​are obtained:
• 38*3*7=34
• 38*3*7=28
• 38*3*7=42
• 38*3*7=48
• 3. Substitute arithmetic signs for the star so that the equations are correct:
• 12*6*2=4
• 12*6*2=70
• 12*6*2=24
• 12*6*2=9
• 12*6*2=0

Each person has the right to consult with someone, so that the significance of the agreement may change if the order of actions changes.

To master the rules of the order of actions, it is necessary in the 3rd and 4th grades to include more complicated expressions, when calculating the values ​​of which students stagnate, not just one, but two or three rules of the order of actions, for example:

• 90*8- (240+170)+190,
• 469148-148*9+(30 100 - 26909).

From what number of traces should be selected so that the stench allows the establishment of actions in order, which creates minds for the clear stagnation of the learned rules.