Column subtraction. Column subtraction rules. Column addition and subtraction simulator. Mathematics Examples for subtracting multi-digit numbers do

Dmitrieva Tatiana Arkadyevna
Position: primary school teacher
Educational institution: Municipal budgetary educational institution "Secondary school No. 2"
Locality: Tarko-Sale
Material name: methodical development
Subject: Flashcards to the topic "Addition, subtraction of multidigit numbers"
Date of publication: 12.01.2017
Section: elementary education

Topic: Addition and subtraction of multidigit numbers.
Card number 1 Find the sum of the numbers. 2342 + 3216 4102 + 2034 +1260 4136 + 3452 38 647 + 41 242 + 20 605 6314 + 3574 247 832 + 699 111 + 102 231 Card # 2 4208 + 791 39 + 657 + 2450 2362 + 630 39296 + 84 752 ++ 45 586 + 1203 450 003 + 284 + 3575 Card number 3 Calculate the amount and check. 190 005 + 87 999 8709 + 13 291 78 500 + 99 900 67 000 + 13 505 157 439 + 7078 178 097 + 237 850 Card No. 4 351kg 700g + 648kg 300g 8t 016kg + 72t 308kg 24km 305m + 39km 195m 9ts 38kg + 4ts 72kg 12kg 581g + 13kg 419g 7m 36cm + 109m 87cm Card # 5 12 rubles. 47kop. + 23 rub. 54kop. 1t 567kg + 3t 878kg 428RUR 09kop. + 119rub. 57kop. 935kg + 548kg
48m 37cm + 52m 24cm 1km 848m + 2km763m Card number 6 Calculate the difference. 68 389 - 40 309 200 000 - 65 809 117 805 - 32 999 12 005 - 797 2700 - 1724 100 500 - 72 341 50 000 - 9730 70 596 - 796 12 658 - 4959 Card number 7 Subtract and check by addition: 6458 - 4349 30 000 - 7004 52 735 - 48 418 50 5421 - 60 024 60 700 - 8244 70 200 - 8509 Card number 8 Perform the steps: 6 c 05 kg - 78 kg 8 t 005 kg - 169 kg 12 km - 7 km 030 m 80 km - 36 km 027 m 10 t 175 kg - 670 kg 99 rubles. 38 kopecks - 89 kopecks. Card number 9 Perform the steps: 45 851 + 37 168 - 74 018 247 086 - 72 546 + 625 400 30 108 - 9524 + 16 479 101 101 - 30 307 + 14 800 Card number 10 Solve the problem:
On Sunday, 917 people visited the museum, of which 475 adults, 148 fewer teenagers than adults, the rest were children. How many children have visited the museum? Calculate: 52 019 + 3109 80 500 - 1408 2t 060kg + 1t 720kg 138 m 36 cm - 88 m 19 cm Card number 11 Solve the problem: 986 kg of carrots were collected from one site, 198 kg less from the second than from the first. And from the third section it is 483 kg more than from the second. How many kilograms of carrots were collected from three sites? Calculate: 20374 - 81 509 98 306 + 404 749 15t 382 kg - 7t 308 kg Card number 12 Solve the problem: One warehouse had 976 tons of flour, another 657 tons of flour more than the first, and the third warehouse 208 t less than the second. How many tons of flour are there in three warehouses? Perform actions: 835 723 - 96 241 11 877 + 3464 12 km 472 m - 8 km 864 m Card number 13 Subtract and check by addition: 200 000 - 85 476 7428 - 6 739 Perform addition and check in two ways (by adding and subtraction): 225 108 + 508 335 Solve the problem: One milkmaid milked 175 liters of milk per day, which is 27 liters less than the other. How many liters of milk did the other milkmaid have?
Card number 14 Subtract and check by addition: 30 207 - 14 538 800 100 - 715 472 Perform addition and check in two ways (addition and subtraction) 17 823 + 32 277 Solve the problem: 198 birches grew on the forest area, which was on 75 more than oak trees. How many oak trees grew on the site? Card number 15 Find the unknown number: X - 4041 \u003d 2368 10 801 - X \u003d 3807 X + 2012 \u003d 4112 1025 + X \u003d 2530 The length of the rectangle is 45 dm, the width is less than the length by 22 dm. Calculate the perimeter of the rectangle. Card number 16 Find the unknown number: X - 12 201 \u003d 16 799 20 305 - X \u003d 15 308 3025 + X \u003d 5345 X + 2341 \u003d 4896 The width of the rectangle is 28 cm, the length is 57 cm greater than the width. Calculate the perimeter of the rectangle. Card No. 17 Perform actions: 360 987 - 278 549 300 001 - 287 009 187 360 + 198 288 56 720 + 38 618 148 m 36 cm - 98 m 09 cm 9 t 609 kg + 8 t 038 kg
Card No. 18 Follow the steps: 7320 - 5653 56 785 + 5 748 100 054 - 9 875 40 200 - 29 317 53 247 - 1358 125 204 + 407 108 4 km 275 m -2 km 835 m 26 rubles. 28 kopecks + RUB 14 76 kopecks. Card number 19 Follow the steps: 12 371 - (5428 + 1371) 2077 + (1356 - 477) Solve the problem: 155 watermelons were collected from melons, and 50 fewer melons. How many watermelons and melons did you put together? Card number 20 Solve the equations: 125 + X \u003d 183 + 54 190 - X \u003d 32 + 18 214 + X \u003d 386 - 21 360 - X \u003d 82 - 32 Solve the problem: There are 150 pages in the book. Nina read 35 pages on the first day. And on the second day 15 more pages. How many pages are left for Nina to read?

Figure: 1. Classes and digits of numbers

Let's call the number of ones in each digit using some numbers as an example.

72439 - in this number nine units, three tens, four hundred, two thousand units, seven tens of thousands.

Number 25346 contains six units, four tens, three hundred, five thousand units and two tens of thousands.

What is the number of units of each digit using the example of a number 3126 ... We check: six units, two tens, one hundred, three thousand units.

Let's fill in the blanks together (see Figure 2).

Figure: 2. Illustration for the problem

1 dozen \u003d 10 units

1 hundred \u003d 10 tens

1 thousand \u003d 10 hundred

1 ten thousand \u003d 10 thousand units

1 hundred thousand \u003d 10 tens of thousands

1 million \u003d 10 hundred thousand

The purpose of our lesson is to learn how to perform written addition and subtraction of multidigit numbers. You already know how to add and subtract three-digit numbers in a column. Adding and subtracting multi-digit numbers is the same.

Let's compare two columns of calculations (see Fig. 3).

Figure: 3. Column addition of multidigit numbers

You have noticed that a new digit has appeared on the right, the digit of one thousand. Let us explain how the calculations are performed: 6 units + 2 units \u003d 8 units.

Then we add tens: 2 tens + 9 tens \u003d 11 tens. 11 dozen is 1 dozen and 1 hundred. Add a hundred to hundreds. 1 hundred + 2 hundreds \u003d 3 hundreds, but we have added one, so we write 4 under the hundreds. We calculate the units of thousands: 3 thousand + 4 thousand \u003d 7 thousand. So the answer is 7418.

Consider subtraction (see Fig. 4).

Figure: 4. Subtracting multi-digit numbers in a column

Compare the two columns of calculations. On the right, the unit of thousands and tens of thousands appeared. Let us explain how the subtraction is performed. It is impossible to subtract 7 from 6 units, so we will take one ten from the previous category: 16 - 7 \u003d 9, write 9 under units. We calculate tens: 4 - 0 \u003d 4, but we occupied one ten, so we write down 3. Subtract hundreds. It is impossible to subtract 4 hundreds from 3 hundred, so we occupy one thousand unit, this is 10 hundred, 13 hundred - 4 hundred \u003d 9 hundred. Subtract units of thousands. We took one unit of thousands, so we subtract 4 - 3 \u003d 1. We rewrite two, since there is no tens of thousands. Answer: 21939.

Task 1. Perform the calculation by writing down the solution in a column: 528047 + 106875. And check the addition using subtraction.

Let us explain how the addition of multi-digit numbers was performed: 7 units + 5 units \u003d 12. 12 is 2 units and 1 dozen. We write 2 under ones, and add ten to tens. We calculate tens: 4 tens + 7 tens \u003d 11 tens, and 1 tens was added, it turned out 12 tens. We write 2 under tens, and add one hundred to hundreds. We calculate hundreds: 0 + 8 \u003d 8, but we added one hundred, so we wrote down 9 under the hundreds: 8 + 6 \u003d 14. 14 thousand units is 4 thousand units and 1 ten thousand, we write down to tens. We count tens of thousands: 2 tens of thousands + 0 and 1 tens of thousands were added, we got 3 tens of thousands. Add hundreds of thousands: 5 + 1 \u003d 6.

We read the answer: 634922 (six hundred thirty four thousand nine hundred twenty two) (see fig. 5).

Figure: 5. Illustration for task 1

To check, we subtract one of the terms from the value of the sum. Let us explain how the subtraction is performed: you cannot subtract 7 from 2, so we will take 1 dozen. 12 - 7 \u003d 5. We calculate tens: we have occupied 1 ten, therefore there is 1 left. It is impossible to subtract 4 from 1, therefore we will borrow 1 hundred, 1 hundred is 10 tens. 11 - 4 \u003d 7. We calculate hundreds: since we borrowed 1 hundred, there are 8.8 - 0 \u003d 8 hundreds left. We calculate the units of thousands: it is impossible to subtract eight from four, therefore we occupy 1 ten thousand. 14 - 8 \u003d 6. We write down in units of thousands. We calculate tens of thousands. We borrowed one ten, there are 2. 2 - 2 \u003d 0. We calculate hundreds of thousands: 6 - 5 \u003d 1. We read the answer: 106875 (one hundred six thousand eight hundred seventy five) (see Fig. 6).

Figure: 7. Illustration for puzzle 2

Let us explain how the subtraction is performed: it is impossible to subtract 6 from 0, so we occupy one ten, 10 - 6 \u003d 4. There are 5 tens left. It is impossible to subtract 7 from 5, so we occupy one hundred, one hundred is 10 dozen. 15 - 7 \u003d 8 tens. There are 4 hundred left. 4 hundreds - 4 hundreds \u003d 0. We calculate the units of thousands: 2 - 1 \u003d 1. We calculate tens of thousands: 2 - 2 \u003d 0. 3 we rewrite, since there is no place of hundreds of thousands in the subtracted. We read the answer: 301084 (three hundred one thousand eighty four).

To check the subtraction by addition, you need to add the subtracted value to the difference (see Fig. 8).

Figure: 8. Illustration for puzzle 2

Let's explain how the addition is performed: 4 + 6 \u003d 10, write 0 under the ones, and add ten to the tens. We calculate tens: 8 + 7 \u003d 15 and 1 dozen added, got 16 tens. We write 6 instead of tens, and add 1 hundred to hundreds. 0 + 4 \u003d 4 yes 1 hundred \u003d 5 hundred. We calculate the units of thousands: 1 + 1 \u003d 2. Add tens of thousands: 0 + 2 \u003d 2. Rewrite hundreds of thousands. We read the result: 322560 (three hundred twenty two thousand five hundred sixty).

We compare with the decreasing and see that the numbers coincide, which means that the subtraction is performed correctly. Let's write down the result: 301084 (three hundred one thousand eighty four).

Let's solve a mathematical puzzle (see fig. 9).

Figure: 9. Rebus

Determine which numbers are missing in the numbers. It is impossible to subtract some number from 4 and get 9, so we will take ten. From 14, you need to subtract 5 to get 9. Subtract 8 and get 0. So, in place of tens, the number 8, but one ten was taken, so we write 9. Determine the number of hundreds: from three you need to subtract two to get one. We write in place of 2 hundreds (see Fig. 10).

Figure: 10. Solving the math puzzle

Today we learned how to perform written addition and subtraction of multidigit numbers.

Bashmakov M.I. Nefedova M.G. Maths. 4th grade. M .: Astrel, 2009.
MI Moro, MA Bantova, GV Beltyukova et al. Mathematics. 4th grade. Part 1 of 2, 2011.
Demidova T.E. Kozlova S.A. Tonkikh A.P. Mathematics. Grade 4 2nd ed., Rev. - M .: Balass, 2013.

Dhomework

1) Task: write it down in a column and solve.

2) The maximum ocean depth is 11,022 m. Calculate the difference between the ocean depth and the highest point on Earth if the height of the highest mountain in the world (Everest) is 8,848 m above sea level.

3) The weed plant cornflower gives 6,680 seeds per year, and such a plant as rye fire is 5260 less, field sow thist is 12,920 more than cornflower. How many seeds do these plants produce together per year?

The ability to count in the mind, of course, is a big and necessary business. But what to do with three, four, five-digit numbers? You can't count them so easily in your mind, and you want to take a piece of paper and add or subtract in a column. Column counting should be easy with some practice. But only if there was this very practice. It is very important to learn how to quickly add and subtract large numbers in a column if it is difficult to do this in your head. For these purposes, our math simulator on this page is intended.

Let us recall how to do column subtraction. To begin with, we write down the decremented and subtracted in a column below each other: units under units, tens under tens, hundreds under hundreds, and so on. Subtract units from units, write the number under the column of units. If there are not enough units in the diminished one, we take ten in it and subtract from the resulting number. And over the top ten we make a note that we have occupied one (put a full stop). Similarly, we count tens, hundreds, and so on from right to left. Do not forget to take into account the occupied tens, hundreds.

Column folding is much easier than subtracting. We also write numbers under each other, units under units, and so on. We start adding units. If, when adding units, you get a dozen, add it to the sum of tens in a column with tens. We count hundreds and thousands in the same way.

To practice, you need to download and print the desired task sheet. To do this, right-click on the desired page and select save image as.

Column Addition and Subtraction Machine Pages

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

place the subtracted under the decrement, write the units under the ones, tens under the tens, etc.
subtract bit by bit.
if it is necessary to take a dozen of the larger category, then put a full stop above the category in which you took it. Put 10 above the rank for which you took it.
if the bit in which we occupied is 0, then we borrow from the next digit of the decreasing one and put a dot above it. Put 9 above the rank for which you took it, because one dozen is 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 is very helpful when subtracting large numbers (as well as column addition). It is best to learn from an 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 we write under the line:

10 + 3 = 13.

Subtract nine from 13.

13 - 9 = 4.

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

4 - 1 = 3.

Result:

Column subtraction of numbers containing zeros.

Again, let's take an example:

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

It will not work to subtract 2 from zero, then we again borrow from the digit on the left. This is zero. We put a point over zero. And again, you won't be able to borrow from zero, then we move on to the next digit. We borrow from one. We put a point over it.

Note: when there is a dot in column subtraction above 0, zero becomes a 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 dot above one, that is, it decreases by 1. 1 - 1 = 0. The resulting zero does not need to be written down.