How to divide decimals by natural numbers? Let's look at the rule and its application using examples.
To divide a decimal fraction by a natural number, you need to:
1) divide the decimal fraction by the number, ignoring the comma;
2) when the division of the whole part is completed, put a comma in the quotient.
Examples.
Divide decimals:
To divide a decimal fraction by a natural number, divide without paying attention to the comma. 5 is not divisible by 6, so we put zero in the quotient. The division of the whole part is completed, we put a comma in the quotient. We take down the zero. Divide 50 by 6. Take 8. 6∙8=48. From 50 we subtract 48, the remainder is 2. We take away 4. We divide 24 by 6. We get 4. The remainder is zero, which means the division is over: 5.04: 6 = 0.84.
2) 19,26: 18
Divide the decimal fraction by a natural number, ignoring the comma. Divide 19 by 18. Take 1 each. The division of the whole part is completed, put a comma in the quotient. We subtract 18 from 19. The remainder is 1. We take away 2. 12 is not divisible by 18, and in the quotient we write zero. We take down 6. We divide 126 by 18, we get 7. The division is over: 19.26: 18 = 1.07.
Divide 86 by 25. Take 3 each. 25∙3=75. From 86 we subtract 75. The remainder is 11. The division of the whole part is completed, in the quotient we put a comma. We take down 5. We take 4 each. 25∙4=100. From 115 we subtract 100. The remainder is 15. We remove zero. We divide 150 by 25. We get 6. The division is over: 86.5: 25 = 3.46.
4) 0,1547: 17
Zero is not divisible by 17; we write zero in the quotient. The division of the whole part is completed, we put a comma in the quotient. We take down 1. 1 is not divisible by 17, we write zero in the quotient. We take down 5. 15 is not divisible by 17, we write zero in the quotient. We take down 4. We divide 154 by 17. We take 9 each. 17∙9=153. From 154 we subtract 153. The remainder is 1. We take away 7. We divide 17 by 17. We get 1. The division is over: 0.1547: 17 = 0.0091.
5) A decimal fraction can also be obtained when dividing two natural numbers.
When dividing 17 by 4, we take 4 each. The division of the whole part is completed, in the quotient we put a comma. 4∙4=16. From 17 we subtract 16. The remainder is 1. We remove zero. Divide 10 by 4. Take 2 each. 4∙2=8. From 10 we subtract 8. The remainder is 2. We remove zero. Divide 20 by 4. Take 5 each. Division is completed: 17: 4 = 4.25.
And a couple more examples of division decimals to natural numbers:
With this math program you can divide polynomials by column.
The program for dividing a polynomial by a polynomial does not just give the answer to the problem, it gives detailed solution with explanations, i.e. displays the solution process to test knowledge in mathematics and/or algebra.
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This way you can spend your own training and/or training their younger brothers or sisters, while the level of education in the area of \u200b\u200bthe problems being solved increases.
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A little theory.
Dividing a polynomial into a polynomial (binomial) by a column (corner)
In algebra dividing polynomials with a column (corner)- an algorithm for dividing a polynomial f(x) by a polynomial (binomial) g(x), the degree of which is less than or equal to the degree of the polynomial f(x).
The polynomial-by-polynomial division algorithm is a generalized form of column division of numbers that can be easily implemented by hand.
For any polynomials \(f(x) \) and \(g(x) \), \(g(x) \neq 0 \), there are unique polynomials \(q(x) \) and \(r(x ) \), such that
\(\frac(f(x))(g(x)) = q(x)+\frac(r(x))(g(x)) \)
and \(r(x)\) has a lower degree than \(g(x)\).
The goal of the algorithm for dividing polynomials into a column (corner) is to find the quotient \(q(x) \) and the remainder \(r(x) \) for a given dividend \(f(x) \) and non-zero divisor \(g(x) \)
Example
Let's divide one polynomial by another polynomial (binomial) using a column (corner):
\(\large \frac(x^3-12x^2-42)(x-3) \)
The quotient and remainder of these polynomials can be found by performing the following steps:
1. Divide the first element of the dividend by the highest element of the divisor, place the result under the line \((x^3/x = x^2)\)
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3. Subtract the polynomial obtained after multiplication from the dividend, write the result under the line \((x^3-12x^2+0x-42-(x^3-3x^2)=-9x^2+0x-42) \)
|
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4. Repeat the previous 3 steps, using the polynomial written under the line as the dividend.
|
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5. Repeat step 4.
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6. End of the algorithm.
Thus, the polynomial \(q(x)=x^2-9x-27\) is the quotient of the division of polynomials, and \(r(x)=-123\) is the remainder of the division of polynomials.
The result of dividing polynomials can be written in the form of two equalities:
\(x^3-12x^2-42 = (x-3)(x^2-9x-27)-123\)
or
\(\large(\frac(x^3-12x^2-42)(x-3)) = x^2-9x-27 + \large(\frac(-123)(x-3)) \)
The division of natural numbers, especially multi-digit ones, is conveniently carried out by a special method, which is called division by a column (in a column). You can also find the name corner division. Let us immediately note that the column can be used to both divide natural numbers without a remainder and divide natural numbers with a remainder.
In this article we will look at how long division is performed. Here we will talk about recording rules and all intermediate calculations. First, let's focus on dividing a multi-digit natural number by a single-digit number with a column. After this, we will focus on cases when both the dividend and the divisor are multi-valued natural numbers. The entire theory of this article is provided with typical examples of division by a column of natural numbers with detailed explanations of the solution and illustrations.
Page navigation.
Rules for recording when dividing by a column
Let's start by studying the rules for writing the dividend, divisor, all intermediate calculations and results when dividing natural numbers by a column. Let's say right away that it is most convenient to do column division in writing on paper with a checkered line - this way there is less chance of straying from the desired row and column.
First, the dividend and divisor are written in one line from left to right, after which a symbol of the form is drawn between the written numbers. For example, if the dividend is the number 6 105 and the divisor is 5 5, then their correct recording when dividing into a column will be as follows:
Look at the following diagram to illustrate where to write the dividend, divisor, quotient, remainder, and intermediate calculations in long division.
From the above diagram it is clear that the required quotient (or incomplete quotient when dividing with a remainder) will be written below the divisor under the horizontal line. And intermediate calculations will be carried out below the dividend, and you need to take care in advance about the availability of space on the page. In this case, you should be guided by the rule: the greater the difference in the number of characters in the entries of the dividend and divisor, the more space will be required. For example, when dividing by a column the natural number 614,808 by 51,234 (614,808 is a six-digit number, 51,234 is a five-digit number, the difference in the number of characters in the records is 6−5 = 1), intermediate calculations will require less space than when dividing the numbers 8 058 and 4 (here the difference in the number of characters is 4−1=3). To confirm our words, we present complete records of division by a column of these natural numbers:
Now you can proceed directly to the process of dividing natural numbers by a column.
Column division of a natural number by a single-digit natural number, column division algorithm
It is clear that dividing one single-digit natural number by another is quite simple, and there is no reason to divide these numbers into a column. However, it will be helpful to practice your initial long division skills with these simple examples.
Example.
Let us need to divide with a column of 8 by 2.
Solution.
Of course, we can perform division using the multiplication table, and immediately write down the answer 8:2=4.
But we are interested in how to divide these numbers with a column.
First, we write down the dividend 8 and the divisor 2 as required by the method:
Now we begin to find out how many times the divisor is contained in the dividend. To do this, we sequentially multiply the divisor by the numbers 0, 1, 2, 3, ... until the result is a number equal to the dividend (or a number greater than the dividend, if there is a division with a remainder). If we get a number equal to the dividend, then we immediately write it under the dividend, and in the place of the quotient we write the number by which we multiplied the divisor. If we get a number greater than the dividend, then under the divisor we write the number calculated at the penultimate step, and in place of the incomplete quotient we write the number by which the divisor was multiplied at the penultimate step.
Let's go: 2·0=0 ; 2 1=2 ; 2·2=4 ; 2·3=6 ; 2·4=8. We have received a number equal to the dividend, so we write it under the dividend, and in place of the quotient we write the number 4. In this case, the entry will accept next view:
The final stage of dividing single-digit natural numbers with a column remains. Under the number written under the dividend, you need to draw a horizontal line, and subtract the numbers above this line in the same way as is done when subtracting natural numbers in a column. The number resulting from the subtraction will be the remainder of the division. If it is equal to zero, then the original numbers are divided without a remainder.
In our example we get
Now we have before us a completed recording of the column division of the number 8 by 2. We see that the quotient of 8:2 is 4 (and the remainder is 0).
Answer:
8:2=4 .
Now let's look at how a column divides single-digit natural numbers with a remainder.
Example.
Divide with a column 7 by 3.
Solution.
At the initial stage, the entry looks like this:
We begin to find out how many times the dividend contains the divisor. We will multiply 3 by 0, 1, 2, 3, etc. until we get a number equal to or greater than the dividend 7. We get 3·0=0<7
; 3·1=3<7
; 3·2=6<7
; 3·3=9>7 (if necessary, refer to the article comparing natural numbers). Under the dividend we write the number 6 (it was obtained at the penultimate step), and in place of the incomplete quotient we write the number 2 (the multiplication was carried out by it at the penultimate step).
It remains to carry out the subtraction, and the division by a column of single-digit natural numbers 7 and 3 will be completed.
Thus, the partial quotient is 2 and the remainder is 1.
Answer:
7:3=2 (rest. 1) .
Now you can move on to dividing multi-digit natural numbers by columns into single-digit natural numbers.
Now we'll figure it out long division algorithm. At each stage, we will present the results obtained by dividing the multi-digit natural number 140,288 by the single-digit natural number 4. This example was not chosen by chance, since when solving it we will encounter all possible nuances and will be able to analyze them in detail.
First we look at the first digit on the left in the dividend notation. If the number defined by this figure is greater than the divisor, then in the next paragraph we have to work with this number. If this number is less than the divisor, then we need to add to the consideration the next digit on the left in the notation of the dividend, and continue to work with the number determined by the two digits under consideration. For convenience, we highlight in our notation the number with which we will work.
The first digit from the left in the notation of the dividend 140288 is the digit 1. The number 1 is less than the divisor 4, so we also look at the next digit on the left in the notation of the dividend. At the same time, we see the number 14, with which we have to work further. We highlight this number in the notation of the dividend.
The following steps from the second to the fourth are repeated cyclically until the division of natural numbers by a column is completed.
Now we need to determine how many times the divisor is contained in the number we are working with (for convenience, let's denote this number as x). To do this, we sequentially multiply the divisor by 0, 1, 2, 3, ... until we get the number x or a number greater than x. When the number x is obtained, we write it under the highlighted number according to the recording rules used when subtracting natural numbers in a column. The number by which the multiplication was carried out is written in place of the quotient during the first pass of the algorithm (in subsequent passes of 2-4 points of the algorithm, this number is written to the right of the numbers already there). When we get a number that is greater than the number x, then under the highlighted number we write the number obtained at the penultimate step, and in place of the quotient (or to the right of the numbers already there) we write the number by which the multiplication was carried out at the penultimate step. (We carried out similar actions in the two examples discussed above).
Multiply the divisor 4 by the numbers 0, 1, 2, ... until we get a number that is equal to 14 or greater than 14. We have 4·0=0<14
, 4·1=4<14
, 4·2=8<14
, 4·3=12<14
, 4·4=16>14 . Since at the last step we received the number 16, which is greater than 14, then under the highlighted number we write the number 12, which was obtained at the penultimate step, and in place of the quotient we write the number 3, since in the penultimate point the multiplication was carried out precisely by it.
At this stage, from the selected number, subtract the number located under it using a column. The result of the subtraction is written under the horizontal line. However, if the result of the subtraction is zero, then it does not need to be written down (unless the subtraction at that point is the very last action that completely completes the process of long division). Here, for your own control, it would not be amiss to compare the result of the subtraction with the divisor and make sure that it is less than the divisor. Otherwise, a mistake was made somewhere.
We need to subtract the number 12 from the number 14 with a column (for the correctness of the recording, we must remember to put a minus sign to the left of the numbers being subtracted). After completing this action, the number 2 appeared under the horizontal line. Now we check our calculations by comparing the resulting number with the divisor. Since the number 2 is less than the divisor 4, you can safely move on to the next point.
Now, under the horizontal line to the right of the numbers located there (or to the right of the place where we did not write down the zero), we write down the number located in the same column in the notation of the dividend. If there are no numbers in the record of the dividend in this column, then the division by column ends there. After this, we select the number formed under the horizontal line, accept it as a working number, and repeat points 2 to 4 of the algorithm with it.
Under the horizontal line to the right of the number 2 already there, we write down the number 0, since it is the number 0 that is in the record of the dividend 140,288 in this column. Thus, the number 20 is formed under the horizontal line.
We select this number 20, take it as a working number, and repeat with it the actions of the second, third and fourth points of the algorithm.
Multiply the divisor 4 by 0, 1, 2, ... until we get the number 20 or a number that is greater than 20. We have 4·0=0<20
, 4·1=4<20
, 4·2=8<20
, 4·3=12<20
, 4·4=16<20
, 4·5=20
. Так как мы получили число, равное числу 20
, то записываем его под отмеченным числом, а на месте частного, справа от уже имеющегося там числа 3
записываем число 5
(на него производилось умножение).
We carry out the subtraction in a column. Since we are subtracting equal natural numbers, then by virtue of the property of subtracting equal natural numbers, the result is zero. We do not write down the zero (since this is not the final stage of division with a column), but we remember the place where we could write it (for convenience, we will mark this place with a black rectangle).
Under the horizontal line to the right of the remembered place we write down the number 2, since it is precisely it that is in the record of the dividend 140,288 in this column. Thus, under the horizontal line we have the number 2.
We take the number 2 as the working number, mark it, and we will once again have to perform the actions of 2-4 points of the algorithm.
We multiply the divisor by 0, 1, 2, and so on, and compare the resulting numbers with the marked number 2. We have 4·0=0<2
, 4·1=4>2. Therefore, under the marked number we write the number 0 (it was obtained at the penultimate step), and in the place of the quotient to the right of the number already there we write the number 0 (we multiplied by 0 at the penultimate step).
We perform the subtraction in a column, we get the number 2 under the horizontal line. We check ourselves by comparing the resulting number with the divisor 4. Since 2<4
, то можно спокойно двигаться дальше.
Under the horizontal line to the right of the number 2, add the number 8 (since it is in this column in the entry for the dividend 140 288). Thus, the number 28 appears under the horizontal line.
We take this number as a working number, mark it, and repeat steps 2-4.
There shouldn't be any problems here if you have been careful up to now. Having completed all the necessary steps, the following result is obtained.
All that remains is to carry out the steps from points 2, 3, 4 one last time (we leave this to you), after which you will get a complete picture of dividing the natural numbers 140,288 and 4 into a column:
Please note that the number 0 is written in the very bottom line. If this was not the last step of division by a column (that is, if in the record of the dividend there were numbers left in the columns on the right), then we would not write this zero.
Thus, looking at the completed record of dividing the multi-digit natural number 140,288 by the single-digit natural number 4, we see that the quotient is the number 35,072 (and the remainder of the division is zero, it is in the very bottom line).
Of course, when dividing natural numbers by a column, you will not describe all your actions in such detail. Your solutions will look something like the following examples.
Example.
Perform long division if the dividend is 7 136 and the divisor is a single-digit natural number 9.
Solution.
At the first step of the algorithm for dividing natural numbers by columns, we get a record of the form
After performing the actions from the second, third and fourth points of the algorithm, the column division record will take the form
Repeating the cycle, we will have
One more pass will give us a complete picture of the column division of the natural numbers 7,136 and 9
Thus, the partial quotient is 792, and the remainder is 8.
Answer:
7 136:9=792 (rest. 8) .
And this example demonstrates what long division should look like.
Example.
Divide the natural number 7,042,035 by the single-digit natural number 7.
Solution.
The most convenient way to do division is by column. 
Answer:
7 042 035:7=1 006 005 .
Column division of multi-digit natural numbers
We hasten to please you: if you have thoroughly mastered the column division algorithm from the previous paragraph of this article, then you almost already know how to perform column division of multi-digit natural numbers. This is true, since stages 2 to 4 of the algorithm remain unchanged, and only minor changes appear in the first point.
At the first stage of dividing multi-digit natural numbers into a column, you need to look not at the first digit on the left in the notation of the dividend, but at the number of them equal to the number of digits contained in the notation of the divisor. If the number defined by these numbers is greater than the divisor, then in the next paragraph we have to work with this number. If this number is less than the divisor, then we need to add to the consideration the next digit on the left in the notation of the dividend. After this, the actions specified in paragraphs 2, 3 and 4 of the algorithm are performed until the final result is obtained.
All that remains is to see the application of the column division algorithm for multi-valued natural numbers in practice when solving examples.
Example.
Let's perform column division of multi-digit natural numbers 5,562 and 206.
Solution.
Since the divisor 206 contains 3 digits, we look at the first 3 digits on the left in the dividend 5,562. These numbers correspond to the number 556. Since 556 is greater than the divisor 206, we take the number 556 as a working number, select it, and move on to the next stage of the algorithm.
Now we multiply the divisor 206 by the numbers 0, 1, 2, 3, ... until we get a number that is either equal to 556 or greater than 556. We have (if multiplication is difficult, then it is better to multiply natural numbers in a column): 206 0 = 0<556
, 206·1=206<556
, 206·2=412<556
, 206·3=618>556. Since we received a number that is greater than the number 556, then under the highlighted number we write the number 412 (it was obtained at the penultimate step), and in place of the quotient we write the number 2 (since we multiplied by it at the penultimate step). The column division entry takes the following form:
We perform column subtraction. We get the difference 144, this number is less than the divisor, so you can safely continue performing the required actions.
Under the horizontal line to the right of the number there we write the number 2, since it is in the record of the dividend 5562 in this column:
Now we work with the number 1,442, select it, and go through steps two through four again.
Multiply the divisor 206 by 0, 1, 2, 3, ... until you get the number 1442 or a number that is greater than 1442. Let's go: 206·0=0<1 442
, 206·1=206<1 442
, 206·2=412<1 332
, 206·3=618<1 442
, 206·4=824<1 442
, 206·5=1 030<1 442
, 206·6=1 236<1 442
, 206·7=1 442
. Таким образом, под отмеченным числом записываем 1 442
, а на месте частного правее уже имеющегося там числа записываем 7
:
We carry out the subtraction in a column, we get zero, but we don’t write it down right away, we just remember its position, because we don’t know whether the division ends here, or whether we’ll have to repeat the steps of the algorithm again:
Now we see that we cannot write any number under the horizontal line to the right of the remembered position, since there are no digits in the record of the dividend in this column. Therefore, this completes the division by column, and we complete the entry:
- Mathematics. Any textbooks for 1st, 2nd, 3rd, 4th grades of general education institutions.
- Mathematics. Any textbooks for 5th grade of general education institutions.
Children in grades 2-3 are learning a new mathematical operation - division. It is not easy for a student to understand the essence of this mathematical operation, so he needs the help of his parents. Parents need to understand exactly how to present new information to their child. TOP 10 examples will tell parents how to teach children how to divide numbers in a column.
Learning long division in the form of a game
Children get tired at school, they get tired of textbooks. Therefore, parents need to give up textbooks. Present information in the form of a fun game.
You can set tasks this way:
1 Organize a place for your child to learn through play. Place his toys in a circle, and give the child pears or candy. Have the student divide 4 candies between 2 or 3 dolls. To achieve understanding on the part of the child, gradually increase the number of candies to 8 and 10. Even if the baby takes a long time to act, do not put pressure or yell at him. You will need patience. If your child does something wrong, correct him calmly. Then, after he completes the first action of dividing the candies between the participants in the game, he will ask him to calculate how many candies went to each toy. Now the conclusion. If there were 8 candies and 4 toys, then each got 2 candies. Let your child understand that sharing means distributing an equal amount of candy to all toys.
2 You can teach math operations using numbers. Let the student understand that numbers can be classified as pears or candy. Say that the number of pears to be divided is the dividend. And the number of toys that contain candy is the divisor.
3 Give your child 6 pears. Give him a task: to divide the number of pears between grandfather, dog and dad. Then ask him to divide 6 pears between grandpa and dad. Explain to your child the reason why the division result was different.
4 Teach your student about division with a remainder. Give your child 5 candies and ask him to distribute them equally between the cat and dad. The child will have 1 candy left. Tell your child why it happened this way. This mathematical operation should be considered separately, as it can cause difficulties.
Playful learning can help your child quickly understand the whole process of dividing numbers. He will be able to learn that the largest number is divisible by the smallest or vice versa. That is, the largest number is candy, and the smallest number is the participants. In column 1 the number will be the number of candies, and 2 will be the number of participants.
Do not overload your child with new knowledge. You need to learn gradually. You need to move on to new material when the previous material is consolidated.
Learning long division using the multiplication table
Students up to 5th grade will be able to understand division more quickly if they have a good understanding of multiplication.
Parents need to explain that division is similar to the multiplication table. Only the actions are opposite. For clarity, we need to give an example:
- Tell the student to freely multiply the values of 6 and 5. The answer is 30.
- Tell the student that the number 30 is the result of a mathematical operation with two numbers: 6 and 5. Namely, the result of multiplication.
- Divide 30 by 6. The result of the mathematical operation is 5. The student will be able to see that division is the same as multiplication, but in reverse.
You can use the multiplication table to illustrate division if the child has mastered it well.
Learning long division in a notebook
Learning should begin when the student understands the material about division in practice, using games and multiplication tables.
You need to start dividing in this way, using simple examples. So, divide 105 by 5.
The mathematical operation needs to be explained in detail:
- Write an example in your notebook: 105 divided by 5.
- Write this down as you would for long division.
- Explain that 105 is the dividend and 5 is the divisor.
- With a student, identify 1 number that can be divided. The value of the dividend is 1, this figure is not divisible by 5. But the second number is 0. The result is 10, this value can be divided in this example. The number 5 is included in the number 10 twice.
- In the division column, under the number 5, write the number 2.
- Ask your child to multiply the number 5 by 2. The result of the multiplication is 10. This value must be written under the number 10. Next, you need to write the subtraction sign in the column. From 10 you need to subtract 10. You get 0.
- Write down in the column the number resulting from the subtraction - 0. 105 has a number left that was not involved in the division - 5. This number needs to be written down.
- The result is 5. This value must be divided by 5. The result is the number 1. This number must be written under 5. The result of the division is 21.
Parents need to explain that this division has no remainder.
You can start division with numbers 6,8,9, then go to 22, 44, 66 , and then to 232, 342, 345 , and so on.
Learning division with remainder
Once the child has mastered the material about division, you can make the task more difficult. Division with a remainder is the next step in learning. You need to explain using available examples:
- Invite your child to divide 35 by 8. Write the problem in the column.
- To make it as clear as possible for your child, you can show him the multiplication table. The table clearly shows that the number 35 includes the number 8 4 times.
- Write down the number 32 under the number 35.
- The child needs to subtract 32 from 35. The result is 3. The number 3 is the remainder.
Simple examples for a child
We can continue with the same example:
- When dividing 35 by 8, the remainder is 3. You need to add 0 to the remainder. In this case, after the number 4 in the column you need to put a comma. Now the result will be fractional.
- When dividing 30 by 8, the result is 3. This number must be written after the decimal point.
- Now you need to write 24 under the value 30 (the result of multiplying 8 by 3). The result will be 6. You also need to add a zero to the number 6. It will turn out to be 60.
- The number 60 contains the number 8 included 7 times. That is, it turns out to be 56.
- When subtracting 60 from 56, the result is 4. This number also needs to be signed 0. The result is 40. In the multiplication table, a child can see that 40 is the result of multiplying 8 by 5. That is, the number 40 includes the number 8 5 times. There is no remainder. The answer looks like this - 4.375.
This example may seem difficult to a child. Therefore, you need to divide values that will have a remainder many times.
Teaching division through games
Parents can use division games to teach their students. You can give your child coloring books in which you need to determine the color of a pencil by dividing. You need to choose coloring pages with easy examples so that the child can solve the examples in his head.
The picture will be divided into parts containing the results of the division. And the colors to use will be examples. For example, the color red is labeled with an example: 15 divided by 3. You get 5. You need to find the part of the picture under this number and color it. Math coloring pages captivate children. Therefore, parents should try this method of teaching.
Learning to divide by column the smallest number by the largest
Division by this method assumes that the quotient will start at 0 and will be followed by a comma.
In order for the student to correctly assimilate the information received, he needs to give an example of such a plan.
Column division is an integral part of the educational material for primary school students. Further success in mathematics will depend on how correctly he learns to perform this action.
How to properly prepare a child to perceive new material?
Column division is a complex process that requires certain knowledge from the child. To perform division, you need to know and be able to quickly subtract, add, and multiply. Knowledge of number digits is also important.
Each of these actions should be brought to automaticity. The child should not have to think for a long time, and also be able to subtract and add not only numbers from the first ten, but within a hundred in a few seconds.
It is important to form the correct concept of division as a mathematical operation. Even when studying multiplication and division tables, the child must clearly understand that the dividend is a number that will be divided into equal parts, the divisor indicates how many parts the number should be divided into, and the quotient is the answer itself.
How to explain the algorithm of a mathematical operation step by step?
Each mathematical operation requires strict adherence to a specific algorithm. Examples of long division should be performed in this order:
- Write the example in a corner, and the places of the dividend and divisor must be strictly observed. To help the child not get confused in the first stages, we can say that we write a larger number on the left and a smaller number on the right.
- Select a part for the first division. It must be divisible by the dividend with a remainder.
- Using the multiplication table, we determine how many times the divisor can fit in the selected part. It is important to indicate to the child that the answer should not exceed 9.
- Multiply the resulting number by the divisor and write it on the left side of the corner.
- Next, you need to find the difference between the part of the dividend and the resulting product.
- The resulting number is written below the line and the next digit number is taken down. Such actions are performed until the remainder is 0.
A clear example for students and parents
Column division can be clearly explained using this example.
- Write down 2 numbers in a column: the dividend is 536 and the divisor is 4.
- The first part for division must be divisible by 4 and the quotient must be less than 9. The number 5 is suitable for this.
- 4 fits into 5 only once, so we write 1 in the answer, and 4 under 5.
- Next, subtraction is performed: 4 is subtracted from 5 and 1 is written under the line.
- The next digit number is added to one - 3. In thirteen (13) - 4 fits 3 times. 4x3 = 12. Twelve is written under the 13th, and 3 is written as the quotient, as the next digit number.
- 12 is subtracted from 13, the answer is 1. The next digit number is taken away again - 6.
- 16 is again divided by 4. The answer is written as 4, and in the division column - 16, and the difference is drawn as 0.
By solving long division examples with your child several times, you can achieve success in quickly completing problems in middle school.
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