A columnar calculator for Android devices will become a wonderful assistant for modern schoolchildren. The program not only gives the correct answer to a mathematical operation, but also clearly demonstrates its step-by-step solution. If you need more complex calculators, you can look at an advanced engineering calculator.
Peculiarities
The main feature of the program is the uniqueness of the calculation of mathematical operations. Displaying the calculation process in a column allows students to familiarize themselves with it in more detail, understand the solution algorithm, and not just get the finished result and copy it into a notebook. This feature has a huge advantage over other calculators because... Quite often at school, teachers require that intermediate calculations be written down in order to make sure that the student performs them in his head and really understands the algorithm for solving problems. By the way, we have another program of a similar kind -.
To start using the program, you need to download a column calculator for Android. You can do this on our website absolutely free of charge without additional registrations or SMS. After installation, the main page will open in the form of a notebook sheet in a cage, on which, in fact, the results of calculations and their detailed solution will be displayed. At the bottom there is a panel with buttons:
- Numbers.
- Signs of arithmetic operations.
- Deleting previously entered characters.
Input is carried out according to the same principle as on. The only difference is in the application interface - all mathematical calculations and their results are displayed in a virtual student notebook.
The application allows you to quickly and correctly perform standard mathematical calculations for a schoolchild:
- multiplication;
- division;
- addition;
- subtraction.
A nice addition to the app is the daily math homework reminder feature. If you want, do your homework. To enable it, go to the settings (click the gear-shaped button) and check the reminder box.
Advantages and disadvantages
- Helps the student not only quickly obtain the correct result of mathematical calculations, but also understand the principle of calculation itself.
- A very simple, intuitive interface for every user.
- You can install the application even on the most budget Android device with operating system 2.2 and later.
- The calculator saves a history of mathematical calculations performed, which can be cleared at any time.
The calculator is limited in mathematical operations, so it cannot be used for complex calculations that an engineering calculator could handle. However, given the purpose of the application itself - to clearly demonstrate to primary school students the principle of columnar calculations, this should not be considered a disadvantage.
The application will also be an excellent assistant not only for schoolchildren, but also for parents who want to interest their child in mathematics and teach him to perform calculations correctly and consistently. If you have already used the Column Calculator application, leave your impressions below in the comments.
The easiest way to divide multi-digit numbers is with a column. Column division is also called corner division.
Before we begin to perform division by a column, we will consider in detail the very form of recording division by a column. First, write down the dividend and put a vertical line to the right of it:
Behind the vertical line, opposite the dividend, write the divisor and draw a horizontal line under it:
Under the horizontal line, the resulting quotient will be written step by step:
Intermediate calculations will be written under the dividend:
The full form of writing division by column is as follows:
How to divide by column
Let's say we need to divide 780 by 12, write the action in a column and proceed to division:
Column division is performed in stages. The first thing we need to do is determine the incomplete dividend. We look at the first digit of the dividend:
this number is 7, since it is less than the divisor, we cannot start division from it, which means we need to take another digit from the dividend, the number 78 is greater than the divisor, so we start division from it:
In our case the number 78 will be incomplete divisible, it is called incomplete because it is only a part of the divisible.
Having determined the incomplete dividend, we can find out how many digits will be in the quotient, for this we need to calculate how many digits are left in the dividend after the incomplete dividend, in our case there is only one digit - 0, this means that the quotient will consist of 2 digits.
Having found out the number of digits that should be in the quotient, you can put dots in its place. If, when completing the division, the number of digits turns out to be more or less than the indicated points, then an error was made somewhere:
Let's start dividing. We need to determine how many times 12 is contained in the number 78. To do this, we sequentially multiply the divisor by the natural numbers 1, 2, 3, ... until we get a number as close as possible to the incomplete dividend or equal to it, but not exceeding it. Thus, we get the number 6, write it under the divisor, and from 78 (according to the rules of column subtraction) we subtract 72 (12 6 = 72). After we subtract 72 from 78, the remainder is 6:
Please note that the remainder of the division shows us whether we have chosen the number correctly. If the remainder is equal to or greater than the divisor, then we did not choose the number correctly and we need to take a larger number.
To the resulting remainder - 6, add the next digit of the dividend - 0. As a result, we get an incomplete dividend - 60. Determine how many times 12 is contained in the number 60. We get the number 5, write it in the quotient after the number 6, and subtract 60 from 60 ( 12 5 = 60). The remainder is zero:
Since there are no more digits left in the dividend, it means 780 is divided by 12 completely. As a result of performing long division, we found the quotient - it is written under the divisor:
Let's consider an example when the quotient results in zeros. Let's say we need to divide 9027 by 9.
We determine the incomplete dividend - this is the number 9. We write 1 into the quotient and subtract 9 from 9. The remainder is zero. Usually, if in intermediate calculations the remainder is zero, it is not written down:
We take down the next digit of the dividend - 0. We remember that when dividing zero by any number there will be zero. We write zero into the quotient (0: 9 = 0) and subtract 0 from 0 in intermediate calculations. Usually, in order not to clutter up intermediate calculations, calculations with zero are not written:
We take down the next digit of the dividend - 2. In intermediate calculations it turned out that the incomplete dividend (2) is less than the divisor (9). In this case, write zero to the quotient and remove the next digit of the dividend:
We determine how many times 9 is contained in the number 27. We get the number 3, write it as a quotient, and subtract 27 from 27. The remainder is zero:
Since there are no more digits left in the dividend, it means that the number 9027 is divided by 9 completely:
Let's consider an example when the dividend ends in zeros. Let's say we need to divide 3000 by 6.
We determine the incomplete dividend - this is the number 30. We write 5 into the quotient and subtract 30 from 30. The remainder is zero. As already mentioned, it is not necessary to write zero in the remainder in intermediate calculations:
We take down the next digit of the dividend - 0. Since dividing zero by any number will result in zero, we write zero in the quotient and subtract 0 from 0 in intermediate calculations:
We take down the next digit of the dividend - 0. We write another zero into the quotient and subtract 0 from 0 in intermediate calculations. Since in intermediate calculations, calculations with zero are usually not written down, the entry can be shortened, leaving only the remainder - 0. Zero in the remainder in at the very end of the calculation is usually written to show that the division is complete:
Since there are no more digits left in the dividend, it means 3000 is divided by 6 completely:
Column division with remainder
Let's say we need to divide 1340 by 23.
We determine the incomplete dividend - this is the number 134. We write 5 into the quotient and subtract 115 from 134. The remainder is 19:
We take down the next digit of the dividend - 0. We determine how many times 23 is contained in the number 190. We get the number 8, write it into the quotient, and subtract 184 from 190. We get the remainder 6:
Since there are no more digits left in the dividend, the division is over. The result is an incomplete quotient of 58 and a remainder of 6:
1340: 23 = 58 (remainder 6)
It remains to consider an example of division with a remainder, when the dividend is less than the divisor. Let us need to divide 3 by 10. We see that 10 is never contained in the number 3, so we write 0 as a quotient and subtract 0 from 3 (10 · 0 = 0). Draw a horizontal line and write down the remainder - 3:
3: 10 = 0 (remainder 3)
Long division calculator
This calculator will help you perform long division. Simply enter the dividend and divisor and click the Calculate button.
Instructions
First, test your child's multiplication skills. If a child does not know the multiplication table firmly, then he may also have problems with division. Then, when explaining division, you can be allowed to peek at the cheat sheet, but you still have to learn the table.
Write the dividend and divisor using a vertical separator bar. Under the divisor you will write down the answer - the quotient, separating it with a horizontal line. Take the first digit of 372 and ask your child how many times the number six “fits” in three. That's right, not at all.
Then take two numbers - 37. For clarity, you can highlight them with a corner. Repeat the question again - how many times the number six is contained in 37. To count quickly, it will come in handy. Put the answer together: 6*4 = 24 – not at all similar; 6*5 = 30 – close to 37. But 37-30 = 7 – six will “fit” again. Finally, 6*6 = 36, 37-36 = 1 – suitable. The first digit of the quotient found is 6. Write it under the divisor.
Write 36 under the number 37 and draw a line. For clarity, you can use the sign in the entry. Under the line, put the remainder - 1. Now “descend” the next digit of the number, two, to one - it turns out to be 12. Explain to the child that numbers always “descend” one at a time. Ask again how many “sixes” there are in 12. The answer is 2, this time without a remainder. Write the second digit of the quotient next to the first. The final result is 62.
Also consider the case of division in detail. For example, 167/6 = 27, remainder 5. Most likely, your child has not yet heard anything about simple fractions. But if he asks questions, the remainder can be explained using the example of apples. 167 apples were divided among six people. Everyone got 27 pieces, and five apples remained undivided. You can also divide them by cutting each into six slices and distributing them equally. Each person got one slice from each apple - 1/6. And since there were five apples, each one had five slices - 5/6. That is, the result can be written like this: 27 5/6.
To reinforce the information, look at three more examples of division:
1) The first digit of the dividend contains the divisor. For example, 693/3 = 231.
2) The dividend ends at zero. For example, 1240/4 = 310.
3) The number contains a zero in the middle. For example, 6808/8 = 851.
In the second case, children sometimes forget to add the last digit of the answer - 0. And in the third, they sometimes skip over zero.
Sources:
- division by column 3rd grade
- How to divide 927 into a column
Children learn concrete meanings much better than abstract ones. How to explain to kid, what is two thirds? Concept fractions requires special introduction. There are some methods that help you understand what a non-integer number is.
You will need
- - special lotto;
- - apple and candy;
- a cardboard circle consisting of several parts;
- - chalk.
Instructions
Try to interest. Play a special game of hopscotch while walking. If you are already tired of jumping into regular ones, but your child has mastered counting well, try this option. Draw hopscotch on the asphalt with chalk as shown in the picture and explain to the child that he can jump like this: 1 - 2 - 3..., or you can do it like this: 1 - 1.5 - 2 - 2.5... Children really like to play and so they are better because between the numbers there are still intermediate values - parts. This is your next step towards learning fractional numbers. An excellent visual aid.
Take a whole apple and offer it to two people at the same time. They will immediately tell you that this is impossible. Then cut the apple and offer it to them again. Now everything is all right. everyone got the same half of an apple. These are parts of one whole.
Offer to split four with you in half. He will do it easily. Then take out another one and offer to do the same. It is clear that you cannot get the whole candy right away and to kid. The solution can be found by cutting the candy in half. Then everyone will get two whole candies and one half.
For older people, use a cutting circle. You can divide it into 2, 4, 6 or 8 parts. We invite the children to take a circle. Then we divide it into two halves. Two halves will make a perfect circle, even if you exchange half with your desk neighbor (the circles should be the same diameter). We divide each half of the loan into half. It turns out that the circle can consist of 4 parts. And each half comes from two halves. Then we write it on the board in the form fractions. Explaining what the numerator is (the parts taken) and the denominator (how many parts the total was divided into). This makes it easier for children to grasp a difficult concept - fractions.
Helpful advice
Be sure to use visual aids when explaining an abstract concept.
The section "Multiplication and Division" is one of the most difficult in the primary school mathematics course. Children usually learn it at the age of 8-9 years. At this time, their mechanical memory is quite well developed, so memorization occurs quickly and without much effort.
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. 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 dividing decimals by natural numbers:
At school these actions are studied from simple to complex. Therefore, it is imperative to thoroughly understand the algorithm for performing these operations using simple examples. So that later there will be no difficulties with dividing decimal fractions into a column. After all, this is the most difficult version of such tasks.
This subject requires consistent study. Gaps in knowledge are unacceptable here. Every student should learn this principle already in the first grade. Therefore, if you miss several lessons in a row, you will have to master the material on your own. Otherwise, later problems will arise not only with mathematics, but also with other subjects related to it.
The second prerequisite for successfully studying mathematics is to move on to examples of long division only after addition, subtraction and multiplication have been mastered.
It will be difficult for a child to divide if he has not learned the multiplication table. By the way, it is better to teach it using the Pythagorean table. There is nothing superfluous, and multiplication is easier to learn in this case.
How are natural numbers multiplied in a column?
If difficulty arises in solving examples in a column for division and multiplication, then you should begin to solve the problem with multiplication. Since division is the inverse operation of multiplication:
- Before multiplying two numbers, you need to look at them carefully. Choose the one with more digits (longer) and write it down first. Place the second one under it. Moreover, the numbers of the corresponding category must be under the same category. That is, the rightmost digit of the first number should be above the rightmost digit of the second.
- Multiply the rightmost digit of the bottom number by each digit of the top number, starting from the right. Write the answer below the line so that its last digit is under the one you multiplied by.
- Repeat the same with another digit of the lower number. But the result of multiplication must be shifted one digit to the left. In this case, its last digit will be under the one by which it was multiplied.
Continue this multiplication in a column until the numbers in the second factor run out. Now they need to be folded. This will be the answer you are looking for.
Algorithm for multiplying decimals
First, you need to imagine that the given fractions are not decimals, but natural ones. That is, remove the commas from them and then proceed as described in the previous case.
The difference begins when the answer is written down. At this moment, it is necessary to count all the numbers that appear after the decimal points in both fractions. This is exactly how many of them need to be counted from the end of the answer and put a comma there.
It is convenient to illustrate this algorithm using an example: 0.25 x 0.33:
Where to start learning division?
Before solving long division examples, you need to remember the names of the numbers that appear in the long division example. The first of them (the one that is divided) is divisible. The second (divided by) is the divisor. The answer is private.
After this, using a simple everyday example, we will explain the essence of this mathematical operation. For example, if you take 10 sweets, then it’s easy to divide them equally between mom and dad. But what if you need to give them to your parents and brother?
After this, you can become familiar with the division rules and master them using specific examples. First simple ones, and then move on to more and more complex ones.
Algorithm for dividing numbers into a column
First, let us present the procedure for natural numbers divisible by a single-digit number. They will also be the basis for multi-digit divisors or decimal fractions. Only then should you make small changes, but more on that later:
- Before doing long division, you need to figure out where the dividend and divisor are.
- Write down the dividend. To the right of it is the divider.
- Draw a corner on the left and bottom near the last corner.
- Determine the incomplete dividend, that is, the number that will be minimal for division. Usually it consists of one digit, maximum two.
- Choose the number that will be written first in the answer. It should be the number of times the divisor fits into the dividend.
- Write down the result of multiplying this number by the divisor.
- Write it under the incomplete dividend. Perform subtraction.
- Add to the remainder the first digit after the part that has already been divided.
- Choose the number for the answer again.
- Repeat multiplication and subtraction. If the remainder is zero and the dividend is over, then the example is done. Otherwise, repeat the steps: remove the number, pick up the number, multiply, subtract.
How to solve long division if the divisor has more than one digit?
The algorithm itself completely coincides with what was described above. The difference will be the number of digits in the incomplete dividend. Now there should be at least two of them, but if they turn out to be less than the divisor, then you have to work with the first three digits.
There is one more nuance in this division. The fact is that the remainder and the number added to it are sometimes not divisible by the divisor. Then you have to add another number in order. But the answer must be zero. If you are dividing three-digit numbers into a column, you may need to remove more than two digits. Then a rule is introduced: there should be one less zero in the answer than the number of digits removed.
You can consider this division using the example - 12082: 863.
- The incomplete dividend in it turns out to be the number 1208. The number 863 is placed in it only once. Therefore, the answer is supposed to be 1, and under 1208 write 863.
- After subtraction, the remainder is 345.
- You need to add the number 2 to it.
- The number 3452 contains 863 four times.
- Four must be written down as an answer. Moreover, when multiplied by 4, this is exactly the number obtained.
- The remainder after subtraction is zero. That is, the division is completed.
The answer in the example would be the number 14.
What if the dividend ends in zero?
Or a few zeros? In this case, the remainder is zero, but the dividend still contains zeros. There is no need to despair, everything is simpler than it might seem. It is enough to simply add to the answer all the zeros that remain undivided.
For example, you need to divide 400 by 5. The incomplete dividend is 40. Five fits into it 8 times. This means that the answer should be written as 8. When subtracting, there is no remainder left. That is, the division is completed, but a zero remains in the dividend. It will have to be added to the answer. Thus, dividing 400 by 5 equals 80.
What to do if you need to divide a decimal fraction?
Again, this number looks like a natural number, if not for the comma separating the whole part from the fractional part. This suggests that the division of decimal fractions into a column is similar to that described above.
The only difference will be the semicolon. It is supposed to be put in the answer as soon as the first digit from the fractional part is removed. Another way to say this is this: if you have finished dividing the whole part, put a comma and continue the solution further.
When solving examples of long division with decimal fractions, you need to remember that any number of zeros can be added to the part after the decimal point. Sometimes this is necessary in order to complete the numbers.
Dividing two decimals
It may seem complicated. But only at the beginning. After all, how to divide a column of fractions by a natural number is already clear. This means that we need to reduce this example to an already familiar form.
It's easy to do. You need to multiply both fractions by 10, 100, 1,000 or 10,000, and maybe by a million if the problem requires it. The multiplier is supposed to be chosen based on how many zeros are in the decimal part of the divisor. That is, the result will be that you will have to divide the fraction by a natural number.
And this will be in the worst case scenario. After all, it may happen that the dividend from this operation becomes an integer. Then the solution to the example with column division of fractions will be reduced to the simplest option: operations with natural numbers.
As an example: divide 28.4 by 3.2:
- First, they must be multiplied by 10, since the second number has only one digit after the decimal point. Multiplying will give 284 and 32.
- They are supposed to be separated. Moreover, the whole number is 284 by 32.
- The first number chosen for the answer is 8. Multiplying it gives 256. The remainder is 28.
- The division of the whole part has ended, and a comma is required in the answer.
- Carry to remainder 0.
- Take 8 again.
- Remainder: 24. Add another 0 to it.
- Now you need to take 7.
- The result of multiplication is 224, the remainder is 16.
- Take down another 0. Take 5 each and you get exactly 160. The remainder is 0.
The division is complete. The result of example 28.4:3.2 is 8.875.
What if the divisor is 10, 100, 0.1, or 0.01?
Just like with multiplication, long division is not needed here. It is enough to simply move the comma in the desired direction for a certain number of digits. Moreover, using this principle, you can solve examples with both integers and decimal fractions.
So, if you need to divide by 10, 100 or 1,000, then the decimal point is moved to the left by the same number of digits as there are zeros in the divisor. That is, when a number is divisible by 100, the decimal point must move to the left by two digits. If the dividend is a natural number, then it is assumed that the comma is at the end.
This action gives the same result as if the number were to be multiplied by 0.1, 0.01 or 0.001. In these examples, the comma is also moved to the left by a number of digits equal to the length of the fractional part.
When dividing by 0.1 (etc.) or multiplying by 10 (etc.), the decimal point should move to the right by one digit (or two, three, depending on the number of zeros or the length of the fractional part).
It is worth noting that the number of digits given in the dividend may not be sufficient. Then the missing zeros can be added to the left (in the whole part) or to the right (after the decimal point).
Division of periodic fractions
In this case, it will not be possible to obtain an accurate answer when dividing into a column. How to solve an example if you encounter a fraction with a period? Here we need to move on to ordinary fractions. And then divide them according to the previously learned rules.
For example, you need to divide 0.(3) by 0.6. The first fraction is periodic. It converts to the fraction 3/9, which when reduced gives 1/3. The second fraction is the final decimal. It’s even easier to write it down as usual: 6/10, which is equal to 3/5. The rule for dividing ordinary fractions requires replacing division with multiplication and divisor with the reciprocal. That is, the example comes down to multiplying 1/3 by 5/3. The answer will be 5/9.
If the example contains different fractions...
Then several solutions are possible. Firstly, you can try to convert a common fraction to a decimal. Then divide two decimals using the above algorithm.
Secondly, every final decimal fraction can be written as a common fraction. But this is not always convenient. Most often, such fractions turn out to be huge. And the answers are cumbersome. Therefore, the first approach is considered more preferable.
