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 ones:

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.

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:

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 =

Text tasks

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.

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 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

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There is a convenient method for finding the difference of two natural numbers - subtraction in a column, or subtraction in a column. This method takes its name from the method of writing the minuend and the difference under each other. So you can carry out both basic and intermediate calculations in accordance with the required digits of numbers.

This method is convenient to use because it is very simple, fast and visual. All seemingly complex calculations can be reduced to addition and subtraction of prime numbers.

Below we'll look at exactly how to use this method. Our reasoning will be supported by examples for greater clarity.

What should be reviewed before learning column subtraction?

The method is based on some simple steps that we have already covered earlier. It is necessary to repeat how to subtract correctly using the addition table. It is also desirable to know the basic property of subtracting equal natural numbers (literally, it is written as a − a = 0). We will need the following equalities a − 0 = a and 0 − 0 = 0 , where a is any arbitrary natural number (if necessary, see the basic properties of finding the difference of integers).

In addition, it is important to know how to determine the digit of natural numbers.

The main thing at the first stage is to write down the initial data correctly. First, write down the first number from which we will subtract. Under it we place the subtrahend. The numbers must be located strictly one under the other, taking into account the category: tens under tens, hundreds under hundreds, units under units. The entry is read from right to left. Next, put a minus on the left side of the column and draw a line under both numbers. The final result will be written under it.

Example 1

Let's use an example to show which counting entry is correct:

With the help of the first, we can find how much 56 - 9 will be, with the help of the second - 3004 - 1670, the third - 203604500 - 56777.

As you can see, using this method, you can perform calculations of varying complexity.

Next, consider the process of finding the difference. To do this, we perform alternate subtraction of the values ​​of the digits: first, we subtract units from units, then tens from tens, then hundreds from hundreds, etc. The values ​​are written under the line separating the source data from the result. As a result, we should get a number, which will be the correct answer to the problem, i.e. the difference between the original numbers.

How exactly the calculations are performed can be seen in this diagram:

We figured out the general picture of recording and counting. However, there are some points in the method that need clarification. To do this, we will give specific examples and explain them. Let's start with the simplest tasks and gradually increase the complexity until we finally understand all the nuances.

We advise you to carefully read all the examples, because each of them illustrates separate incomprehensible points. If you reach the end and remember all the explanations, then the calculation of the difference of natural numbers in the future will not cause you the slightest difficulty.

Example 2

Condition: find the difference 74,805 - 24,003 using column subtraction.

Solution:

We write these numbers one under the other, correctly placing the digits under each other, and underline them:

Subtraction starts from right to left, that is, from units. We consider: 5 - 3 = 2 (if necessary, repeat the tables for adding natural numbers). We write the total under the line where the units are indicated:

Subtract tens. Both values ​​in our column are zero, and subtracting zero from zero always gives zero (remember, we mentioned that we will need this subtraction property later). The result is written in the right place:

The next step is to find the value of the thousand difference: 4 − 4 = 0 . The resulting zero is written to its proper place and as a result we get:

We got 50 802 , which will be the correct answer for the above example. This completes the calculations.

Answer: 50 802 .

Let's take another example:

Example 3

Condition: calculate how much will be 5 777 - 5 751 using the method of finding the difference by a column.

Solution:

The steps we need to take have already been given above. We execute them sequentially for new numbers and as a result we get:

The result is preceded by two zeros. Because they are the first, then you can safely discard them and get 26 in the answer. This number will be the correct answer of our example.

Answer: 26 .

If you look at the conditions of the two examples above, it is easy to see that so far we have taken only numbers that are equal in number of characters. But the column method can also be used when the minuend includes more characters than the subtrahend.

Example 4

Condition: find the difference 502 864 number 2 330 .

Solution

We write the numbers under each other, observing the desired correlation of digits. It will look like this:

Now we calculate the values ​​one by one:

– units: 4 − 0 = 4;

- tens: 6 - 3 \u003d 3;

– hundreds: 8 − 3 = 5;

- thousand: 2 − 2 = 0.

Let's write down what we got:

The subtrahend has values ​​in the place of tens and hundreds of thousands, but the minuend does not. What to do? Recall that emptiness in mathematical examples is equivalent to zero. So we need to subtract zeros from the original values. Subtracting zero from a natural number always gives zero, therefore, all that remains for us is to rewrite the original bit values ​​in the answer area:

Our calculations are complete. We got the total: 502 864 - 2 330 = 500 534 .

Answer: 500 534 .

In our examples, the values ​​of the digits of the subtrahend always turned out to be less than the values ​​of the minuend, so this did not cause any difficulties in the calculation. What if it is impossible to subtract the value of the bottom row from the value of the top row without going into a minus? Then we need to "borrow" the higher order values. Let's take a specific example.

Example 5

Condition: find the difference 534 - 71 .

We write the column already familiar to us and take the first step of calculations: 4 - 1 = 3. We get:

Next, we need to move on to counting tens. To do this, we need to subtract 7 from 3. This operation cannot be performed with natural numbers, because it makes sense only for a minuend that is greater than the subtrahend. Therefore, in this example, we need to "borrow" a unit from the highest order and thereby "exchange" it. That is, we kind of change 100 for 10 tens and take one of them. In order not to forget about this, we mark the desired digit with a dot, and in tens we write 10 in a different color. We have a record like this:

The resulting result is written in the right place under the line:

It remains for us to finish the count by calculating hundreds. We have a point above the number 5: this means that we took ten from here for the previous digit. Then 5 − 1 = 4 . Nothing needs to be subtracted from the four, since the subtracted in the discharge of hundreds of values ​​\u200b\u200bhas no meaning. We write 4 in place and get the answer:

Answer: 463 .

Often, you have to perform the "exchange" action several times within one example. Let's take a look at this problem.

Example 6

Condition: how much is 1 632 - 947?

Solution

In the first stage of the calculation, it is necessary to subtract the two from the seven, so we immediately "occupy" the ten for exchange for 10 units. We mark this action with a dot and consider 10 + 2 - 7 = 5. Here's what our entry looks like with marks:

Next, we need to count the tens. The specified point means that for calculations we take a number one less in this bit: 3 − 1 = 2 . From the deuce, we have to subtract the four, so we "exchange" hundreds. We get (10 + 2) − 4 = 12 − 4 = 8 .

Moving on to counting hundreds. Of the six, we have already occupied one, so 6 − 1 = 5. We subtract nine from five, for which we take the thousand we have and "exchange" it for 10 hundred. So (10 + 5) − 9 = 15 − 9 = 6 . Now our note entry looks like this:

It remains for us to do the calculations in the thousandth place. We have already borrowed one unit from here, so 1 − 1 = 0 . We write the result under the final line and see what happens:

This completes the calculations. Zero at the beginning can be discarded. So 1632 − 947 = 685 .

Answer: 685 .

Let's take an even more complex example.

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

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.

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 the units.

Now we subtract tens from tens, but the subtrahend does not have tens, so we omit the ten of the reduced in response.

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 the units

Now 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 the transition through the ten

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

Subtract units. It is impossible to subtract 9 from 7, we take one ten from the tens of the reduced one. In order not to forget, we put a dot over the tens.

17 – 9 = 8

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

2 tens - 1 tens = 1 tens

As a result, we get the difference:

27 – 9 = 18

Now, for example, take three-digit numbers:

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

12 – 8 = 4 the result is written under the units.

We occupied one ten of the tens for units, which means that in the reduced one there are no longer three tens, but two ( 3 tens - 1 tens = 2 tens).

Two tens less than six, take one hundred or 10 tens out of hundreds ( 2 tens + 10 tens = 12 tens write 10 over the tens of the minuend), and in order not to forget, we put an end to the hundreds. Subtract tens:

12 tens - 6 tens = 6 tens The result is written under the tens.

We occupied one hundred out of hundreds reduced for 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 to do if in the category from which you need to take ten, is equal to zero? For example:

We start with units. 2 less 8 , that is, it is necessary to take from tens. But for a decrease in tens 0 , which means that for tens you need to borrow from hundreds. In the hundreds place in the minuend too 0 , borrow from thousands. In order not to forget, we put a point over thousands.

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

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

Counting units:

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

Remaining in tens of minuends 9 , we consider:

9 – 6 = 3 write the result under tens.

Hundreds of diminishing left 9 , subtracted has no hundreds, omit 9 hundreds in response.

In the rank of thousands of diminished was 1 , we occupied it (dot over thousands), so there are no more thousands left. As a result, we get:

1002 – 68 = 934

So let's sum it up.

To find the difference between two numbers (column subtraction) :

1. we put the subtrahend under the minuend, we write units under units, tens under tens, and so on.
2. Subtract bit by bit.
3. If you need to take a ten from the next category, then put a dot over the category from which you borrowed. Above the category for which we occupy, we put 10.
4. If the digit from which we borrow is 0, then for it we borrow from the next digit of the reduced, over which we put a dot. Above the category for which they occupied, we put 9, since one ten was occupied.