Multiplication. Multiplication Test examples of division by 2 and 3

And multiplication. The multiplication operation will be discussed in this article.

Multiplying numbers

Multiplication of numbers is mastered by children in the second grade, and there is nothing complicated about it. Now we will look at multiplication with examples.

Example 2*5. This means either 2+2+2+2+2 or 5+5. Take 5 twice or 2 five times. The answer, accordingly, is 10.

Example 4*3. Likewise, 4+4+4 or 3+3+3+3. Three times 4 or four times 3. Answer 12.

Example 5*3. We do the same as the previous examples. 5+5+5 or 3+3+3+3+3. Answer 15.

Multiplication formulas

Multiplication is the sum of identical numbers, for example, 2 * 5 = 2 + 2 + 2 + 2 + 2 or 2 * 5 = 5 + 5. Multiplication formula:

Where, a is any number, n is the number of terms of a. Let's say a=2, then 2+2+2=6, then n=3 multiplying 3 by 2, we get 6. Let's look at it in reverse order. For example, given: 3 * 3, that is. 3 multiplied by 3 means that three must be taken 3 times: 3 + 3 + 3 = 9. 3 * 3=9.

Abbreviated multiplication

Abbreviated multiplication is a shortening of the multiplication operation in certain cases, and abbreviated multiplication formulas have been derived specifically for this purpose. Which will help make calculations the most rational and fastest:

Abbreviated multiplication formulas

Let a, b belong to R, then:

The square of the sum of two expressions is equal to the square of the first expression plus twice the product of the first expression and the second plus the square of the second expression. Formula: (a+b)^2 = a^2 + 2ab + b^2

The square of the difference of two expressions is equal to the square of the first expression minus twice the product of the first expression and the second plus the square of the second expression. Formula: (a-b)^2 = a^2 - 2ab + b^2

Difference of squares two expressions is equal to the product of the difference of these expressions and their sum. Formula: a^2 - b^2 = (a - b)(a + b)

Cube of sum two expressions is equal to the cube of the first expression plus triple the product of the square of the first expression and the second plus triple the product of the first expression and the square of the second plus the cube of the second expression. Formula: (a + b)^3 = a^3 + 3a(^2)b + 3ab^2 + b^3

Difference cube two expressions is equal to the cube of the first expression minus triple the product of the square of the first expression and the second plus triple the product of the first expression and the square of the second minus the cube of the second expression. Formula: (a-b)^3 = a^3 - 3a(^2)b + 3ab^2 - b^3

Sum of cubes a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Difference of cubes two expressions is equal to the product of the sum of the first and second expressions and the incomplete square of the difference of these expressions. Formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Sign up for the course "Speed up mental arithmetic, NOT mental arithmetic" to learn how to quickly and correctly add, subtract, multiply, divide, square numbers and even extract roots. In 30 days, you'll learn how to use easy tricks to simplify arithmetic operations. Each lesson contains new techniques, clear examples and useful tasks.

Multiplying fractions

While looking at adding and subtracting fractions, the rule was brought up to bring fractions to a common denominator in order to complete the calculation. When multiplying this do No need! When multiplying two fractions, the denominator is multiplied by the denominator, and the numerator by the numerator.

For example, (2/5) * (3 * 4). Let's multiply two thirds by one quarter. We multiply the denominator by the denominator, and the numerator by the numerator: (2 * 3)/(5 * 4), then 6/20, make a reduction, we get 3/10.

Multiplication 2nd grade

The second grade is just the beginning of learning multiplication, so second graders solve simple problems to replace addition with multiplication, multiply numbers, and learn the multiplication table. Let's look at multiplication problems at the second grade level:

Oleg lives in a five-story building, on the top floor. The height of one floor is 2 meters. What is the height of the house?

The box contains 10 packages of cookies. There are 7 of them in each package. How many cookies are in the box?

Misha arranged his toy cars in a row. There are 7 of them in each row, but there are only 8 rows. How many cars does Misha have?

There are 6 tables in the dining room, and 5 chairs are pushed behind each table. How many chairs are there in the dining room?

Mom brought 3 bags of oranges from the store. The bags contain 22 oranges. How many oranges did mom bring?

There are 9 strawberry bushes in the garden, and each bush has 11 berries. How many berries grow on all the bushes?

Roma laid 8 pipe parts one after another, each of the same size, 2 meters each. What is the length of the complete pipe?

Parents brought their children to school on September 1st. 12 cars arrived, each with 2 children. How many children did their parents bring in these cars?

Multiplication 3rd grade

In third grade, more serious tasks are given. In addition to multiplication, Division will also be covered.

Multiplication tasks will include: multiplying two-digit numbers, multiplying by columns, replacing addition with multiplication and vice versa.

Column multiplication:

Column multiplication is the easiest way to multiply large numbers. Let's consider this method using the example of two numbers 427 * 36.

1 step. Let's write the numbers one below the other, so that 427 is at the top and 36 at the bottom, that is, 6 under 7, 3 under 2.

Step 2. We begin multiplication with the rightmost digit of the bottom number. That is, the order of multiplication is: 6 * 7, 6 * 2, 6 * 4, then the same with three: 3 * 7, 3 * 2, 3 * 4.

So, first we multiply 6 by 7, answer: 42. We write it this way: since it turned out 42, then 4 are tens, and 2 are units, the recording is similar to addition, which means we write 2 under the six, and 4 we add the number 427 to the two.

Step 3. Then we do the same with 6 * 2. Answer: 12. The first ten, which is added to the four of the number 427, and the second - ones. We add the resulting two with the four from the previous multiplication.

Step 4. Multiply 6 by 4. The answer is 24 and add 1 from the previous multiplication. We get 25.

So, multiplying 427 by 6, the answer is 2562

REMEMBER! The result of the second multiplication should begin to be written under SECOND number of the first result!

Step 5. We perform similar actions with the number 3. We get the multiplication answer 427 * 3 = 1281

Step 6. Then we add up the obtained answers during multiplication and get the final multiplication answer 427 * 36. Answer: 15372.

Multiplication 4th grade

The fourth class is already the multiplication of large numbers only. The calculation is performed using the column multiplication method. The method is described above in accessible language.

For example, find the product of the following pairs of numbers:

988 * 98 =
99 * 114 =
17 * 174 =
164 * 19 =

Presentation on multiplication

Download a presentation on multiplication with simple tasks for second graders. The presentation will help children better navigate this operation, because it is designed colorfully and in a playful style - the best way for a child to learn!

Multiplication table

Every student in the second grade learns the multiplication table. Everyone should know it!

Examples for multiplication

Multiplying by one digit

9 * 5 =
9 * 8 =
8 * 4 =
3 * 9 =
7 * 4 =
9 * 5 =
8 * 8 =
6 * 9 =
6 * 7 =
9 * 2 =
8 * 5 =
3 * 6 =

Multiplying by two digits

4 * 16 =
11 * 6 =
24 * 3 =
9 * 19 =
16 * 8 =
27 * 5 =
4 * 31 =
17 * 5 =
28 * 2 =
12 * 9 =

Multiplying two-digit by two-digit

24 * 16 =
14 * 17 =
19 * 31 =
18 * 18 =
10 * 15 =
15 * 40 =
31 * 27 =
23 * 25 =
17 * 13 =

Multiplying three-digit numbers

630 * 50 =
123 * 8 =
201 * 18 =
282 * 72 =
96 * 660 =
910 * 7 =
428 * 37 =
920 * 14 =

Games for developing mental arithmetic

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

Game "Quick Count"

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

Game "Mathematical matrices"

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

Game "Number Span"

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

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

Game "Guess the operation"

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

Game "Simplification"

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

Game "Quick addition"

The game "Quick Addition" develops thinking and memory. The main essence of the game is to choose numbers whose sum is equal to a given number. In this game, a matrix from one to sixteen is given. A given number is written above the matrix; you need to select the numbers in the matrix so that the sum of these digits is equal to the given number. If you answered correctly, you score points and continue playing.

Visual Geometry Game

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

Game "Mathematical Comparisons"

The game "Mathematical Comparisons" develops thinking and memory. The main essence of the game is to compare numbers and mathematical operations. In this game you need to compare two numbers. At the top there is a question written, read it and answer the question correctly. You can answer using the buttons below. There are three buttons “left”, “equal” and “right”. If you answered correctly, you score points and continue playing.

Development of phenomenal mental arithmetic

We have looked at only the tip of the iceberg, to understand mathematics better - sign up for our course: Accelerating mental arithmetic.

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

Speed reading in 30 days

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

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

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

Money and the Millionaire Mindset

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

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

Topic: Multiplication and division tables by 2. (Reinforcement lesson)

Goal: strengthening computational skills in multiplication and division tables.

Lesson objectives:

1. Consolidate knowledge of multiplication and division tables; develop the ability to solve compound problems; continue to build computing skills.

2. Develop logical and economic thinking; ability to draw conclusions and generalize.

3. Working in groups, cultivate such personality qualities as cooperation, mutual assistance, tolerance; respect for work and working people.

Lesson type : a lesson in improving and consolidating skills.

During the classes.

1. Organizational moment. Psychological mood of students.

The bell rang and class began.

- Guys,imagine that your palms are a small mirror, look into it, smile at yourself - you see how cute and smart you are! Look at each other, smile, and your mood will be cheerful and upbeat, you will want to learn new things, because it is so interesting!

There lived a sage who knew everything. One man decided to prove that the sage does not know everything. Holding a butterfly in his palms, he asked: “Tell me, sage, which butterfly is in my hands: dead or alive?” And he himself thinks: “If the living one says, I will kill her, if the dead one says, I will release her.” The sage, after thinking, replied: “Everything is in your hands.”

Your knowledge is also in your hands. Let us prove this with our work in class.

(Slide 1)

II. Updating basic knowledge.

To work quickly and deftly

We need mental training.

a) Which number is the odd one out?(Slide 2)

What task do you need to do with numbers? (Remove extra number)

7 14 21 27 28 35 42 49

5 10 11 15 20 25 30 35

4 8 12 16 17 20 24 28

What knowledge did you need to complete the task? (Multiplication tables)

Assessment.

b) Say the word.

I invite you to find out the topic of today's lesson by asking questions.

1. An action that can replace the sum of identical terms (multiplication)

2. The number being divided by (divisor)

3. The number that is being divided (divisible)

4. Result of multiplication (product)

5. Result of division action (quotient)

6. Multiplication action component (multiplier)

Slide 3. Assessment.

III. Independent formulation of the topic and purpose of the lesson. Goal setting for the lesson.

Who guessed what the topic of the lesson is?

Multiplication and division table.

Guys, what goal will we set for ourselves?

Slide 4

Today we will consolidate our knowledge of the multiplication and division tables, we will use the table to solve problems, equations, and find the value of an expression.

Problematic question.

Do you think it’s possible to learn something new by repeating and reinforcing? We need to figure it out.

4. Oral counting

1. Statement of the problem. Mystery.

To find out what we will talk about today, you will need to guess the Russian folk riddle “A bunch of piglets are lying, whoever touches them, they will squeal.” Doubt the answer? Now we will solve this problem by performing calculations.

Slide 5

What's in front of us? (block diagram)

How will we perform the calculations? (according to algorithm)

What is an algorithm? (perform actions in order)

Write down the numbers 13, 4, 8, 17, 5 in ascending order (4, 5, 8, 13, 17)

Slide 6

What word did you get? (bees)

Who else will we talk about in class?

Assessment.

Slide 7

Guys, bees are tireless workers. And the agricultural industry is beekeeping. What does this industry do? (keeping bees)

What profession does a person engage in beekeeping? (beekeeper).

Guys, do you have a beekeeper in your village?

Do you think he knows everything about bees? (Yes)

The main thing in this profession is that the beekeeper must know everything about bees.

What do you know about bees?

Unfortunately, we cannot know everything about bees, but we will try to find out as much as possible. I'm sure you will succeed.

Today one of the bees will accompany us in class. So, let's go get the bee.

Work in pairs. Finding the value of expressions with variables.

- Our road starts from the hive. There are usually many hives in an apiary. Each hive has its own entrance - an entrance. In order to open the entrance, we need to complete the task. What goal will we set for completing this task? (execute variable expressions) -What is a variable expression?


s:2


C*2

Assessment. Mutual check and self-check against the standard.

Slide 8

You know the multiplication and division tables very well, the entrance to the hives is open and it is no coincidence that our hives turned out to be exactly these colors. (Yellow, blue, white). The bee simply does not distinguish other colors. But she sees ultraviolet rays, which are beyond our eyes.

IV. Logical task.

Do you know how many eyes a bee has? (No)

Let's do the math orally.

A bee has as many eyes as you have, again as many, and half as many more. (A bee has 5 eyes. 2 large ones, which in turn consist of 10 thousand eyes, located on the sides of the head and 3 small ones on the forehead between them)

V. Work on consolidating the material covered.

1. Mathematical dictation. Work in notebooks.

Beekeepers usually assign their own numbers to the hives in the apiary. There are such numbers in our apiary. - But we will find out when we complete the task. Write down only the answers.

1) Product of numbers 2 and 4

2) Increase 2 by 9 times

3) How many times is 14 greater than 2

4) 1 factor is 2, the second is the same. Work?

5) Reduce 20 by 2 times

6) What number was halved if you got 5?

7) How much did you multiply 8 if you got 16?

Slide 9

8 18 7 4 10 10 2

Assessment. Peer review from the slide.

2. Speech about bees. (Ruban Vanya.)

Hello guys! I'm a worker bee. We produce wax, propolis, the most valuable medicine - honey and bee bread. Perga is bee bread made from pollen and nectar. We, the bees, eat it.

What do you know about the bee family? (The main one in the bee family is the queen - she is the queen. The rest of the bees are workers. They do the work of guards, cell cleaners, fans, nectar collectors, cell builders. Drones also live with them, which do nothing, but are needed for procreation.)

3. Writing expressions and finding their values. Slide 10

It's time for the bee to go to work. What time does a student’s working day start? (8 hours) How do you determine time? (by the hour)

The bee has a good sense of time. For this she does not need either a watch or the sun. She needs flowers. She flies out whenThe flower clock starts working.

How do you understand my words?
So we will work with colors and find the meanings of expressions. The first number in the mathematical expression shows the time when the flower “wakes up”, the answer you found is when it “falls asleep”.

What is important to know to complete this task? (procedure)

Rosehip 2*7-10:2=

Mac 5+ 7*2 - 11=

Assessment. Peer review.

4. The task of finding the perimeter of a rectangle. Slide 11

What do we see on the slide? (frame)

Why does a beekeeper need it?

What kind of work can we do? (find the sides and perimeter of the rectangle).

S - 12 dm2

Length - 3 dm

What formulas helped?

Formulas for finding perimeter and area.

What else helped?

Multiplication and division table.

5. Differentiated work.

Work from textbook No. 2 (strong students) Peer review.

Work with cards (weak students) Self-test.

5. Working on the task. (Cards)

Bees are such hard workers! And we will solve the problem about them.

Read the problem, there are several possible solutions to it. You need to choose one correct solution and mark it with a plus. Explain your choice.

Task . Uncle Vitya pumped out 7 kg of honey from one hive, and 2 times more from the other. How many kg of honey did Uncle Vitya pump out from two hives?

Slide 12

VII. Lesson summary.

Our lesson is coming to an end. At the beginning of the lesson, I asked you if it was possible to learn something new during the repetition and consolidation lesson. What conclusion did you come to?

What new did you learn in the lesson? (industry - beekeeping, profession - beekeeper. The more bees fly to work, the greater the harvest we will reap, the more beautiful our Earth will be with fragrant flowers.) - What did you learn?

Our bee thanks you for your work.

Did you enjoy collaborating, working in pairs, collectively?

You, too, worked like bees today, and I really enjoyed working with you.

It's no secret how important it is to know the multiplication and division tables, in particular when performing arithmetic calculations and solving examples in mathematics.

However, what if a child is frightened by this huge set of numbers called the “Multiplication and Division Table”, and knowing it by heart seems like a completely impossible task?

Then we hasten to reassure - Learning the entire multiplication table is very easy! To do this, you need to remember only 36 combinations of numbers (links of three numbers). Here we do not take into account multiplication by 1 and 10, since this is an elementary action that does not require much effort in memorization.

Description of how the online simulator works

This simulator works on the basis of a specially developed algorithm for increasing the complexity of examples: starting with the simplest numbers “2 x 2”, gradually increasing the complexity to “9 x 9”. Thereby smoothly drawing you into the learning process.

Thus, you will have to memorize the multiplication table in small portions, which will significantly reduce the load, since children will direct their attention to just a few examples, forgetting about the entire “large” volume.

The Simulator has a settings menu for selecting the table learning mode. It is possible to select an action - “Multiplication” or “Division”, a range of examples “The entire table” or “For some number”. All this is advanced functionality of the site and is available after payment.

Each new example is accompanied help tip, this way it will be easier for the child to start learning and remember new combinations unknown to him.

If, during the course of learning, any example causes difficulty, you can quickly remind yourself of its result by using additional hint, this will help you cope more effectively with memorizing difficult examples.

Percentage scale It will quickly let you understand what level of knowledge of the multiplication tables you have.

An example is considered fully learned if the correct answer has been given 4 times in a row. However, upon reaching 100% , we encourage you not to give up studying, but to come back the next day and refresh your knowledge by going through all the examples again. After all, it is regular exercise that develops memory and consolidates skills!

Description of the online simulator interface

Firstly, the simulator has a “quick access panel”, which includes 4 buttons. They allow you to: go to the main page of the site, turn on or off sound signals, reset learning results (start learning over), and also get to the reviews and comments page.

Secondly, this is the basic structure of the program.

Above all is percentage scale, displaying the approximate level of knowledge of the multiplication tables.

Below goes example field, which needs to be answered. During the answer, it will change its color: it will turn red if an incorrect answer was given, green if a correct answer was given, blue after using the hint, and yellowish when a new example is shown.

Next is message line. It displays text information about errors, correct answers, as well as help and additional tips.

At the end is screen keyboard, containing only the buttons necessary for work: all the numbers, “backspace” - if you need to correct the answer, the “Check” and “Additional hint” buttons.

We are sure that this “Multiplication tables in 20 minutes” simulator will help.