TRAINING CARD ON THE TOPIC: "SOLUTION OF EQUATIONS".
Compiled by: Antonenko Svetlana Yuryevna, mathematics teacher of the first qualification category, MBOU ESS №9,
Discipline: mathematics
Subject: "Solving Equations"
Class: 5
Textbook: Vilenkin N. Ya., Zhokhov V. I., Chesnokov A. S., Shvartsburd S. I.Mathematics. Grade 5: Textbook for educational institutions. Moscow: Mnemosyne, 2015.
Students should know: What is an equation and its root? What does it mean to solve an equation? Components in addition, subtraction and multiplication. How to find the unknown term, multiplier and minuend?
Working hours with the training card: 15 - 20 min.
This card can be used both in the classroom and for individual lessons with backward students. The task of the student is to disassemble the sample and, by analogy, solve the equations from the textbook. The analyzed examples are presented with a detailed consideration of the solution algorithm. Using cards, students can master the material on their own.
I suggest checking the assimilation of the material with the help of independent work, consisting of three equations. It takes 15 minutes to complete. When checking, it is advisable to give a mark of "5" for three correctly completed tasks, a mark of "4" for two correctly completed tasks, a mark of "3" for one correctly completed task, subject to some progress in solving another one.
Instructions for working with a training card
Working time with the card: 10-15 min.
Review theory.
Please review the sample solution carefully.
Saying each action, complete the task according to the model.
Check your answer with the one provided.
THEORY
1. Equation call an equality containing the letter whose value is to be found.
2. The meaning of the letter, in which of equations , it turns out the correct numerical equality, calledthe root of the equation.
3. solve the equation - means to find all its roots (or to make sure that this equation does not have any roots).
Components when added.
term + term = sum
To find unknown term , it is necessary to subtract the known term from the sum.
Subtraction components.
minuend - subtrahend = difference
To find unknown minuend , you need to add the subtrahend and the difference.
Components when multiplied.
factor ∙ multiplier = product
To find unknown multiplier , it is necessary to divide the product by another factor.
subtraction property .
EXAMPLE 1 .
Decide for yourself: No. 487 (b) p. 77.
| Let's solve the equation | Sample! | № 487(b) p. 77 |
| Components when multiplied. Factor ∙ multiplier = product |
|
|
| We divide the product of 289 by the known factor 17 | ||
| Emphasize the unknown term | ||
| Subtract from the left and right sides 8 | ||
| We consider and we get | X = 9 | |
| Write down the answer | Answer:9 | Answer:3 |
| EXAMPLE 2. Decide for yourself: No. 487 (a) p. 77.
EXAMPLE 3. Decide for yourself: No. 487 (d) p. 77.
|
▫ And the past also showed assistance in the armed struggle against the established government... And it happened. I do not declare that it is right with everyone and everywhere, but there was and there is confirmation of this.
▫ Olga Alekseevna, I accept with gratitude, respect and responsibility. Not for PR. For the state ... (c).
▫ `....Unfortunately, the `declaration` of Metropolitan Sergius did not stop the wave of the `Great Terror`, which claimed the lives of thousands of Orthodox clergy, often `guilty` only of not renouncing their rank....` ==== ============================================ And this is quite understandable . What sane person would believe the "crocodile tears" of this declaration? Pure self-preservation instinct and duplicity. The present time has shown their attempts to get into the affairs of the state, influence ideology, education, receive benefits ...
▫ Nina Ivanovna, it's all good. But ... `The uselessness of Marxism in the defense of the Motherland was well understood by Stalin` - even without comment here. And you say what I saw as rewriting ... Yes, in this one too. Alexander Nevsky, Dimitry Donskoy, Kuzma Minin, Dimitry Pozharsky, Alexander Suvorov, Mikhail Kutuzov - right: he listed the military leaders who beat the enemy. Why not?! What does the ROC have to do with it, what does the church have to do with it, what does Orthodoxy have to do with it? First of all, these are warriors and patriots. One of them even led the Horde to Russia ... And that was it. And a lot of people died because of it. But a warrior. And a figure of scale is not enough of a state. You might think that if they were adherents of the beliefs of the ancient Scandinavians, they would not be able to fight and do what they did?! The wars were not religious, by the way, in nature. The Horde generally had a tambourine, sorry, who is there and what; the rest crossed arms with their fellow Christians. Nina Ivanovna, speaking about the role of Orthodoxy in the Victory, please do not forget to tell about the warm contacts of the Valaam Monastery with the Finns; about what was going on and by whom in the Pskov region during the war. After all, if you do not rewrite History, then it is necessary to tell about these figures covered with crosses, about their service to the enemy. About prayers in honor of Hitler ... Isn't it? ================ I would not call it evasion, Nina Ivanovna: the post continues a long topic about education. Pre-revolutionary period, Soviet period. So: you and I were formed ... so to speak ... during the Soviet period. In one and the same. But the views turned out to be different: I have an attitude towards the pre-revolutionary period and its obligatory attributes (which are manifesting themselves now in a way that I can’t say a good word about): your attitude is completely opposite. Very (in my opinion) reminiscent of that distant time. Not in education. And in the sphere in which it was placed in those days. By whom placed - I hope, I don’t even need to explain. By the way, practically the same thing we can observe now: as they say, but the faces are still the same. And good luck to you, and an easy network, Nina Ivanovna!
▫ Alexander Leonidovich, and I am grateful to you for your posts. They do not allow conscience to lull for the sake of the situation and under the pressure of propaganda. Sorry for the off.
With the help of this lesson, you will learn how to solve complicated equations. You can easily understand how to simplify the equation before directly finding the root. Also review and remember what equations are. Find out what the root of the equation is, how to find it. Learn to solve and, most importantly, check your calculations. In this lesson, you will get to know step by step instructions solutions of complicated equations. Solve many interesting tasks and learn important definitions.
Decision: 1. Let's analyze each entry on the board (Fig. 1). The first line is equality without unknowns - an example. The second line is an inequality. It is in the third line that there is an equation, because only in this entry there is an equality with an unknown number and this number is indicated by a Latin letter. It can be concluded that there is only one equation in Figure 1.
solve the equation is to find the value of the unknown for which the equality is true (or to prove that such values do not exist).
Solve the equation (Fig. 1).
Decision: 1. The sum of an unknown number and fifteen is equal to the quotient of numbers sixty-eight and two. Since the sum in this equation is numerical expression, first we simplify the expression and find the value of the quotient. Now, in order to find the unknown term, it is necessary to subtract the known term from the sum. After we find the value of the unknown - root of the equation, you need to perform a check - substitute the value of the root in the equation and calculate the value, compare the results. If the results match, the equation is correct. If the results do not match, you must solve the equation first.
Solve the equations (fig. 2).
Rice. 2. Equations ()
Decision: 1. In the first equation, you can first simplify its right side - find the difference. Then find the unknown term and check.
2. In order to solve the second equation, you need to find the sum on the right side. Then determine the unknown term and perform a check.
Bibliography
- Mathematics. 4th grade. Proc. for general education institutions. At 2 h. Part 1 / [M.I. Moro, M.A. Bantova, G.V. Beltyukov and others] - 8th ed. - M.: Enlightenment, 2011. - 112 p. : ill. - (School of Russia). Istomina N.B. Mathematics. 4th grade. - M.: Association XXI century.
- Peterson L.G. Mathematics, 4th grade. - M.: Juventa.
Homework
- Internet portal Festival.1september.ru ().
- Internet portal School-172.my1.ru ().
- Internet portal Mathematics-tests.com ().
DEPARTMENT OF LABOR AND SOCIAL PROTECTION OF THE POPULATION OF THE CITY OF MOSCOW
DEPARTMENT OF SOCIAL PROTECTION OF THE POPULATION
TROITSKY AND NOVOMOSKOVSKY ADMINISTRATIVE DISTRICT OF THE CITY OF MOSCOW
STATE BUDGET GENERAL EDUCATIONAL INSTITUTION OF THE CITY OF MOSCOW
TRINITY REHABILITATION AND EDUCATIONAL CENTER "SOLNYSHKO"
st. Pushkovykh, 5, Troitsk, Moscow, 108840
Phone/Fax: 8-495-851-13-05, 8-495-851-50-03 e-mail: [email protected]
Educational cards on the topic:
"Equations with one variable"
math teachers
Irinevich E.M.
Moscow, Troitsk
Equations with one variable
Explanatory note
Learning cards, in the amount of 80 (30 + 50), for students in grades 7-8 in algebra contain training exercises that allow students to learn how to solve linear equations, equations that reduce to linear, and also quadratic equations. When solving linear equations of the form ah=in attention should be paid to the fact that if a is not equal to 0, then the equation ah=in is called a first-degree equation with one variable and has one root, and linear equation may have no roots, one root, or infinitely many.
A sufficient number of quadratic equations are also presented. When solving a quadratic equation using a formula, one usually first calculates the discriminant and compares it with zero. After that, depending on the result, either the roots are found by the formula, or they conclude that there are no roots. Note that the first coefficient cannot be zero. If at least one of the coefficients in or with equals zero, then quadratic equation called incomplete.
Students must distinguish between three types of incomplete quadratic equations:
Type equation =0 always has only one root x=0.
Type equation a+in=0 always has two roots, and one of the roots is 0.
Type equation +c=0 either has no roots or has two roots that are opposite numbers.
With the help of quadratic equations, you can simplify the solution of many problems.
Instructions for using cards
These cards can be used by the teacher at any stage of the lesson, depending on the goals and objectives. The amount of time allotted to work with the cards also depends on the stage at which they are used, as well as the type of school and student population. So, in correctional classes, it will take much more time to work out assignments than in a class with more successful children. Each card has an even number of tasks, which will allow them to be used both by options and for one option. The tasks themselves are arranged in increasing difficulty. So, for example, tasks under No. 1, 2 are simple, their students are basically able to solve, they are intended for repetition. Tasks No. 3 - No. 12 are more difficult, since you first need to simplify it: open the brackets, bring like terms, perform actions with negative numbers, with ordinary and decimals. As a result of such transformations, an equation is obtained that is equivalent to the given one; its roots are also roots given equation. In tasks No. 13, 26, 30 equations with parameters are presented. Tasks for compiling equations are given in No. 14 and in
No. 15. Some equations are solved by factoring. There are 30 equations in total.
Given 50 problems for solving equations.
Approximate time to work with cards 10 - 15 minutes.
Linear equations and equations reducing to them.
#1 Solve the equation:
a) x + 12 = 67; d) 15 - y = 8;
b) z + 35 = 87; e) 83 - a = 43;
c) y - 93 = 18: e) m + 23 = 92.
No. 2. Find the root of the equation:
a) 5x = 60; d) 6y = -18;
b) 9y = 72; e) -2x = 10;
c) 10z = 15; f) 11y = 0.
#3 Solve the equation:
a) 4x + x = 70; d) 8x - 7x + 8 = 12;
b) 4 * 25 * x = 800; e) y * 5 * 20 = 500;
c) 13y + 15y - 24 = 60; e) 6z + 5z - 44 = 0.
#4 Solve the equation:
a) 55: x + 9 = 20; d) 48: (9c - c) = 2;
b) 88: x - 24 = 64; e) (y + 6) - 2 = 15;
c) p * 38 - 76 = 38; e) 2 (a - 5) = 24.
No. 5. Find the root of the equation:
a) (x + 15) - 8 = 17; d) 32 - x = 32 + x;
b) (y - 35) + 12 = 32; e) x - 35 - 64 = 16;
c) 55 - (x - 15) = 30; f) 28 - y +35 = 53.
No. 6. Find the root of the equation:
a) 35x = 175; d) 2* (x - 5) = 36;
b) m: 35 = 18; e) (y + 25): 8 = 16;
c) (n -12) * 8 = 56; e) 24 * (z + 9) = 288.
No. 7. Solve the equation:
a) 2-3(x+2) = 5-2x; d) 0.4x \u003d 0.4-2 (x + 2);
b) 0.2 - 2(x + 1) = 0.4x; e) 5(2+1.5x)-0.5x=24;
c) 3-5(x+1) = 6-4x; f) 3(0.5x-4)+8.5x=18.
No. 8. Solve the equation:
a) 4x - 5.5 \u003d 5x - 3 (2x-1.5);
b) 4 - 5 (3x + 2.5) = 3x + 9.5;
c) 0.4 (6x - 7) = 0.5 (3x + 7).
#9 Solve the equation:
a) + = ; d) + = ;
b) - = - 3; e) + = 5;
c) - = -1; e) + = 4.
#10 Solve the equation:
a) = ; d) - 2 = ;
b) = ; e) - = 2;
c) = ; e) - = 3.
No. 11. Solve the equation:
a) = 5; d) + 2 = ;
b) = 5; e) + = 4.
c) (4x+2)=2x -1; f) 2x-12= (3x + 2).
No. 12. Solve the equation:
a) x \u003d 1; d) x - =;
b) = 5; e) (x+5) = 0.2 (3x-1);
c) 7 - x \u003d 3; e) x + 11 \u003d 1 - x.
#13 Solve the equation for X:
a) x - a \u003d 2; d) 3x + m = 0;
b) 1 - x \u003d c + 2; e) 2x - a \u003d b + x;
c) x + b = 0: e) 4x + a = x + c.
№ 14. At what value of the variable:
a) the value of the expression 3y + 4 is equal to the value of the expression 3 - 2y;
b) are the values of the expressions 4x - 5 and 14 + 5x opposite?
No. 15. Find the value of the variable, in which:
a) the value of the expression 7 + 5x is 2 times greater than the value of the expression 3x;
b) the value of the expression 8x + 3 is 10 more than the value of the expression 4 - 2x;
c) The value of the expression 2x - 4 times 3 less value expressions 2x;
d) the value of the expression 15 - 3x is 2 less than the value of the expression 2x + 3.
Quadratic equations
No. 16. Which of these equations is square:
a) = + 2; d) 2x(x+5) = 7;
b) - + 5x + 8 \u003d 0; e) 2 - 3x = 0;
c) 5 \u003d 4 - 3x; f) h + = 0?
No. 17. For each equation, indicate the coefficients a, b, c:
a) - = 0; d) 2 + x + = 0;
b) 2 - 5x + 10 = 0; e) 2x - 7 =;
c) 0.5 - x -3 = 0; f) 4 - 3 = 11x.
No. 18. Having calculated the discriminant, determine whether the equation has roots, and if it has, then find them:
a) + 7x -; d) 5- = 0; b) 9 + 12y + 4 = 0; e) - y + 3 = 0; + x + 6 = 0; e) 4 - 4x + 1 = 0.
No. 19. Solve the equation:
a) + 3x +; d) + = 0; b) 4 - 11y - 3 = 0; e) - y + 20 = 0; + 7x + 2 = 0; e) -7 + 5x + 2 = 0.
#20 Calculate the discriminant of the equation and answer the following questions:
Does the equation have roots?
If it has, how much?
Are roots rational or irrational?
a) + 3x -; d) - = 0; b) 5 - y + 2 = 0; e) - 11y + 10 = 0; + 7x - 1 = 0; f) 3 + 2x - 2= 0.
No. 21. Find the roots of the equation:
a) - 10x (x-3) -; b)) = 0; c) 3 + 8(1 - y) = 0; d) 2 - 3y(y+5) - 9(y+5) = 0;
No. 22. Determine how many roots the equation has:
a) (4( 
b) (( 
a) (3( 
b) (( 
Incomplete quadratic equations
#23 Solve the equations:
b) = 0; e) - 6y = 0;
0; e) - 2x = 0.
No. 24. Find the roots of the equation:
a) - 36; d) 25 - 81 = 0; b) - 25 = 0; e) = 0;
0; f) 1-9=0.
No. 25. Find the roots of the equation:
a) - x; d) + = 0; b) + 4= 0; e) + 2 = 0; - x = 0; e) 18 + 2x = 0.
No. 26. Does the solution have an incomplete quadratic equation + c if:
a) a > 0, c > 0; a) a< 0, с > 0;
a) a > 0, c< 0; а) а < 0, с < 0 ?
Vieta's theorem
No. 27. Determine the signs of the roots of the equation (if any) without solving the equation:
a) - 4x +; d) - 10 = 0; b) - 6y + 8 = 0; e) + 10y + 21 = 0; - 15x + 44 = 0; e) - 8x - 48 = 0.
No. 28. Solve the equation orally:
a) - 3x +; d) -5 = 0; b) + 5y + 6 = 0; e) + y - 20 = 0; + 5x - 14 = 0; e) - 2x - 15 = 0.
№ 29. Check if the given numbers are the roots of the equation:
a) - 8x +, 1 and 7;
b) - 6y + 8 = 0; e) + 10y + 21 = 0 - 15x + 44 = 0; e) - 8x - 48 = 0.
a) One of the roots of the equation +14x + is 7. Find the second root and the number with.
b) One of the roots of the equation +px+ is equal to. Find the second root and coefficient R.
c) The difference of the roots of the equation + 6x + q is 8. Find its roots and the number q.
d) The difference of the roots of the equation + 3x + c is 2.5. Find a number with.
Solving Problems with Equations.
The student thought of a number. If you subtract 7 from it and divide the result by 3, you get 5. What number was the student thinking?
I thought of a number. If we multiply it by 5, and reduce the product by 18, we get half the intended number. Find this number.
The sum of the two numbers is 13.6 and the difference is 1.6. Find these numbers.
The sum of the two numbers is 105, their ratio is 1:2. Find these numbers.
Find a number whose half is greater than its third by 0.5.
father 5 times older than son and the son is 32 years younger than his father. How old are each of them?
A field of 430 hectares is divided into two parts so that one of them is 130 hectares larger than the other. Find the area of each piece.
A rope 84 m long is cut into two pieces, one of which is 3 times longer than the other. Find the length of each piece.
A rope 25 m long is cut into two pieces, one of which is 50% longer than the other. Find the lengths of these parts of the rope.
10. The perimeter of a rectangle is 118 cm, one side is 12 cm longer than the other. Find the lengths of the sides of the rectangle.
11. Three tractor drivers plowed together 72 hectares. The first plowed 6 hectares more than the second, and the second - 9 hectares more than the third. How many hectares did each tractor driver plow?
12. There are 79 students in three classes. The second has 3 students more than the first, and the second has 9 hectares more than the third. How many students are in each class?
13. The father is 40 years old, and the son is 10. In how many years will the father be three times older than the son?
14. There are 54 kg of apples in three baskets. In the first basket 12 kg less than in the second, and in the third - twice as much as in the first. How many kilograms of apples are in each basket?
15. Boat speed in standing water 20 km/h The speed of the river is 2 km/h. Find the distance between two piers if the boat makes a round trip in 5 hours.
16. A boat in still water travels 15 km per hour, the speed of the river is 2 km / h. Find the distance between two piers if a boat passes it half an hour faster in one direction than in the opposite direction.
17. From the station to the camp site, tourists walked at a speed of 4 km / h, and back - at a speed of 5 km / h, and therefore spent an hour less time on the same path. Find the distance from the station to the hostel.
18. A helicopter flew the distance between two cities with a tailwind in 5.5 hours, and with a headwind in 6 hours. Find the distance between the cities and the own speed of the helicopter if the wind speed was 10 km / h.
Solving problems by compiling quadratic equations
19. Find two numbers whose sum is 61 and whose product is 900.
20. Find two numbers whose difference is 11 and the product is 312.
21. Find the length and width of a rectangular area if its area is 800 and the length is 20 m longer than the width.
22. The perimeter of a rectangular field is 6 km, and its area is 200 hectares. Find the length and width of the field.
23. Product of two consecutive numbers more than their sum by 239. Find these numbers.
24. The square of the sum of two consecutive natural numbers is greater than the sum of their squares by 264. Find these numbers.
25. Find three consecutive integers whose sum of squares is 434.
26. Find common fraction, whose numerator is 2 more than the denominator and 40 less than the square of the denominator.
27. The denominator of a fraction is 3 more than the numerator. If you add the reciprocal of this fraction, you get it. Find a fraction.
28. The cinema had 320 seats. After the number of seats in each row was increased by 4 and one more row was added, the hall became 420 seats. How many rows are there in the cinema?
29. A tourist sailed on a motorboat up the river for 15 km, and went down the raft back. By boat he sailed 10 hours less than by raft. Find the speed of the river if the speed of the boat in still water is 12 km/h.
30. Halfway between A and B, the train was delayed for 10 minutes. To arrive at point B on schedule, the initial speed of the train had to be increased by 12 km/h. Find the initial speed of the train if the distance from A to B is 120 km.
31. A motorcycle traveled from one city to another for 4 hours. Returning back, he drove the first 100 km at the same speed, and then reduced it by 10 km / h and therefore spent 30 minutes more on the way back. Find the distance between cities.
32. Father and son walked 480 m, and the father took 200 steps less than his son. Find the step length of each of them if the step of the father is 20 cm longer than the step of the son.
33. Two harvesters harvested wheat from the field in 4 days. If one of them harvested half of all the wheat and the other the rest, then all the wheat would be harvested in 9 days. In how many days could each combine separately harvest all the wheat from the field?
34. The team planned to sow 200 hectares before a certain date, but sowed daily 5 hectares more than planned, and therefore finished sowing 2 days ahead of schedule. In how many days did the brigade finish sowing?
35. Two workers, of which the second starts work 1.5 days later than the first, can complete the work in 7 days. In how many days could each of them separately complete all the work if it is known that the second worker can complete it 3 days faster than the first?
36. Two hundred bees sat equally on each blossoming cherry branch. If 5 less branches bloomed, then each village would have two more bees. How many branches blossomed on the cherry and how many bees were on each?
37. Several points are placed on the plane so that no three of them lie on the same line. If each of them is connected by segments with all other given points, 153 segments will be obtained. How many points are given?
38. 66 games were played in the chess tournament. Find the number of participants in the tournament if it is known that each participant played one game with each.
39. 56 matches were played at the district football championship, and each team played with each team twice. How many teams were in the game?
40. A photograph measuring 12 x 18 cm is glued onto a sheet so that a frame of the same width is obtained. Determine the width of the frame if you know that the photo, including the frame, occupies an area of 280
41. Two skaters are moving in the same direction on a circular path 2 km long, converging every 20 minutes. Find the speed of each skater if the first skater runs the circle 1 minute faster than the second.
43. A water tank is filled with two pipes in 2 hours 55 minutes. The first pipe can fill it 2 hours faster than the second. How long does it take each pipe separately to fill the tank?
44. The perimeter of a rectangle is 26 cm, and the sum of the areas of the squares built on two adjacent sides of the rectangle is 89 cm. Find the sides of this rectangle.
45. Of two pieces of metal, the first had a mass of 880 g, and the second 858 g, and the volume of the first piece is 10 less than the volume of the second. Find the density of each metal if the density of the first is 1 g/ greater than the density of the second.
46. Under the rides, they took a rectangular area, one of the sides of which is 4 m larger than the other. Its area is 165
47. A rectangular garden plot with an area of 600 is surrounded by a fence, the length of which is 100 m. What are the sides of the plot? What is 30 cm. Find the sides of a plot of the same area if the length of the fence around it is 140 m?
49. One leg right triangle 7 cm more than the other, and the perimeter of the triangle is 30 cm. Find all the sides of the triangle.
50. Two roads intersect at right angles. Two cyclists left the intersection at the same time, one heading south and the other heading east. The speed of the second was 4 km/h more than the speed of the first. An hour later, the distance between them was 20 km. Determine the speed of each cyclist.
Literature:
Algebra.7 class: textbook. for general education institutions, ed. G.V. Dorofeeva, I.F. Sharygin. Ros. acad. education, publishing house "Enlightenment".
Algebra.8 class: textbook. for general education institutions, ed. G.V. Dorofeeva, I.F. Sharygin. Ros. acad. education, publishing house "Enlightenment".
Collection of tasks for conducting a written exam in algebra for the course of the basic school. Grade 9 L.V. Kuznetsova, E.A. Bunimovich and others. M.: Bustard
Tasks on the topic: "Solving simple and complex equations"
Additional materials
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Interactive simulators for grade 3
T.E.Demidova B.P.Geydman Mathematics in 10 minutes
Addition and Subtraction Equations
1. Solve the equations.
10. Insert instead of ... a number so that the correct equality is obtained.
| 12 + ... = 67 | 56 - ... = 48 | ... + 23 = 92 | ... - 45 = 32 |
| 45 - ... = 11 | 59 - ... = 29 | ... + 32 = 94 | ... + 53 = 88 |
11. Solve problems.
11.1. Before the renovation, there were 34 tables in the school cafeteria. After the repair, another 46 tables were brought. How many tables are in the dining room?
11.2. There were 12 sacks of flour in the warehouse, then another 58 sacks and 14 more sacks were brought. How many bags of flour are in stock?
11.3. Polina picked 18 strawberries from the garden, then 32 more. How many strawberries did Polina collect in total?
Multiplication and division equations
1. Solve the equations.
| 56:x=8 | x * 17 = 68 | y: 25 = 2 |
| 28:y=4 | 12*y=60 | y * 4 = 100 |
2. Solve problems.
2.1. There were 16 chairs in the cafe. After the renovation of the cafe, the number of chairs increased 3 times. How many chairs are in the cafe after renovation?
2.2. There were 56 machines in the machine shop of the plant. One fourth of the machines were sent for repair. How many machines were sent for repair and how many remained in the shop?
2.3. At the market, the seller sold currant berries, in total he had 68 kg of berries. During the day, he sold half of the berries he had. How many kg of berries did he sell?
3. Make up equations containing the operation of multiplication or division, and solve them.
3.1. Use numbers: 8, 56 and variable X.
3.2. Use numbers: 6, 42 and variable A.
3.3. Use numbers: 3, 69 and variable B.
3.4. Use numbers: 4, 92 and variable X.
3.5. Use numbers: 39, 3 and variable A.
3.6. Use numbers: 18, 2 and variable B.
