Is addition decimals . In this article we will look at the rules for adding finite decimal fractions, use examples to look at how to add finite decimal fractions in a column, and also dwell on the principles of adding infinite periodic and non-periodic decimal fractions. In conclusion, we will focus on adding decimals with natural numbers, ordinary fractions and mixed numbers.

Note that in this article we will only talk about adding positive decimals (see positive and negative numbers). The remaining options are covered by material from the articles addition of rational numbers and addition of real numbers.

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General principles of adding decimals

Example.

Add the decimal 0.43 and the decimal 3.7.

Solution.

The decimal fraction 0.43 corresponds to the common fraction 43/100, and the decimal fraction 3.7 corresponds to the common fraction 37/10 (if necessary, see the conversion of final decimal fractions to common ones). Thus, 0.43+3.7=43/100+37/10.

This completes the addition of finite decimal fractions.

Answer:

4,13 .

Now let's add periodic decimal fractions to our consideration.

Example.

Add the ending decimal 0.2 with the periodic decimal 0.(45) .

Solution.

Then .

Answer:

0,2+0,(45)=0,65(45) .

Now let us dwell on the principle of addition of infinite non-periodic decimal fractions.

Recall that infinite non-periodic decimal fractions, unlike finite and periodic decimal fractions, cannot be represented in the form ordinary fractions(they represent irrational numbers), so the addition of infinite non-periodic fractions cannot be reduced to the addition of ordinary fractions.

When performing the addition of infinite non-periodic fractions, they are replaced with approximate values, that is, they are first rounded (see rounding numbers) to a certain level. By increasing the accuracy with which approximations of the original infinite non-periodic decimal fractions are taken, more exact value the result of the addition. Thus, addition of infinite non-periodic decimal fractions comes down to adding finite decimal fractions.

Let's look at the example solution.

Example.

Add the infinite non-periodic decimal fractions 4.358... and 11.11002244....

Solution.

Let's round the added decimal fractions to hundredths (we will no longer be able to round the fraction 4.358... to thousandths, since the value of the ten-thousandth place is unknown), we have 4.358...≈4.36 and 11.11002244...≈11.11. Now all that remains is to add the final decimal fractions: .

Answer:

4,358…+11,11002244…≈15,47 .

To conclude this point, we will say that the addition of positive decimal fractions is characterized by all the properties of the addition of natural numbers. That is, the combinatory property of addition allows us to uniquely determine the addition of three and more decimal fractions, and the commutative property of addition allows you to rearrange the decimal fractions being added.

Adding decimal fractions in a column

It is quite convenient to perform column addition of finite decimal fractions. This method allows you to avoid converting added decimal fractions to ordinary fractions.

To execute column addition of decimal fractions, necessary:

• write one fraction under another so that the same digits are under each other, and the comma is under the comma (for convenience, you can equalize the number of decimal places by adding a certain number of zeros to one of the fractions on the right);
• then, without paying attention to the commas, perform the addition in the same way as adding a column of natural numbers;
• In the resulting amount, place a decimal point so that it is located under the decimal points of the terms.

For clarity, let's look at an example of adding decimal fractions in a column.

Example.

Add the decimals 30.265 and 1055.02597.

Solution.

Let's perform column addition of decimal fractions.

First, let's equalize the number of decimal places in the fractions being added. To do this, you need to add two zeros to the right in the fraction 30.265, which will result in an equal fraction 30.26500.

Now we write the fractions 30.26500 and 1 055.02597 in a column so that the corresponding digits are under each other:

We perform addition according to the rules of column addition, not paying attention to commas:

All that remains is to put a decimal point in the resulting number, after which the addition of decimal fractions in a column takes on the finished form:

Answer:

30,26500+1 055,02597=1 085,29097 .

Adding decimals with natural numbers

We'll announce it right away rule for adding decimals with natural numbers: to add a decimal fraction and natural number you need to add this natural number to the whole part of the decimal fraction, and leave the fractional part the same. This rule applies to both finite and infinite decimal fractions.

Let's look at an example of applying this rule.

Example.

Calculate the sum of the decimal fraction 6.36 and the natural number 48.

Solution.

The integer part of the decimal fraction 6.36 is equal to 6, if we add the natural number 48 to it, we get the number 54. Thus, 6.36+48=54.36.

Answer:

6,36+48=54,36 .

Adding decimals with fractions and mixed numbers

The addition of a finite decimal or an infinite periodic decimal with a common fraction or mixed number can be reduced to the addition of common fractions or the addition of a common fraction and mixed number. To do this, it is enough to replace the decimal fraction with an equal ordinary fraction.

Example.

Add the decimal fraction 0.45 and the common fraction 3/8.

Solution.

Let's replace the decimal fraction 0.45 with an ordinary fraction: . After this, the addition of the decimal fraction 0.45 and the common fraction 3/8 is reduced to the addition of the common fractions 9/20 and 3/8. Let's finish the calculations: . If necessary, the resulting ordinary fraction can be converted to a decimal.

Like addition, subtracting decimals depends on writing the numbers correctly.

Rule for subtracting decimals

1) COMMA UNDER THE COMMA!

This part of the rule is the most important. When subtracting decimal fractions, they should be written so that the commas of the minuend and subtrahend are strictly one below the other.

2) We equalize the number of digits after the decimal point. To do this, including where the number of digits after the decimal point is smaller, we add zeros after the decimal point.

3) Subtract the numbers, not paying attention to the comma.

4) Remove the comma under the commas.

Examples for subtracting decimals.

To find the difference between the decimal fractions 9.7 and 3.5, we write them so that the commas in both numbers are strictly one below the other. Then we subtract, ignoring the comma. In the resulting result, we remove the comma, that is, we write under the commas of the minuend and subtrahend:

2) 23,45 — 1,5

In order to subtract another from one decimal fraction, you need to write them so that the commas are located exactly one below the other. Since 23.45 has two digits after the decimal point, and 1.5 has only one, we add a zero to 1.5. After this, we carry out subtractions, not paying attention to the comma. As a result, we remove the comma under the commas:

23,45 — 1,5=21,95.

We begin subtracting decimal fractions by writing them so that the commas are located exactly one below the other. The first number has one digit after the decimal point, the second has three, so we write zeros in place of the missing two digits in the first number. Then we subtract the numbers, ignoring the comma. In the resulting result, remove the comma under the commas:

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

4) 2,8703 — 0,507

To subtract these decimal fractions, we write them so that the decimal point of the second number is located exactly under the decimal point of the first. The first number has four digits after the decimal point, the second number has three, so we add a final zero after the decimal point to the second number. After this, we subtract these numbers like ordinary natural numbers, without taking into account the comma. In the resulting result, write a comma under the commas:

2,8703 — 0,507 = 2,3663.

5) 35,46 — 7,372

We begin subtracting decimal fractions by writing the numbers in such a way that the commas are one below the other. We add a zero after the decimal point to the first number so that both fractions have three digits after the decimal point. Then we subtract, ignoring the comma. In the answer we remove the comma under the commas:

35,46 — 7,372 = 28,088.

To subtract a decimal fraction from a natural number, put a comma at the end and add the required number of zeros after the decimal point. Why do we subtract without taking into account the comma? In response, we remove the comma exactly under the commas:

45 — 7,303 = 37,698.

7) 17,256 — 4,756

We perform this example on subtracting decimal fractions in the same way. The result is a number with zeros after the decimal point at the end. We do not write them in the answer: 17.256 - 4.756 = 12.5.

Lesson topic: “Adding decimals”

Teacher 1st qualification category MBOUSOSH s. Terbuny : Kirikova Marina Alexandrovna

Class: 5

Lesson type: learning new material

Goals and tasks training session:

Educational :

Repeat addition of ordinary fractions; read and write decimal number; comparison of decimal numbers

Introduce the algorithm for adding decimals

Show how this algorithm is used to add decimals

Teach students how to add decimals

Educational:

Develop verbal-logical thinking, mathematical speech

Teach the ability to generalize and draw conclusions, apply knowledge in a new situation

Expanding students' knowledge about the world around them

Increase ICT competence of students

Develop an environmental culture

Educational:

Promote the development of interest in the subject

Cultivate perseverance to achieve the final result

Ability to work in groups (pairs), team

Promote the development of cognitive activity and hard work

Bring up careful attitude to nature

Instill love for our small Motherland

Equipment:

computer, screen, projector

Progress of the training session:

Stage 1. Organizational moment.

Checking readiness for the lesson.Organization of students’ emotional mood for communication and interaction in the process of using existing knowledge and skills.

Stage 2. Motivation.

This legend came from the depths of the Middle Ages. A German merchant asked for advice on where to educate his son. They answered him. If you want your son to know addition, subtraction and multiplication, they can teach this here in Germany. But so that he also knows division, it is better to send him to Italy. The professors there studied this operation well. As we can see, even simple arithmetic operations were quite complex. From those times, the Germans still have the saying “in die Bruche kommen” (literally: “to fall into fractions”). This meant finding oneself in a difficult position, which one found oneself in when carrying out division. Nowadays, such operations based on a different, Arabic system of notation for numbers and other algorithms have become much easier.Today we will work not only with decimal fractions, we will study and learn how to apply one of the algorithms for working with decimal fractions, but we will also talk about one of global problems modernity. Which one do you think? Do you think environmental problems are relevant for our area?

Stage 3. Updating knowledge.

Frontal conversation.

1) What numbers are called decimal fractions? Answer: A decimal is a number whose fractional denominator is 10, 100, 1000, etc., which is written using a comma (written first whole part, and then, separated by a comma, the numerator of the fractional part).

2) How can you change the number of decimal places in a decimal fraction? Answer: If you add a zero or discard the zero at the end of a decimal fraction, you get a fraction equal to the given one.

3) Can a natural number be represented as a decimal fraction? Answer: Yes. To do this, you need to put a comma after the last digit in the number and add the required number of zeros

Oral exercises.

1.Read the fraction: 1925.2016.

2.a) Round to the nearest thousand? (1925.202)

b) Round to the nearest tenth? (1925.2)

c) Round to units? (1925)

1925. What happened this year? (Date of formation of our school).

3.Name a number between 0.3 and 0.4

4.What natural number is contained between 89.9 and 90.1? (90, how old is our school)

5. Arrange the fractions in ascending order: 20.01; 20.001;20.1(20.001; 20.01;20.1). Write down the date of the lesson - 20.01

6. Equalize the number of digits after the decimal point 0.2;0.02; 0.002. What needs to be done for this?(0.200;0.020;0.002)

4. Setting the topic, goals and objectives of the lesson.

Pollution problem environment in our area – one of the most relevant.

Harmful substances are constantly being released into the atmosphere. In the Lipetsk region, about

2012 322.9 thousand tons;

2013 353.1 thousand tons;

2014 330 thousand tons;

2015 330 thousand tons harmful substances. Is the emission of harmful substances increasing or decreasing? What measures are being taken to improve the environment?

How many tons of harmful substances were released in two last year? (660 thousand tons) What did they do with the numbers? How to add natural numbers?

Can we find out how many thousand tons have entered the atmosphere over these years?

What do you need to know? (Rule for adding decimals)

How do we record a lesson for him? (Adding decimals)

Lesson objectives? (Learn to add decimals, find the meaning of expressions, solve problems)

What plan will we work on? (Let's study the rule. Consider examples of adding decimal fractions. Find the value of the expression containing the sum of decimal fractions)

5. Studying new material.

Calculate 24+32=…(56) How did you perform the addition? (Bitwise)

And now 2.4+3.2=...(2 +3=5=5.6) Is it convenient to add decimals this way? (No)

How else can you add decimals? (Bitwise)

2,4

3,2

.....

5,6

If the number of digits after the decimal point in a decimal fraction is different, then what to do in this case? (Equalize the number of digits after the decimal point and perform addition one by one.

2. Write them one below the other so that the comma is under the comma.

3. Perform addition (subtraction) without paying attention to the comma.

4. Place a comma under the comma in the answer.

Consider example 5, 2 + 1.13

Add up the decimal fractions
Strictly write the number below the number,
And keep all the commas,
Write them in a row, don’t forget!

How to conveniently record an action?

It is convenient to add decimal fractions in a column. Read rule p.195 yourself.

6.Primary consolidation.

№705(a,c,e) at the board

№705 (g,f) independently

№706 (c-1 option, d-2nd) Who is faster? Checking at the board.

№717(Oral).

Physical education minute

Let's return to the environmental problem and find out how many tons of harmful substances have entered the atmosphere over the past 4 years in the Lipetsk region.

(322.9+353.1+330+330) thousand tons = 1336 thousand tons - harmful substances

Answer: 1336 thousand tons.

7.Independent work (training) Reconciliation against the standard.

Calculate and fill out the table. Having completed all the tasks correctly, you will receive the word “ecology” translated from Greek

5,8+22,191

3,99+0,06

8,9021+0,68

2,7+1,35

0,769+42,389

129+9,72

4.05-i;43.158-i;27.991-f;9.5821-l;138.72-i

Answer: dwelling (house)

8.Repetition. Inclusion in the knowledge system

Find the mistake. What is broken, what are the rules for adding decimal fractions?

1)0,2+0,15=0,17;

2)1,9+2,7=4,8;

3)5,48+4,52=100

Information about homework: P.42; No. 706 (e, f); No. 717 (v. g); No. 719

9.Reflection

1) What task was set in the lesson? Did you manage to solve it?

2) What else do you need to do to learn how to add decimals?

3) Complete the sentence: I was... I learned in class... I learned...

4) Image globe posted on the board. Everyone should attach a happy or sad emoticon, arguing why that particular one.

5) Should we take care of our planet? What do you need to do for this?

Arithmetic calculations such as addition And subtracting decimals, are necessary in order to obtain the desired result when operating with fractional numbers. The particular importance of carrying out these operations is that in many areas of human activity the measures of many entities are represented precisely decimals. Therefore, to carry out certain actions with many objects of the material world, it is required fold or subtract exactly decimals. It should be noted that in practice these operations are used almost everywhere.

Procedures adding and subtracting decimals in its mathematical essence it is carried out almost exactly in the same way as similar operations for integers. When implementing it, the value of each digit of one number must be written under the value of a similar digit of another number.

Subject to the following rules:

First, it is necessary to equalize the number of those signs that are located after the decimal point;

Then you need to write the decimal fractions one below the other in such a way that the commas contained in them are located strictly below each other;

Carry out the procedure subtracting decimals in full accordance with the rules that apply to subtracting integers. In this case, you do not need to pay any attention to commas;

After receiving the answer, the comma in it must be placed strictly under those that are in the original numbers.

Operation adding decimals carried out in accordance with the same rules and algorithm as described above for the subtraction procedure.

Example of adding decimals

Two point two plus one hundredth plus fourteen point ninety-five hundredths equals seventeen point sixteen hundredths.

2,2 + 0,01 + 14,95 = 17,16

Examples of adding and subtracting decimals

Mathematical operations addition And subtracting decimals in practice they are used extremely widely, and they often relate to many objects of the material world around us. Below are some examples of such calculations.

Example 1

According to design estimates, the construction of a small production facility requires ten point five cubic meters of concrete. Using modern technologies construction of buildings, contractors, without compromising the quality characteristics of the structure, managed to use only nine point nine cubic meters of concrete for all work. The savings amount is:

Ten point five minus nine point nine equals zero point six cubic meter of concrete.

10.5 – 9.9 = 0.6 m3

Example 2

Engine mounted on old model car, consumes eight point two liters of fuel per hundred kilometers in the urban cycle. For the new power unit, this figure is seven point five liters. The savings amount is:

Eight point two liters minus seven point five liters equals zero point seven liters per hundred kilometers in urban driving.

8.2 – 7.5 = 0.7 l

The operations of adding and subtracting decimal fractions are used extremely widely, and their implementation does not pose any problems. In modern mathematics, these procedures have been worked out almost perfectly, and almost everyone has mastered them well since school.

Chapter 2 FRACTIONAL NUMBERS AND ACTIONS WITH THEM

§ 37. Addition and subtraction of decimal fractions

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

During addition and subtraction, decimal fractions are written in a “column” - one below the other, so that the digits of the same name are located under each other. So the comma will appear below the comma. Next, we perform the action in the same way as with natural numbers, not paying attention to commas. In the sum (or difference), we place a comma under the commas of the addends (or the commas of the minuend and subtractor).

Example 1: 37.982 + 4.473.

Explanation. 2 thousandths plus 3 thousandths equals 5 thousandths. 8 acres plus 7 acres equals 15 acres, or 1 tenth and 5 acres. We write down 5 acres, and remember 1 tenth, etc.

Example 2. 42.8 - 37.515.

Explanation. Since diminishing and subtrahend have different quantities decimal places, then you can add the required number of zeros in decreasing order. Figure out for yourself how the example was done.

Note that when adding and subtracting zeros, you don’t have to add them, but mentally imagine them in those places where there are no digit units.

When adding decimal fractions, the previously studied commutative and connecting properties of addition come true:

Entry level

1228. Count (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. Calculate:

1230. Count (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. Calculate:

1232. Calculate:

1233. There were 2.7 tons of sand on one machine, and 3.2 tons on the other. How much sand was on the two machines?

1234. Perform 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. Perform 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 the 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 flying carpet flew 17.4 km in 2 hours, and in the first hour it flew 8.3 km. How far did the magic carpet fly in the second hour?

1239. 1) Multiply the number 7.2831 by 2.423.

2) Reduce the number 5.372 by 4.47.

Intermediate level

1240. Solve the equations:

1) 7.2 + x = 10.31; 2) 5.3 - x = 2.4;

3) x - 2.8 = 1.72; 4) x + 3.71 = 10.5.

1241. Solve the equations:

1) x - 4.2 = 5.9; 2) 2.9 + x = 3.5;

3) 4.13 - x = 3.2; 4) x + 5.72 = 14.6.

1242. What is the most convenient way to add? Why?

4.2 + 8.93 + 0.8 = (4.2 + 8.93) + 0.8 or

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

1243. Count (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 meaning 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 meaning 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. From a metal pipe 7.92 m long, first 1.17 m was cut off, and then another 3.42 m. What is the length of the remaining pipe?

1247. The apples and the box weigh 25.6 kg. How many kilograms do the apples weigh if the empty box weighs 1.13 kg?

1248. Find the length of the broken line ABC , if AB = 4.7 cm and BC is 2.3 cm less than AB.

1249. One can contains 10.7 liters of milk, and the other contains 1.25 liters less. How much milk is in two cans?

1250.Calculate:

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. Calculate:

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 = 8.91, b = 0.13.

1253. The speed of a boat in still water is 17.2 km/h, and the speed of the current is 2.7 km/h. Find the speed of the boat with and against the current.

1254. Fill out the table:

Own speed, km/h	Speed currents, km/h	Downstream speed, km/h	Speed ​​against the current, km/h
13,1
17,2		18,5
12,35			10,85
		13,5
	1,65		12,95

1255. Find the missing numbers in the chain:

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

1257. Draw an arbitrary triangle, measure its sides in centimeters and find the perimeter of the triangle.

1258. On the segment AC we marked point B (Fig. 258).

1) Find AC if AB = 3.2 cm, BC = 2.1 cm;

2) find BC if AC = 12.7 dm, AB = 8.3 dm.

Rice. 257

Rice. 258

Rice. 259

1259. How many centimeters is the segment Is AB longer than segment CD (Fig. 259)?

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

1261. The base of an isosceles triangle is 8.2 cm, and the side is 2.1 cm less than the base. Find the perimeter of the triangle.

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

Sufficient level

1263. Write down a sequence of five numbers if:

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

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

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

1265. On the first day, tourists walked 8.3 km, which is 1.8 km more than on the second day, and 2.7 km less than on the third. How many kilometers did the tourists walk in three days?

1266. Perform 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. Perform addition, choosing a convenient calculation order:

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 numbers instead of asterisks:

1269. Put the following numbers in the cells to form correctly completed examples:

1270. Simplify the expression:

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

1271. Simplify the expression:

1) 8.42 + 3.17 - x; 2) 3.47 + y - 1.72.

1272. Find the pattern and write down the three occurrences of the numbers in the sequence:

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

1273. Solve the equations:

1) 13.1 - (x + 5.8) = 1.7;

2) (x - 4.7) - 2.8 = 5.9;

3) (y - 4.42) + 7.18 = 24.3;

4) 5.42 - (in - 9.37) = 1.18.

1274. Solve the equations:

1) (3.9 + x) - 2.5 = 5.7;

2) 14.2 - (6.7 + x) = 5.9;

3) (in - 8.42) + 3.14 = 5.9;

4) 4.42 + (y - 1.17) = 5.47.

1275. Find the value of an expression in a convenient way, using the properties of subtraction:

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 value of an expression in a convenient way, using the properties of subtraction:

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. Calculate by writing down these values ​​in 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 isosceles triangle is

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

1279. The speed of a freight train is 52.4 km/h, a passenger train is 69.5 km/h. Determine whether these trains are moving away or approaching each other and how many kilometers per hour if they left at the same time:

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

2) from two points, the distance between which is 300 km, and the passenger one catches up with the freight one;

1280. The speed of the first cyclist is 18.2 km/h, and the second is 16.7 km/h. Determine whether the cyclists are moving away or approaching each other and by how many kilometers per hour if they left at the same time:

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

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

3) from one point in opposite directions;

4) from one point in one direction.

1281. Calculate, answer rounded to hundredths:

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

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

1282. Calculate by writing down these values ​​in centners:

1) 8 ct - 319 kg;

2) 9 c 15 kg + 312 kg;

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

4) 5 t 2 c 13 kg + 7 t 3 c 7 kg.

1283. Calculate by writing down these values ​​in 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 isosceles triangle is

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 sides is 3.1 cm. Find the length of the side that is not equal to the given one.

1286. Three boxes contain 109.6 kg of tomatoes. The first and second boxes together contain 69.9 kg, and the second and third boxes contain 72.1 kg. How many kilograms of tomatoes are in each box?

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

1288. Find the numbers a and b in the chain:

High level

1289. Place “+” and “-” signs instead of asterisks so that the equality holds:

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 lent him 1.7 UAH, Dale gained 1.2 UAH. less than Chip's. How much money did Dale have at first?

1291. Two brigades are asphalting the highway and moving towards each other. When the first brigade paved 5.92 km of the highway, and the second - 1.37 km less, then 0.85 km remained before their meeting. How long was the section of highway that needed to be paved?

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

1) increase one of the terms by 3.7, and the other by 8.2;

2) increase one of the terms by 18.2, and decrease the other by 3.1;

3) reduce one of the terms by 7.4, and the other by 8.15;

4) increase one of the terms by 1.25, and decrease the other by 1.25;

5) increase one of the terms by 7.2, and decrease the other by 8.9?

1293. How will the difference change if:

1) decreasing decrease by 7.1;

2) decreasing increase by 8.3;

3) increase the deductible by 4.7;

4) reduce the deductible by 4.19?

1294. The difference between two numbers is 8.325. What is the new difference equal to if the diminishing difference is increased by 13.2 and the subtrahend is increased by 5.7?

1295. How will the difference change if:

1) increase the decreasing by 0.8, and the subtracting - by 0.5;

2) increase the decreasing by 1.7, and the subtracting by 1.9;

3) increase the decreasing by 3.1, and the subtractive decrease by 1.9;

4) decrease the diminishing by 4.2, and increase the subtrahend by 2.1?

Exercises to repeat

1296. Compare the meanings of 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. In the dining room there are two types of first courses, 3 types of second courses and 2 types of third courses. In how many ways can you choose a three-course lunch in this cafeteria?

1298. The perimeter of a rectangle is 50 dm. The length of the rectangle is 5 dm greater than the width. Find the sides of the rectangle.

1299. Write the largest decimal fraction:

1) with one decimal place, less than 10;

2) with two decimal places, less than 5.

1300. Write the smallest decimal fraction:

1) with one decimal place, greater than 6;

2) with two decimal places, greater than 17.

Home independent work № 7

2. Which of the inequalities is true:

A ) 2.3 > 2.31; B) 7.5< 7,49;

B ) 4.12 > 4.13; D) 5.7< 5,78?

3. 4,08 - 1,3 =

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

4. Write the decimal fraction 4.0701 as a mixed number:

5. Which of the rounding to hundredths is done correctly:

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 = 7.48.

A) 13.61; B) 1.35; B) 13.51; D) 12.61.

7. Which of the proposed equalities is correct:

A) 7 cm = 0.7 m; B) 7 dm2 = 0.07 m2;

V) 7 mm = 0.07 m; D) 7 cm3 = 0.07 m3?

8. Names of the largest natural number that does not exceed 7.0809:

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

9. How many numbers are there that can be put instead of an asterisk in the approximate equality 2.3 * 7 * 2.4 so that rounding to the nearest decimal is done correctly?

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

10. 4 a 3 m2 =

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

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

A) 3.08; B) 3.901; B) 3.699; D) 3.83.

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

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

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

Knowledge test tasks No. 7 (§34 - §37)

1. Compare decimal fractions:

1) 47.539 and 47.6; 2) 0.293 and 0.2928.

2. Perform addition:

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

3. Perform subtraction:

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

4. Round up to:

1) tenths: 4.597; 0.8342;

2) hundredths: 15.795; 14.134.

5. Express in kilometers and write as a decimal fraction:

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

6. The boat's own speed is 15.7 km/h, and the speed of the current is 1.9 km/h. Find the speed of the boat with and against the current.

7. On the first day, 7.3 tons of vegetables were delivered to the warehouse, which is 2.6 tons more than on the second day, and 1.7 tons less than on the third day. How many tons of vegetables were delivered to the warehouse in three days?

8. Find the meaning of the expression by choosing a convenient procedure:

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

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

10. Additional task. Write down all the numbers that can be put in place of * so that the inequality is approximated correctly:

1) 3,81*5 ≈3,82; 2) 7,4*6≈ 7,41.

11. Additional task. At what natural values n inequality 0.7< n < 4,2 и 2,7 < n < 8,9 одновременно являются правильными?