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Addition and subtraction by a column. Subtraction of numbers, formula. An example of subtracting two-digit numbers by a column

Today, in most cases, children master the simplest mathematical operations in preschool age. Parents try to teach their kids the basics of mathematics on their own, so that when they enter school, they already have a small but solid knowledge base. One skill that can be easily learned at home is counting.

Preparation for training

Before starting the study of counting in a column, parents need to make sure that the child is ready for classes. First of all, a young mathematician should easily count from 0 to 10 and easily distinguish all these numbers in writing. If the skill has not yet been consolidated or has not been mastered at all, it is imperative to fill in the gap. The most effective methods are presented in the article "".

In addition, the child should already understand the principles of simple mathematical operations, namely addition and subtraction. You should train daily, honing your skills on nearby objects - toys, sweets, apples, counting sticks, etc. As soon as the child is confident enough to add and subtract single-digit numbers, you can move on to more complex tasks.

We count in a column

It is clear that adding and subtracting single-digit numbers in a column is meaningless - the child, as a rule, performs these actions in the mind. Difficulties arise when working with two-digit numbers - it is difficult for a beginner mathematician to concentrate and calculate everything without a visual representation. In this case, a method proven by several generations comes to the aid of the child - counting in a column.

Of course, mathematics teachers know how to teach a child to count with a column, but parents most often do not even know where to start classes. And you need to start from the base - explanations of such mathematical concept, as bit depth. It is important for a child to understand how two-digit (and then three-digit) numbers are composed and how they are written when counting in a column. You can immediately perform a very simple but effective exercise - writing in a column of unambiguous and two-digit numbers. The task of such an exercise is to teach the child to correctly place numbers with different digits under each other. The kid must understand that units are written under units, tens under tens, hundreds under hundreds, etc.

Having mastered this basic skill, the child can move on to the next stage - directly counting. It is necessary to explain to the baby that you need to add and subtract numbers by digits - units with units, tens with tens, hundreds with hundreds. Moreover, the account must be kept from units, that is, from right to left.

Some difficulties arise when adding numbers whose digits add up to more than "10", for example, 24 + 18. The child needs to be told that in this case the sum of units - "4" and "8" is "12". At the same time, under the units in the total amount, you also need to write only one, i.e. "2". And tens - "1" - must be "left in the mind." When adding dozens already - "2" and "1" in this example - it is necessary to add the ten "left in the mind", i.e. "1". As a result, adding tens looks like 2 + 1 + 1 and gives a total of "4". The final sum is "42". Similar actions must be performed when subtracting, when the digits of the minuend are less than the digits of the subtrahend. For example, 41 - 15. Only in this case it is necessary not to add the numbers “left in the mind”, but to subtract them.

So, in itself, the method of teaching a child to count in a column is quite understandable. But in addition to it, parents should familiarize themselves with general tips that will help make classes with the baby more effective:

Be consistent and patient . Many adults believe that they are determined by age and the speed of mastering new things. educational material. However, forcing children to engage in an accelerated program is not worth it. You need to “grow up” to counting in a column, having first studied the basics, which have already been mentioned above.

Repetition is the mother of learning. The success of classes depends on the amount of time devoted to practice. At every opportunity, turn to the child “for help” - ask him to count the numbers in a column and be sure to thank him when you get the result.

Use additional materials . Children's books on mathematics, workbooks, diagrams and pictures will help children learn the material faster, because, as a rule, they perceive information presented visually better.

Turn learning into play. This advice is universal for all training sessions. If you have the opportunity to include a game element in the learning process, the child will be more attentive and enthusiastic.

It is important to understand that the ability to count in a column does not determine. Therefore, you should not make high demands on the baby - he will definitely be able to independently perform mathematical operations in a column when he himself is ready for this.

To find the difference using the " column subtraction”(in other words, how to count in a column or a subtraction by a column), you must follow these steps:

put the subtrahend under the minuend, write units under units, tens under tens, and so on.
subtract bit by bit.
if you need to take a ten from a larger category, then put a dot over the category in which you took it. Above the category for which they took, put 10.
if the digit in which we occupied is 0, then we take the decreasing one from the next digit and put a dot over it. Above the category for which they took, put 9, because. one dozen are busy.

The examples below will show you how to subtract two-digit, three-digit and any multi-digit numbers in a column.

Subtraction of numbers in a column helps a lot when subtracting large numbers (as well as addition in a column). The best way to learn is by example.

It is necessary to write the numbers one under the other in such a way that the rightmost digit of the 1st number becomes under the rightmost digit of the 2nd number. The number that is greater (decreasing) is written on top. On the left between the numbers we put the action sign, here it is “-” (subtraction).

2 - 1 = 1 . What we get is written under the line:

10 + 3 = 13.

Subtract nine from 13.

13 - 9 = 4.

Since we took ten from four, it decreased by 1. In order not to forget about this, we have a point.

4 - 1 = 3.

Result:

Column subtraction from numbers containing zeros.

Again, let's look at an example:

We write the numbers in a column. Which is more - on top. We start subtracting from right to left, one digit at a time. 9 - 3 = 6.

Subtracting 2 from zero will not work, then again we borrow from the number on the left. This is zero. We put a point above zero. And again, you won’t be able to borrow from zero, then we move on to the next digit. We borrow from the unit. We put a dot on it.

Note: when there is a dot in the subtraction above 0, zero becomes nine.

There is a dot above our zero, which means it has become a nine. Subtract 4 from it. 9 - 4 = 5 . There is a point above the unit, that is, it decreases by 1. 1 - 1 = 0. The resulting zero does not need to be recorded.

How to subtract in a column

The subtraction of multi-digit numbers is usually performed in a column, writing the numbers one under the other (decreasing from above, subtracted from below) so that the digits of the same digits stand one under the other (units under units, tens under tens, etc.). An action sign is placed between the numbers on the left. Draw a line under the subtrahend. The calculation begins with the discharge of units: units are subtracted from units, then from tens - tens, etc. The result of the subtraction is written under the line:

Consider an example when in some place the digit of the minuend is less than the digit of the subtrahend:

We cannot subtract 9 from 2, what should we do in this case? In the category of units, we have a shortage, but in the category of tens, the reduced one already has 7 tens, so we can transfer one of these tens to the category of units:

In the category of units, we had 2, we threw a dozen, it became 12 units. Now we can easily subtract 9 from 12. We write 3 under the line in the units place. In the tens place, we had 7 units, we threw one of them into simple units, 6 tens remained. We write under the line in the tens place 6. As a result, we got the number 63:

The subtraction by a column is usually not written down in such detail, instead, a point is placed above the digit of the digit, from which the unit will be occupied, so as not to remember which digit will need to be additionally subtracted by the unit:

At the same time, they say this: you can’t subtract 9 from 2, we take one, subtract 9 from 12 - we get 3, we write 3, we had 7 units in the tens place, we threw one, 6 left, we write 6.

Now consider column subtraction from numbers containing zeros:

Let's start subtracting. We subtract 3 from 7, write 4. We cannot subtract 5 from zero, so we are forced to take a unit in the highest digit, but we also have 0 in the highest digit, so for this digit we are forced to take in a higher digit. We take a unit from the category of thousands, we get 10 hundreds:

We take one of the units of the hundreds digit to the least significant digit, we get 10 tens. Subtract 5 from 10, write 5:

In the hundreds place, we have 9 units left, so we subtract 6 from 9, write 3. In the thousands place, we had a unit, but we spent it on the lower digits, so zero remains here (you don’t need to write it down). As a result, we got the number 354:

Such a detailed record of the solution was given to make it easier to understand how subtraction by a column is performed from numbers containing zeros. As already mentioned, in practice the solution is usually written like this:

And all the mentioned actions are performed in the mind. To make subtraction easier, remember a simple rule:

If there is a dot above zero when subtracting, zero becomes 9.

Column Subtraction Calculator

This calculator will help you subtract numbers by a column. Just enter the minuend and subtrahend and click the Calculate button.

This is finding one of the terms by the sum and the other term.

The original amount is called reduced, known term - deductible, and the result (i.e., the desired term) is called difference.

Number subtraction properties

1. a - (b + c) = (a - b) - c = (a - c) - b ;

2. (a + b) - c = (a - c) + b = a + (b - c) ;

3. a - (b - c) = (a - b) + c .

For a visual representation of arithmetic operations (both addition and subtraction), you can use number line- this is a straight line, which consists of a point of origin (this point corresponds to zero) and two rays propagating from it, one of which corresponds to positive numbers, and the other to negative ones.

Example of subtraction on the number line

On this number line, you can see that the numbers to the left of 0 have a negative value. Subtracting one from a negative number (in this case -1) three times, we get the number -1.

Subtracting from the positive number 4, the positive number 3 (or the negative number -1 three times), we get one

Example

4 - 3 = 1 ;	3 - 4 = - 1 ;
-1 -3 = - 4 ;

Subtraction of numbers by a column

Units are subtracted first, then tens, hundreds, and so on. The difference of each column is written below it. If necessary, from the adjacent left column (i.e. from the highest order) is engaged 1 .

Let's take a look at a few examples of columnar subtraction below.

An example of subtracting two-digit numbers by a column

Example of subtracting three-digit numbers in a column

The principle of subtracting three-digit numbers is similar to the method of subtracting two-digit numbers, in this case the numbers are no longer tens, but hundreds.

An example of subtracting four-digit numbers by a column

The principle of subtracting four-digit numbers is similar to the method of subtracting three-digit numbers, in this case the numbers are no longer hundreds, but thousands.

It is very important even in Everyday life. Subtraction can often come in handy when counting change in a store. For example, you have one thousand (1000) rubles with you, and your purchases amount to 870. You, before paying, will ask: “How much change will I have?”. So, 1000-870 will be 130. And there are many different such calculations and without mastering this topic, it will be difficult in real life. Subtraction is an arithmetic operation during which the second number is subtracted from the first number, and the result will be the third.

The addition formula is expressed as follows: a - b = c

a- Vasya initially had apples.

b- the number of apples given to Petya.

c- Vasya has apples after the transfer.

Substitute in the formula:

Subtraction of numbers

Subtracting numbers is easy for any first grader to master. For example, 5 must be subtracted from 6. 6-5=1, 6 is greater than 5 by one, which means that the answer will be one. You can add 1+5=6 to check. If you are not familiar with addition, you can read ours.

A large number is divided into parts, let's take the number 1234, and in it: 4-ones, 3-tens, 2-hundreds, 1-thousands. If you subtract units, then everything is easy and simple. But let's take an example: 14-7. In the number 14: 1 is ten, and 4 is units. 1 ten - 10 units. Then we get 10 + 4-7, let's do this: 10-7 + 4, 10 - 7 \u003d 3, and 3 + 4 \u003d 7. Correct answer found!

Let's consider an example 23 -16. The first number is 2 tens and 3 ones, and the second is 1 tens and 6 ones. Let's represent the number 23 as 10+10+3 and 16 as 10+6, then represent 23-16 as 10+10+3-10-6. Then 10-10=0, 10+3-6 remains, 10-6=4, then 4+3=7. Answer found!

Similarly, it is done with hundreds and thousands

Column subtraction

Answer: 3411.

Subtraction of fractions

Imagine a watermelon. A watermelon is one whole, and cutting in half, we get something less than one, right? Half unit. How to write it down?

½, so we denote half of one whole watermelon, and if we divide the watermelon into 4 equal parts, then each of them will be denoted ¼. And so on…

how to subtract fractions

Everything is simple. Subtract from 2/4 ¼-th. When subtracting, it is important that the denominator (4) of one fraction coincides with the denominator of the second. (1) and (2) are called numerators.

So let's subtract. Make sure the denominators are the same. Then we subtract the numerators (2-1)/4, so we get 1/4.

Subtraction limits

Subtracting limits is not difficult. Here a simple formula is enough, which says that if the limit of the difference of functions tends to the number a, then this is equivalent to the difference of these functions, the limit of each of which tends to the number a.

Subtraction of mixed numbers

A mixed number is an integer with a fractional part. That is, if the numerator is less than the denominator, then the fraction is less than one, and if the numerator is greater than the denominator, then the fraction is greater than one. A mixed number is a fraction that is greater than one and has an integer part highlighted, let's use an example:

To subtract mixed numbers, you need:

Bring fractions to a common denominator.

Enter the integer part into the numerator

Make a calculation

subtraction lesson

Subtraction is an arithmetic operation, during which the difference of 2 numbers is searched and the answers are the third. The addition formula is expressed as follows: a - b = c.

You can find examples and tasks below.

At fraction subtraction it should be remembered that:

Given a fraction 7/4, we get that 7 is greater than 4, which means that 7/4 is greater than 1. How to select the whole part? (4+3)/4, then we get the sum of fractions 4/4 + 3/4, 4:4 + 3/4=1 + 3/4. Outcome: one whole, three fourths.

Subtraction Grade 1

The first class is the beginning of the journey, the beginning of learning and learning the basics, including subtraction. Education should be conducted in the form of a game. Always in the first grade, calculations begin with simple examples on apples, sweets, pears. This method is used not in vain, but because children are much more interested when they are played with. And this is not the only reason. Children have seen apples, sweets and the like very often in their lives and have dealt with the transfer and quantity, so it will not be difficult to teach the addition of such things.

Subtraction tasks for first graders can come up with a whole cloud, for example:

Task 1. In the morning, walking through the forest, the hedgehog found 4 mushrooms, and in the evening, when he came home, the hedgehog ate 2 mushrooms for dinner. How many mushrooms are left?

Task 2. Masha went to the store for bread. Mom gave Masha 10 rubles, and bread costs 7 rubles. How much money should Masha bring home?

Task 3. In the morning there were 7 kilograms of cheese on the counter in the store. Before lunch, visitors bought 5 kilograms. How many kilograms are left?

Task 4. Roma took out the sweets that his dad gave him into the yard. Roma had 9 candies, and he gave 4 to his friend Nikita. How many candies does Roma have left?

First-graders mostly solve problems in which the answer is a number from 1 to 10.

Subtraction Grade 2

The second class is already higher than the first, and, accordingly, examples for solving too. So let's get started:

Numerical assignments:

Single digits:

10 - 5 =
7 - 2 =
8 - 6 =
9 - 1 =
9 - 3 - 4 =
8 - 2 - 3 =
9 - 9 - 0 =
4 - 1 - 3 =

Double figures:

10 - 10 =
17 - 12 =
19 - 7 =
15 - 8 =
13 - 7 =
64 - 37 =
55 - 53 =
43 - 12 =
34 - 25 =
51 - 17 - 18 =
47 - 12 - 19 =
31 - 19 - 2 =
99 - 55 - 33 =

Text problems

Subtraction 3-4 grade

The essence of subtraction in grades 3-4 is subtraction in a column of large numbers.

Consider the example 4312-901. To begin with, let's write the numbers one under the other, so that from the number 901 the unit is under 2, 0 under 1, 9 under 3.

Then we subtract from right to left, that is, from the number 2, the number 1. We get the unit:

Subtracting nine from three, you need to borrow 1 ten. That is, subtract 1 ten from 4. 10+3-9=4.

And since 4 took 1, then 4-1 = 3

Answer: 3411.

Subtraction Grade 5

Fifth grade is the time to work on complex fractions with different denominators. Let's repeat the rules: 1. Numerators are subtracted, not denominators.

So let's subtract. Make sure the denominators are the same. Then we subtract the numerators (2-1)/4, so we get 1/4. When adding fractions, only the numerators are subtracted!

2. To subtract, make sure the denominators are equal.

If there is a difference between fractions, for example, 1/2 and 1/3, then you will have to multiply not one fraction, but both to bring to a common denominator. The easiest way to do this is to multiply the first fraction by the denominator of the second, and the second fraction by the denominator of the first, we get: 3/6 and 2/6. Add (3-2)/6 and get 1/6.

3. Reducing a fraction is done by dividing the numerator and denominator by the same number.

The fraction 2/4 can be reduced to the form ½. Why? What is a fraction? ½ \u003d 1: 2, and if you divide 2 by 4, then this is the same as dividing 1 by 2. Therefore, the fraction 2/4 \u003d 1/2.

4. If the fraction is greater than one, then you can select the whole part.

Subtraction presentation

The link to the presentation is below. The presentation covers the basics of sixth grade subtraction:Download Presentation

Presentation of addition and subtraction

Examples for addition and subtraction

Games for the development of mental counting

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

Game "Quick Score"

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

Game "Numerical coverage"

The game "number coverage" will load your memory while practicing with this exercise.

The essence of the game is to remember the number, which takes about three seconds to memorize. Then you need to play it. As you progress through the stages of the game, the number of numbers grows, start with two and go on.

Game "Mathematical Comparisons"

A wonderful game with which you can relax your body and tense your brain. The screenshot shows an example of this game, in which there will be a question related to the picture, and you will have to answer. Time is limited. How many times can you answer?

Game "Guess the operation"

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

Game "Simplify"

The game "Simplify" 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 action is given, the student needs to calculate this example and write the answer. Below are three answers, count and click the number you need with the mouse. If you answer correctly, you score points and continue playing.

Game "Visual Geometry"

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, they must be quickly counted, then they close. Four numbers are written below the table, you must select one correct number and click on it with the mouse. If you answer correctly, you score points and continue playing.

Piggy bank game

The game "Piggy bank" develops thinking and memory. The main essence of the game is to choose which piggy bank has more money. In this game, four piggy banks are given, you need to count which piggy bank has more money and show this piggy bank with the mouse. If you answer correctly, then you score points and continue to play further.

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

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