How to deduct negative decimal fractions. Tasks on the topic addition and subtraction of decimal fractions

Date: 02/25/16. I argue:

Subject: Subtraction of decimal fractions

Objectives:

To form knowledge of the knowledge about subtracting decimal fractions

Develop intelligence and students and cognitive interest

Implement labor education

Equipment: Textbook, cool board

Type of lesson : Combined

Method: Work with lagging

During the classes :

Greeting

Checking missing

Check homework

Frontal survey

Explanation of the new material:

As well as addition, subtracting decimal fractions We produce according to the rules Natural numbers.

The main rules for subtracting decimal fractions.

You equalize the number of semicolons.

We write down the decimal fraction with each other so that the commas are in each other.

We carry out the subtraction of decimal fractions, not paying attention to the commas, according to the rules of subtraction in the column of natural numbers.

We put a comma in the answer under commas.

If you feel confident in decimal fractions and understand well what is called tenth, hundredths, etc., we suggest you try another way of subtracting (addition) decimal fractions without writing them in a column. Another waysubtract decimal fractions , as well as addition, is based on three major rules.

Deduct decimal fractionsfrom right to left . That is, starting with the right digit after the comma.

When subtracting greater numbers from the smaller, the neighbor left to the left of the smallest digit is occupying a dozen.

As usual, consider an example:

We deduct right to left with the right digit. We have the right digit in both fractions - hundredths. 1 - in the first number, 1 - in the second. Here and deduct them. 1 - 1 \u003d 0. It turned out 0, it means on the place of the hundredth of the new number we write zero.

Tenths deduct from the tenths. 2 - in the first number, 3 - in the second number. Since 2 (less) we cannot subtract 3 (more), we occupy a dozen at the neighbor on the left for 2. We have it 5. Now we are not out of 2, we subtract 3 out of 12, and we subtract 3 out of 12.
12 − 3 = 9.
At the place of the tenths of the new number I write 9. Do not forget that after classes a dozen of 5, we must subtract out of 5 units. To do not forget it to put over 5 empty circle.

Finally, we subtract entire parts. 14 - in the first number (do not forget that we outlined 1 from 5), 8 - in the second number. 14 - 8 \u003d 6

Remember!

In the second number, the right figure is 2 (hundredths), and in the first number of cells there is no explicit form. Therefore, to the first number to the right of 9, add zero and deduct according to the basic rules.

Chapter 2 Fractional numbers and actions with them

§ 37. Addition and subtraction of decimal fractions

Decimal fractions write down the same principle as natural numbers. Therefore, addition and subtraction are performed according to the corresponding schemes for natural numbers.

During the addition and subtraction of decimal fractions are recorded by a "column" - each other so that the discharges of the same name stood under each other. Thus, the comma will be dirty. Next, we perform the action as well as with natural numbers, not paying attention to the comma. In the amount (or difference), the comma is put under the commas of the terms (or commas reduced and subtractor).

Example 1. 37.982 + 4,473.

Explanation. 2 thousandth plus 3 thousands are equal to 5 thousandths. 8 acres plus 7 acres are 15 acres, or 1 tenth and 5 acres. We write 5 acres, and 1 tenth remember, etc.

Example 2. 42.8 - 37,515.

Explanation. Since decreasing and subtractable have a different number of decimal signs, you can assign in a decreasing required amount zeros. Descending yourself, as an example is made.

Note that when adding and subtracting zero, you can not add, but mentally represent them in those places where there are no discharge units.

In addition to decimal fractions, the previously studied stopping and connecting properties of addition are made:

First level

1228. Called (orally):

1) 8 + 0,7; 2) 5 + 0,32;

3) 0,39 + 1; 4) 0,3 + 0,2;

5) 0,12 + 0,37; 6) 0,1 + 0,01;

7) 0,02 + 0,003; 8) 0,26 + 0,7;

9) 0,12 + 0,004.

1229. Called:

1230. Called (orally):

1) 4,72 - 2; 2) 13,892 - 10; 3) 0,8 - 0,6;

4) 6,7 - 0,3; 5) 2,3 - 1,2; 6) 0,05 - 0,02;

7) 0,19 - 0,07; 8) 0,47 - 0,32; 9) 42,4 - 42.

1231. Called:

1232. Called:

1233. On one machine there were 2.7 tons of sand, and on the other - 3.2 tons. How many sand was on two machines?

1234. Fit addition:

1) 6,9 + 2,6; 2) 9,3 + 0,8; 3) 8,9 + 5;

4) 15 + 7,2; 5) 4,7 + 5,29; 6) 1,42 + 24,5;

7) 10,9 + 0,309; 8) 0,592 + 0,83; 9) 1,723 + 8,9.

1235. Find the amount:

1) 3,8 + 1,9; 2) 5,6 + 0,5; 3) 9 + 3,6;

4) 5,7 + 1,6; 5) 3,58 + 1,4; 6) 7,2 + 15,68;

7) 0,906 + 12,8; 8) 0,47 + 0,741; 9) 8,492 + 0,7.

1236. Follow the subtraction:

1) 5,7 - 3,8; 2) 6,1 - 4,7; 3) 12,1 - 8,7;

4) 44,6 - 13; 5) 4 - 3,4; 6) 17 - 0,42;

7) 7,5 - 4,83; 8) 0,12 - 0,0856; 9) 9,378 - 8,45.

1237. Find a difference:

1) 7,5 - 2,7; 2) 4,3 - 3,5; 3) 12,2 - 9,6;

4) 32,7 - 5; 5) 41 - 3,53; 6) 7 - 0,61;

7) 8,31 - 4,568; 8) 0,16 - 0,0913; 9) 37,819 - 8,9.

1238. The carpet-aircraft for 2 hours flew 17.4 km, and in the first hour he flew 8.3 km. How much flew a carpet-aircraft for the second hour?

1239. 1) Multiply the number 7.2831 by 2.423.

2) Reduce the number 5,372 per 4.47.

Average level

1240. Share equation:

1) 7.2 + x \u003d 10.31; 2) 5.3 - x \u003d 2.4;

3) x - 2.8 \u003d 1.72; 4) x + 3,71 \u003d 10.5.

1241. Share equation:

1) x - 4.2 \u003d 5.9; 2) 2.9 + x \u003d 3.5;

3) 4,13 - x \u003d 3.2; 4) x + 5.72 \u003d 14.6.

1242. How is it more convenient to add? Why?

4.2 + 8.93 + 0.8 \u003d (4.2 + 8.93) + 0.8 or

4,2 + 8,93 + 0,8 = (4,2 + 0,8) + 8,93.

1243. Committed (orally) in a convenient way:

1) 7 + 2,8 + 1,2; 2) 12,4 + 17,3 + 0,6;

3) 3,42 + 4,9 + 5,1; 4) 12,11 + 7,89 + 13,5.

1244. Find the value of the expression:

1) 200,01 + 0,052 + 1,05;

2) 42 + 4,038 + 17,25;

3) 2,546 + 0,597 + 82,04;

4) 48,086 + 115,92 + 111,037.

1245. Find the value of the expression:

1) 82 + 4,042 + 17,37;

2) 47,82 + 0,382 + 17,3;

3) 15,397 + 9,42 + 114;

4) 152,73 + 137,8 + 0,4953.

1246. OT metal pipe A length of 7.92 m was cut off first 1.17 m, and then another 3.42 m. What is the length of the remaining pipe?

1247. Apples together with a drawer weigh 25.6 kg. How many kilograms weigh apples, if the empty box weighs 1.13 kg?

1248. Find the length of the brokenABC if Av \u003d 4.7 cm, and the aircraft is 2.3 cm less aw.

1249. In one bidon there is 10.7 liters of milk, and in another 1.25 l less. How much milk in two bidones?

1250. Passed:

1) 147,85 - 34 - 5,986;

2) 137,52 - (113,21 + 5,4);

3) (157,42 - 114,381) - 5,91;

4) 1142,3 - (157,8 - 3,71).

1251. Called:

1) 137,42 - 15 - 9,127;

2) 1147,58 - (142,37 + 8,13);

3) (159,52 - 142,78) + 11,189;

4) 4297,52 - (113,43 + 1298,3).

1252. Find the value of the expression A - 5.2 -b, if a \u003d 8.91, b \u003d 0.13.

1253. The speed of the boat in standing water is 17.2 km / h, and the flow rate is 2.7 km / h. Find the speed of the boat for the flow and against the flow.

1254. Fill in table:

Own speed, kM / C.	Speed flow kM / C.	Speed \u200b\u200bfor flow, km / h	Speed \u200b\u200bagainst current, km / h
13,1
17,2		18,5
12,35			10,85
		13,5
	1,65		12,95

1255. Find the missed numbers in the chain:

1256. Measure in centimeters side of the quadrilateral shown in Figure 257, and find its perimeter.

1257. Hatch an arbitrary triangle, measure it sides in centimeters and find the perimeter of the triangle.

1258. On the CU segment designated a point in (Fig. 258).

1) Find the AC if Av \u003d 3.2 cm, Sun \u003d 2.1 cm;

2) Find Sun, if ac \u003d 12.7 dm, av \u003d 8.3 dm.

Fig. 257.

Fig. 258.

Fig. 259.

1259. How many centimeters cutAB Long CD segment (Fig. 259)?

1260. One side of the rectangle is 2.7 cm, and the other is 1.3 cm in short. Find the perimeter of the rectangle.

1261. The basis of an equally chained triangle is 8.2 cm, and the lateral side is 2.1 cm less base. Find the perimeter of the triangle.

1262. The first side of the triangle is 13.6 cm, the second is 1.3 cm in short. Find a third side of the triangle if its perimeter is 43.1 cm.

Enough level

1263. Write a sequence of five numbers if:

1) the first number is 7.2, and each next to 0.25 more than the previous one;

2) the first number is 10.18, and each next to 0.34 is less than the previous one.

1264. The first drawer had 12.7 kg of apples, which is 3.9 kg more than in the second. In the third drawer, apples were 5.13 kg less than in the first and second together. How many kilograms of apples was in three boxes together?

1265. The first day tourists took place 8.3 km, which is 1.8 km more than the second day, and 2.7 km less than the third. How many kilometers tourists passed in three days?

1266. Fit addition, choosing a convenient calculation order:

1) 0,571 + (2,87 + 1,429);

2) 6,335 + 2,896 + 1,104;

3) 4,52 + 3,1 + 17,48 + 13,9.

1267. Make addition, choosing a convenient order of calculation:

1) 0,571 + (2,87 + 1,429);

2) 7,335 + 3,896 + 1,104;

3) 15,2 + 3,71 + 7,8 + 4,29.

1268. Put the numbers instead of stars:

1269. Put into the cells such numbers to form correctly executed examples:

1270. Simsity Expression:

1) 2.71 + x - 1.38; 2) 3.71 + C + 2.98.

1271. Simsity Expression:

1) 8.42 + 3,17 - x; 2) 3.47 +y - 1.72.

1272. Find regularity and write down the three onset of them of the number of sequences:

1) 2; 2,7; 3,4 ... 2) 15; 13,5; 12 ...

1273. Share equation:

1) 13.1 - (x + 5.8) \u003d 1.7;

2) (x - 4.7) - 2.8 \u003d 5.9;

3) (y - 4.42) + 7.18 \u003d 24.3;

4) 5.42 - (B - 9.37) \u003d 1.18.

1274. Share equation:

1) (3,9 + x) - 2.5 \u003d 5.7;

2) 14,2 - (6,7 + x) \u003d 5.9;

3) (B - 8.42) + 3,14 \u003d 5.9;

4) 4.42 + (y - 1.17) \u003d 5.47.

1275. Find the expression value in a convenient way, using the deduction properties:

1) (14,548 + 12,835) - 4,548;

2) 9,37 - 2,59 - 2,37;

3) 7,132 - (1,132 + 5,13);

4) 12,7 - 3,8 - 6,2.

1276. Find the expression value in a convenient way, using the deduction properties:

1) (27,527 + 7,983) - 7,527;

2) 14,49 - 3,1 - 5,49;

3) 14,1 - 3,58 - 4,42;

4) 4,142 - (2,142 + 1,9).

1277. Called by writing these values \u200b\u200bin decimeters:

1) 8.72 dm - 13 cm;

2) 15.3 dm + 5 cm + 2 mm;

3) 427 cm + 15.3 dm;

4) 5 m 3 dm 2 cm 4 m 7 dm 2 cm.

1278. The perimeter of an elevated triangle is equal

17.1 cm, and the lateral side is 6.3 cm. Find the length of the base.

1279. The speed of the trading train is 52.4 km / h, passenger is 69.5 km / h. Determine, these trains are deleted or brought together and how many kilometers per hour, if they came out at the same time:

1) from two points, the distance between which 600 km, towards each other;

2) from two points, the distance between which 300 km, and the passenger catch up with the commodity;

1280. The speed of the first cyclist is 18.2 km / h, and the second is 16.7 km / h. Determine, cyclists are removed or brought closer and how many kilometers per hour, if they left at the same time:

1) from two points, the distance between which 100 km, towards each other;

2) from two points, the distance between which is 30 km, and the first catch up with the second;

3) from one point in opposite directions;

4) from one point in one direction.

1281. Called, the answer is rounded to hundredths:

1) 1,5972 + 7,8219 - 4,3712;

2) 2,3917 - 0,4214 + 3,4515.

1282. Called by writing these values \u200b\u200bin centners:

1) 8 c - 319 kg;

2) 9 C 15 kg + 312 kg;

3) 3 t 2 c - 2 C 3 kg;

4) 5 tons 2 C 13 kg + 7 t 3 C 7 kg.

1283. Called by writing these values \u200b\u200bin meters:

1) 7.2 m - 25 dm;

2) 2.7 m + 3 dm 5 cm;

3) 432 dm + 3 m 5 dm + 27 cm;

4) 37 dm - 15 cm.

1284. The perimeter of an equally sized triangle is equal

15.4 cm, and the base is 3.4 cm. Find the length of the side.

1285. The perimeter of the rectangle is 12.2 cm, and the length of one of the parties is 3.1 cm. Find the length of the side that is not equal to this.

1286. In three boxes 109.6 kg of tomatoes. In the first and second boxes together 69.9 kg, and in the second and third 72.1 kg. How many kilograms of tomatoes in each drawer?

1287. Find numbers a, b, s, d in the chain:

1288. Find numbers a andb in a chain:

High level

1289. Put instead of stars signs "+" and "-" so that equality is carried out:

1) 8,1 * 3,7 * 2,7 * 5,1 = 2;

2) 4,5 * 0,18 * 1,18 * 5,5 = 0.

1290. Chip had 5.2 UAH. After Dale lended to him 1.7 UAH. Daila has become 1.2 UAH. Less than the chip. How much money was Daila first?

1291. Two brigades asphalt highway and move towards each other. When the first brigade was asphalted by 5.92 km of the highway, and the second is 1.37 km less, then 0.85 km remained to their meeting. What is the length of the highway area, which was necessary to be asphalt?

1292. How will the sum of two numbers change if:

1) one of the components to increase by 3.7, and the other is 8.2;

2) one of the components to increase by 18.2, and the other is reduced by 3.1;

3) one of the components to decrease by 7.4, and the other - by 8.15;

4) one of the components to increase by 1.25, and the other is reduced by 1.25;

5) One of the components to increase by 7.2, and the other is reduced by 8.9?

1293. How will the difference change, if:

1) decreasing reduced by 7.1;

2) decreasing increase by 8.3;

3) subtractable to increase by 4.7;

4) subtractable to reduce 4.19?

1294. The difference of two numbers is 8.325. What is the new difference, if a decreasing increase by 13.2, and the subtractable increase by 5.7?

1295. How will the difference change, if:

1) increase decreasing by 0.8, and subtractable - by 0.5;

2) increase decreasing by 1.7, and subtractable - by 1.9;

3) decreasing increase by 3.1, and subtractable to decrease by 1.9;

4) Reduced to reduce by 4.2, and the subtractable increase by 2.1?

Exercises for repetition

1296. Compare the values \u200b\u200bof expressions without performing actions:

1) 125 + 382 and 382 + 127; 2) 473 ∙ 29 472 ∙ 29;

3) 592 - 11 and 592 - 37; 4) 925: 25 and 925: 37.

1297. There are two types of first dishes in the dining room, 3 types of second and 2 types of third dishes. How many ways can you choose a three-course lunch in this dining room?

1298. The perimeter of the rectangle is 50 dm. The length of the rectangle is 5 dm more width. Find the side of the rectangle.

1299. Record the greatest decimal fraction:

1) with one decimal sign, less than 10;

2) with two decimal signs, less than 5.

1300. Write down the smallest decimal fraction:

1) with one decimal sign, more than 6;

2) with two decimal signs, more than 17.

Home independent work № 7

2. Which of the inequalities is true:

A) 2.3\u003e 2.31; B) 7.5< 7,49;

B. ) 4,12\u003e 4.13; D) 5,7< 5,78?

3. 4,08 - 1,3 =

A) 3.5; B) 2.78; C) 3.05; D) 3.95.

4. write down the decimal fraction 4,0701 mixed number:

5. Which rounding to the hundredths are correct:

A. ) 2.729 ≈ 2.72; B) 3.545 ≈ 3.55;

B. ) 4.729 ≈ 4.7; D) 4,365 ≈ 4.36?

6. Find the root of the equation x - 6,13 \u003d 7.48.

A) 13.61; B) 1.35; C) 13,51; D) 12.61.

7. Which of the proposed equations is correct:

A) 7 cm \u003d 0.7 m; B) 7 dm2 \u003d 0.07 m2;

in) 7 mm \u003d 0.07 m; D) 7 cm3 \u003d 0.07 m3?

8. Names The greatest natural number, which does not exceed 7,0809:

A) 6; B) 7; AT 8; D) 9.

9. How many numbers exist that can be put instead of an asterisk in an approximate equality of 2.3 * 7 * 2.4 so that rounding before the rebels was performed correctly?

A) 5; B) 0; AT 4; D) 6.

10. 4 A 3 m2 \u003d

A) 4.3 A; B) 4.003 A; C) 4.03 A; D) 43.

11. Which of the proposed numbers can be substituted instead and to double the inequality of 3.7< а < 3,9 была правильной?

A) 3.08; B) 3,901; C) 3,699; D) 3.83.

12. How will the sum of the three numbers change, if the first term increase by 0.8, the second is to increase by 0.5, and the third is to reduce 0.4?

A. ) will increase by 1.7; B) will increase by 0.9;

B. ) will increase by 0.1; D) decrease by 0.2.

Tasks for checking Knowledge number 7 (§34 - §37)

1. Compare decimal fractions:

1) 47,539 and 47.6; 2) 0.293 and 0.2928.

2. Firm addition:

1) 7,97 + 36,461; 2) 42 + 7,001.

3. Follow the subtraction:

1) 46,63 - 7,718; 2) 37 - 3,045.

4. Rounded to:

1) the tenths: 4,597; 0,8342;

2) hundredths: 15,795; 14,134.

5. Express in kilometers and write down the decimal fraction:

1) 7 km 113 m; 2) 219 m; 3) 17 m; 4) 3129 m.

6. Own boat speed is 15.7 km / h, and the flow rate is 1.9 km / h. Find the speed of the boat for the flow and against the flow.

7. The first day of the warehouse was taken by 7.3 tons of vegetables, which is 2.6 tons greater than the second, and 1.7 tons less than the third day. How many tons of vegetables brought to a warehouse for three days?

8. Find the value of the expression, choosing a convenient procedure:

1) (8,42 + 3,97) + 4,58; 2) (3,47 + 2,93) - 1,47.

9. Write three numbers, each of which is less than 5.7, but more than 5.5.

10. Additional task. Write all the numbers that can be put instead * so that inequality is correct:

1) 3,81*5 ≈3,82; 2) 7,4*6≈ 7,41.

11. Additional task. At what kind of natural valuesn inequalities 0,7< n < 4,2 и 2,7 < n < 8,9 одновременно являются правильными?

Lesson on the topic: "Deduction rules for decimal fractions. Examples"

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Methods for subtracting decimal fractions

Remove the decimal fractions in two ways.

The first method is similar to subtracting natural numbers by the column.
Let's consider this method on the example. Dana decimal fractions: 45.68 and 4.1, we define: what is their difference?
First equalize the number of semicolons. To do this, to the right of the decimal fraction 4.1 I will approve zero and get 4.10. The value of the decimal fraction does not change, because We have not transferred a decimal separation comma.
Next, we have decisive decimal fractions under the other and, starting from the most extreme right column, we will deduct the numbers of the lower row of the top row numbers. At the end do not forget to put a comma.
As a result of these operations, we will receive the difference in decimal fractions.
Everything is simple and understandable. The only difficulty may occur if, when subtracting the discharge of the number of reduced less discharge of the number of subtractable.

Consider another example of subtracting decimal fractions.
Dana decimal fractions: 23,18 and 3.2.
First, in line with the number of discharges and get: 23,18 and 3.20.
We write decimal fractions in the column of each other /

Starting from the right extreme row, we subtract the numbers of the lower row from the digits of the upper row. If the number 1 is subtracting the number 2, then we get a negative number. Therefore, we take a dozen units from a neighboring discharge and it turns out that we produce the subtraction of the number 2 from among the number 11. As a result, we have:
Deduction algorithm decimal fractions:
1. Align the decimal fractions by the number of numbers after the comma.
2. We write down the decimal fractions in the column in each other.
3. We produce deduction of decimal fractions according to the rules for subtracting natural numbers, not paying attention to the presence of decimal semicol.
4. After the end of subtraction, do not forget to put a decimal comma.

The second way of subtracting decimal fractions

This method is more complicated, less visually required and requires little experience. But it is more fast, since there is no need to record numbers in the column and equalize the number of decimal signs.
The most important thing in this method remember the rule: the tenth shares of the number can be subtracted only from the tenths, hundredths - from hundredths, etc. If in any discharge is reduced less subtracted, then dozens of units take from the neighboring discharge left.

Consider an example. Decimal fractions are given: 5.13 and 3.4.
We subtract the hundredths of the shares, we get 3.

We subtract the tenths. IN this example We need to take ten units from the neighboring discharge, because When subtracting tenths, reduced less subtracted.

5,13 - 3,4 = 1,73

And as usual, the results of subtraction must be checked by adding. For our example, this is:

Objectives lesson:

• the formation of knowledge of the rules for the addition and subtraction of decimal fractions and the ability to apply them in the simplest cases;
• development of skills to compare, detect patterns, generalize;
• raising independence when performing tasks.

Equipment: Computer, projector, magnetic boards for students, individual multi-level cards.

LESSON STRUCTURE:

1. Organizational moment.
2. Activation of previously gained knowledge.
3. Studying a new material.
4. Primary consolidation of the material studied.
5. Test.
6. Handling homework.
7. Summing up the lesson.

DURING THE CLASSES

I. Organizational moment

Checked the readiness of the class to the lesson. It is noted that the students recently got acquainted with the concept of "decimal fraction", learned to read and compare decimal fractions. The lesson will consider the question of how to add and subtract decimal fractions. The subject of the lesson is recorded. Slide 1.

II. Activation of previously gained knowledge

Kohl will soon talk about decimal fractions today, let's remember:

• Which of these frains can be written in the form of decimal:

Slide 2.(Students call the fraction).

Imagine a fraction in the form of decimal. (Students are shown on magnetic boards).
Once again, let's remember which fractions can be written in the form of decimal. ( Pupils give an answer).

Imagine in the form of decimal fractions:

Slide 3.(On magnetic boards, students show entries).

• We read numbers:

0,62; 7,321; 21,0001; 63,01246. Slide 4.

III. Studying a new material

– Guys, and which of the above examples concerns today's theme. (Students answer that the last).
- Let's write this example into a notebook and find the amount.

Let's write this example in the form of decimal fractions.

We get the same result, folding the numbers in the column.

- What did we get with you? (The amount of decimal fractions).
- Let's say how we did it. Slide 6.

- Okay!

Pupils are invited to find the amount of decimal fractions, in which a different number of digits after a comma 6.23 + 173.3. The question is asked: "How to act in this case?". (Students answer that there are different number of semicolons in the terms of the scene).

- How to be? (You need to equalize, adding zero to the right at the second term).

6,32 + 173,7 = 6,32 + 173,70

And now you can record numbers in the column and find the amount.

The algorithm for the addition of decimal fractions is complemented and looks like this:

- How to find the difference between two decimal fractions? (Similar).

The algorithm is complemented and looks like this:

- So, how to fold or subtract decimal fractions?

The algorithm is repeated by students and appears on the screen.

IV. Primary consolidation of knowledge gained

1. Calculate orally (examples of students are offered on signs, and answers - on magnetic boards):

2. Solving exercises.

№1213 (A, G, B), №1214 (A, D, E), №1219 (B, E, L).

Examples are solved at the boards with comments. Slide 7.

V. Test

– So, now we will check how you remember the rules for the addition and subtraction of decimal frains.
Orally repeats once again the algorithm.
Students are offered three types of cards (Appendix 3. )
Students are displayed on signs. With successful tasks, all students on the signs should be written the word "plus". Slide 8.

Vi. Summing up the lesson

- What did you like in today's lesson?
- What did not like?
- What did we learn from you at the lesson? (Fold and deduct decimal fractions).
- What is the way to do it quickly? (Addition and subtraction "in the column").
- And how to do it?

Students pronounce the algorithm.

VII. Setting a homework

- Using this algorithm at home, you follow these tasks: No. 1255 (A, G, E), No. 1256 (E, s), and also familiarize yourself with paragraph 32 of the textbook. Compare the algorithm proposed in the textbook with our.
- The lesson is over.

Like addition, deduction of decimal fractions depends on the correct recording of numbers.

Deduction rule decimal fractions

1) comma dressed!

This part of the rule is the most important. When subtracting decimal fractions, they should be recorded so that the commas reduced and subtracts were strictly one under the other.

2) equalize the number of numbers after the comma. For this, among other things, where the number of numbers after the comma is less, we add after the semicolons at the end of the zeros.

3) we subtract the number, not paying attention to the comma.

4) demolish the comma under commas.

Examples for subtracting decimal fractions.

To find the difference in decimal fractions 9.7 and 3.5, we write them so that the commas in both numbers are strictly one under the other. Then we subtract, not paying attention to the comma. In the resulting result, the comma demolish, that is, recorded under commas reduced and submitted:

2) 23,45 — 1,5

In order to make another decimal fraction, you need to record them so that the commas are located exactly alone. Since 23.45 after the semicolons, two digits, and in 1.5 - only one, add in 1.5 zero. After that, we conduct subtraction, not paying attention to the comma. To the result, demolish the comma under the commas:

23,45 — 1,5=21,95.

The subtraction of decimal frains begin with their record so that the commas are located exactly one under one. In the first number after the comma, one digit, in the second - three, therefore in the place of the missing two digits in the first number write zeros. Then we subtract the number, not paying attention to the comma. In the result, demolished the comma under commas:

63,5-8,921=54,579.

4) 2,8703 — 0,507

To subtract these decimal fractions, write them so that the comma of the second number is accurately submitted by the first. In the first number after the semicolons, four digits, in the second - three, so the second number is complementary after the semicolon is zero at the end. After that, we subtract these numbers as ordinary natural, without taking into account the comma. In the result, we write the comma under commas:

2,8703 — 0,507 = 2,3663.

5) 35,46 — 7,372

Subtract decimal fractions start from the number of numbers in such a way that the commas are one to another. We are complemented by zero after the semicolons the first number so that in both fractions after the comma, there are three digits. Then we subtract, not paying attention to the comma. In response, demolish the comma on the commas:

35,46 — 7,372 = 28,088.

To out natural Number Identify the decimal fraction, in his record at the end we put the comma and attribute the required number of zeros after the comma. Why subtract, without taking into account the comma. In response, demolish the comma smoothly under commas:

45 — 7,303 = 37,698.

7) 17,256 — 4,756

This example of subtracting decimal fractions is performed similarly. As a result, the number with zeros after the comma at the end was obtained. Do not write them in the answer: 17,256 - 4.756 \u003d 12.5.