How to subtract by column

Subtraction of multi-digit numbers is usually performed in a column, writing the numbers under each other (minuend from above, subtract from below) so that the digits of the same digits are located under each other (units under units, tens under tens, etc.). An action sign is placed on the left between the numbers. A line is drawn under the deductible. The calculation begins with the units digit: units are subtracted from ones, then tens are subtracted from tens, etc. The result of the subtraction is written under the line:

Let's consider an example when in some digit the digit of the minuend fewer numbers s subtrahend:

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

In the units category we had 2, we threw a ten, 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 transferred one of them to simple units, leaving 6 tens. We write 6 under the line in the tens place. As a result, we get the number 63:

Column subtraction is usually not written down in such detail; instead, a dot is placed above the digit of the digit in which a unit will be occupied, so as not to remember which digit will need to additionally subtract a unit:

At the same time, they say this: you cannot subtract 9 from 2, we take one, from 12 we subtract 9 - we get 3, we write 3, in the tens place we had 7 units, we transferred one, there are 6 left, we write 6.

Now let's look at column subtraction from numbers containing zeros:

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

We place one of the units in the hundreds place in the low order, resulting in 10 tens. Subtract 5 from 10, write 5:

In the hundreds place we have 9 units left, so we subtract 6 from 9 and write 3. In the thousands place we had a unit, but we spent it on the lower digits, so there remains a zero here (there is no 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 column subtraction 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 this simple rule:

When subtracting by a column, if there is a dot above the zero, the zero turns into 9.

Column subtraction calculator

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

Today, in most cases, children master the simplest mathematical operations even at the age of 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.

Preparing for training

Before starting to study counting, parents need to make sure their child is ready for classes. First of all, a young mathematician should count from 0 to 10 without any problems and easily distinguish all these numbers in writing. If the skill has not yet been consolidated or has not been mastered at all, you must definitely start filling the gap. Most effective techniques 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, candies, 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 his mind. Difficulties arise when working with two-digit numbers - it is difficult for a novice 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, math teachers know how to teach a child to count with a column, but parents most often have no idea where to start. And we need to start from the base - an explanation of such a 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 columns. You can immediately perform a very simple but effective exercise - writing single-digit and double-digit numbers in a column. The purpose of this exercise is to teach the child to correctly place numbers with different bit depths one below the other. The child must understand that units are written under ones, 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 child that numbers need to be added and subtracted by digits - ones with ones, tens with tens, hundreds with hundreds. Moreover, counting must be done from units, i.e. 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 the units “4” and “8” is “12.” In this case, under the units in the final amount, you also need to write only one, i.e. “2”. And tens - “1” - must be “left in mind.” When adding already tens - “2” and “1” in this example - you must also add the ten “left in mind”, i.e. “1”. As a result, adding tens looks like 2 + 1 + 1 and gives a total of “4”. The final total is "42". Similar actions must be performed when subtracting, when the digits of the minuend are smaller than the digits of the subtrahend. For example, 41 - 15. Only in this case you need to not add the numbers “left in your mind”, but subtract them.

So, the methodology itself for teaching a child to count in a column is quite clear. But besides this, parents should familiarize themselves with general tips that will help make activities with their baby more effective:

• Be consistent and patient . Many adults believe that they are determined by their age and how quickly they learn new things. educational material. However, you should not force children to study according to an accelerated program. You need to “grow up” to counting in a column by first studying 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 your 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 better perceive information presented visually.


• Turn your learning into play. This advice is universal for everyone. training sessions. If you have the opportunity to include a playful element in the learning process, the child will be more attentive and engaged.

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

In order to subtract one number from another, we place the subtrahend under the minuend, as follows: units under units, tens under tens. For example, let’s take a two-digit number as a minuend, and a single-digit number as a subtrahend.

7 – 5 = 2 We write the result under units.

Now we subtract tens from tens, but the subtrahend has no tens, so we omit the ten of the minuend in the answer.

27 – 5 = 22

Now let’s take both two-digit numbers:

Subtract the units of the subtrahend from the units of the minuend:

6 – 4 = 2 write the result under units

Now we subtract the tens of the subtrahend from the tens of the minuend:

8 – 3 = 5 We write the result under tens.

As a result, we get the difference:

86 – 34 = 52

Subtraction with passing tens

Let's try to find the difference of the following numbers:

Subtract the units. You cannot subtract 9 from 7; we take one ten from the tens of the minuend. In order not to forget, we dot the tens.

17 – 9 = 8

Now we subtract tens from tens. The subtrahend has no tens, but we borrowed one ten from the minuend:

2 tens – 1 ten = 1 ten

As a result, we get the difference:

27 – 9 = 18

Now let's take three-digit numbers as an example:

Subtract the units. 2 less 8 , so we occupy one ten of the tens of the minuend: 2 + 10 = 12 (we write 10 above the ones). In order not to forget, we dot the tens.

12 – 8 = 4 We write the result under units.

We took one ten out of tens for units, which means that in the minuend there are no longer three tens, but two ( 3 tens – 1 ten = 2 tens).

Two tens is less than six, we occupy one hundred or 10 tens out of hundreds ( 2 tens + 10 tens = 12 tens we write 10 over the tens of the minuend), and so as not to forget we put a dot over the hundreds. Subtract tens:

12 tens – 6 tens = 6 tens We write the result under tens.

We borrowed one hundred from hundreds of tens, which means we don’t have 9 hundreds, and 8 hundreds ( 9 hundreds – 1 hundred = 8 hundreds). Subtract hundreds:

8 hundreds – 7 hundreds = 1 hundred . We write the result under hundreds.

As a result we get:

932 – 768 = 164

Let's complicate the task. What should you do if the place from which you need to take a ten is zero? For example:

Let's start with units. 2 less 8 , that is, you need to borrow from tens. But the one being reduced by tens 0 , which means that for tens you need to borrow from hundreds. In the hundreds place in the minuend too 0 , we borrow from thousands. In order not to forget, we put a dot over thousands.

In hundreds of diminished remains 9 , since we take one hundred for tens: 10 – 1 = 9 we write 9 over hundreds.

It also remains in the tens 9 , since we took one ten for units: 10 – 1 = 9 we write 9 over tens, and over units we write 10 .

We count units:

12 – 8 = 4 We write the result under the units.

There are tens of diminished left 9 , we consider:

9 – 6 = 3 We write the result under tens.

Hundreds of diminished remains 9 , the subtrahend does not have hundreds, we omit 9 in response there were hundreds.

In the category of thousands of decrementables there was 1 , we occupied it (dot above thousands), which means there are no more thousands left. As a result we get:

1002 – 68 = 934

So, let's summarize.

To find the difference of two numbers (subtraction by column) :

1. We place the subtrahend under the minuend, write units under units, tens under tens, and so on.
2. Let's subtract bit by bit.
3. If you need to take a ten from the next rank, then put a dot above the rank from which you took it. We put 10 above the category for which we are occupying.
4. If there is a 0 in the digit from which we are borrowing, then we borrow for it from the next minuend digit, over which we put a dot. We put 9 above the rank for which we borrowed, since we borrowed one ten.

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

The original amount is called reducible, the known term is deductible, and the result (i.e. the required term) is called difference.

Properties of number subtraction

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 is a straight line that consists of the origin point (this point corresponds to zero) and two rays extending 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 ;

Subtracting numbers in a column

Units are subtracted first, then tens, hundreds, etc. The difference of each column is written below it. If necessary, it is taken from the adjacent left column (i.e. from the highest digit) 1 .

Let's look at some examples of columnar subtraction below.

An example of subtracting two-digit numbers in a column

An 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 in 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.

Is quite important even in Everyday life. Subtraction can often come in handy when counting change at the store. For example, you have one thousand (1000) rubles with you, and your purchases amount to 870. Before you have paid, you will ask: “How much change will I have left?” 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 arithmetic operation, during which the second number is subtracted from the first number, and the result is the third.

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

a– Vasya had apples initially.

b– the number of apples given to Petya.

c– Vasya has apples after the transfer.

Let's put it into the formula:

Subtracting numbers

Subtraction of numbers is easy for any first grader to learn. For example, you need to subtract 5 from 6. 6-5=1, 6 is greater than the number 5 by one, which means the answer will be one. To check, you can add 1+5=6. 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 units, 3 tens, 2 hundreds, 1 thousand. If you subtract the units, then everything is easy and simple. But let's take an example: 14-7. In the number 14: 1 is tens, and 4 is ones. 1 ten – 10 units. Then we get 10+4-7, let’s do this: 10-7+4, 10 – 7 =3, and 3+4=7. The answer was found correctly!

Consider example 23 -16. The first number is 2 tens and 3 ones, and the second is 1 ten and 6 ones. Let's imagine the number 23 as 10+10+3, and 16 as 10+6, then imagine 23-16 as 10+10+3-10-6. Then 10-10=0, that leaves 10+3-6, 10-6=4, then 4+3=7. The answer has been found!

The same is done with hundreds and thousands.

Column subtraction

Answer: 3411.

Subtracting Fractions

Let's imagine a watermelon. A watermelon is one whole, and if we cut it in half, we get something less than one, right? Half a unit. How to write this down?

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

subtracting fractions, how is it?

It's simple. Subtract ¼ from 2/4. 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. We made sure that the denominators were the same. Then we subtract the numerators (2-1)/4, so we get 1/4.

Subtracting limits

Subtracting limits is not difficult. A simple formula is enough here, 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.

Subtracting Mixed Numbers

A mixed number is a whole number 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 whose integer part is highlighted; let’s illustrate it with an example:

To subtract mixed numbers, you need:

Reduce fractions to a common denominator.

Add the whole part to the numerator

Perform calculation

Subtraction lesson

Subtraction is an arithmetic operation in which the difference between two numbers is sought and the answer is the third. The addition formula is expressed as follows: a - b = c.

You can find examples and tasks below.

At subtracting fractions it should be remembered that:

Given the fraction 7/4, we find that 7 is greater than 4, which means 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. Result: one whole, three quarters.

Subtraction 1st grade

First grade is the beginning of the journey, the beginning of teaching and learning the basics, including subtraction. Learning should be done in a playful way. Always in the first class, 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 it's not the only reason. Children have seen apples, candies and the like very often in their lives and have dealt with transfer and quantity, so teaching the addition of such things will not be difficult.

You can come up with a whole bunch of subtraction problems for first graders, for example:

Task 1. In the morning, while 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 to buy bread. Mom gave Masha 10 rubles, and bread costs 7 rubles. How much money should Masha bring home?

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

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

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

Subtraction 2nd grade

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

Numerical tasks:

Single digit numbers:

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

Double figures:

1. 10 - 10 =
2. 17 - 12 =
3. 19 - 7 =
4. 15 - 8 =
5. 13 - 7 =
6. 64 - 37 =
7. 55 - 53 =
8. 43 - 12 =
9. 34 - 25 =
10. 51 - 17 - 18 =
11. 47 - 12 - 19 =
12. 31 - 19 - 2 =
13. 99 - 55 - 33 =

Word problems

Subtraction grade 3-4

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

Let's look at the example 4312-901. First, let's write the numbers one below the other, so that out of the number 901, one is under 2, 0 is under 1, 9 is under 3.

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

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 5th grade

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. We made sure that the denominators were 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 perform subtraction, make sure the denominators are equal.

If you come across a difference between fractions, for example, 1/2 and 1/3, then you will have to multiply not one fraction, but both, in order to bring it 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 converted to the form ½. Why? What is a fraction? ½ = 1:2, and if you divide 2 by 4, then this is the same as dividing 1 by 2. Therefore, the fraction 2/4 = 1/2.

4. If the fraction is greater than one, then the whole part can be selected.

Given the fraction 7/4, we find that 7 is greater than 4, which means 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. Result: one whole, three quarters.

Subtraction presentation

The link to the presentation is below. The presentation examines the basic questions of sixth grade subtraction: Download presentation

Presentation of addition and subtraction

Examples for addition and subtraction

Games for developing mental arithmetic

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

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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, and 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 play it back. As you progress through the stages of the game, the number of numbers increases, starting with two and further.

Game "Mathematical Comparisons"

A great 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 need to answer. Time is limited. How much time will you have to answer?

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.

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 "Piggy Bank"

The Piggy Bank game develops thinking and memory. The main essence of the game is to choose which piggy bank has more money. In this game there are four piggy banks, you need to count which piggy bank has the most money and show this piggy bank with the mouse. If you answered correctly, then you score points and continue playing.

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