Addition of decimal numbers. Addition rule and subtraction of decimal fractions

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

Procedures addition and subtraction of decimal fractions in its mathematical essence, it is carried out in almost exactly the same way as analogous operations for integers. In its implementation, the value of each digit of one number must be written under the value of a similar digit of another number.

Submits to the following rules:

First, you need to make the equalization of the number of those signs that are located after the decimal point;

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

Carry out the procedure subtracting decimal fractions in full accordance with the rules that apply to the subtraction of integers. You don't need to pay any attention to the commas;

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

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

Example of adding decimal fractions

Two point two tenths 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 decimal fractions

Mathematical operations additions and subtracting decimal fractions 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 the design and estimate documentation, for the construction of a small production facility ten point five tenths of a cubic meter of concrete is required. Using modern technologies erection of buildings, to contractors without prejudice to quality characteristics the structures were used to carry out all the work only nine point nine tenths of a cubic meter of concrete. The amount of savings is:

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

10.5 - 9.9 = 0.6 m 3

Example 2

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

Eight point two liters minus seven point five liters is equal to zero point seven tenths of a liter per hundred kilometers in urban driving.

8.2 - 7.5 = 0.7L

The operations of addition and subtraction of decimal fractions are used extremely widely, and their implementation does not present any problems. In modern mathematics, these procedures are worked out almost perfectly, and almost everyone is fluent in them since school.

Like addition, subtracting decimal fractions depends on how the numbers are written correctly.

Decimal subtraction rule

1) COMMA COMMA!

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

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

3) Subtract the numbers, ignoring the comma.

4) Remove the comma under the commas.

Examples for subtracting decimal fractions.

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

2) 23,45 — 1,5

To subtract another from one decimal fraction, you need to write them down so that the commas are located exactly one below the other. Since 23.45 after the decimal point has two digits, and 1.5 has only one, we add zero to 1.5. After that, 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 start subtracting decimal fractions by writing them so that the commas are located exactly one under one. In the first number after the decimal point, there is one digit, in the second - 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, we remove the comma under the commas:

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

4) 2,8703 — 0,507

To subtract these decimal fractions, write them down so that the comma of the second number is located exactly below the comma of the first. In the first number after the decimal point there are four digits, in the second - three, so we supplement the second number after the decimal point with a zero at the end. After that, we subtract these numbers as usual natural numbers, excluding the comma. In the resulting result, write a comma under the commas:

2,8703 — 0,507 = 2,3663.

5) 35,46 — 7,372

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

35,46 — 7,372 = 28,088.

In order to subtract a decimal fraction from a natural number, put a comma in its entry at the end and add required amount zeros after the decimal point. Why subtract without taking into account the comma. In response, demolish the comma exactly below the commas:

45 — 7,303 = 37,698.

7) 17,256 — 4,756

We perform this example for subtracting decimal fractions in the same way. As a result, we got 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.

Is an addition of decimal fractions... In this article, we will look at the rules for adding finite decimal fractions, using examples, we will analyze how the addition of finite decimal fractions in a column is carried out, and also dwell on the principles of adding infinite periodic and non-periodic decimal fractions. In conclusion, let's dwell on the addition of decimal fractions with natural numbers, ordinary fractions and mixed numbers.

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

Page navigation.

General principles of adding decimal fractions

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 fractions). Thus, 0.43 + 3.7 = 43/100 + 37/10.

This completes the addition of the final decimal fractions.

Answer:

4,13 .

Now let's add periodic decimals to the discussion.

Example.

Add the final decimal 0.2 with the periodic decimal 0, (45).

Solution.

Then .

Answer:

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

Now let's dwell on the principle of adding infinite non-periodic decimal fractions.

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

When adding infinite non-periodic fractions, they are replaced with approximate values, that is, they are preliminarily rounded (see rounding numbers) to a certain level. By increasing the precision with which the approximate values of the original infinite non-periodic decimal fractions are taken, a more accurate value of the addition result is obtained. Thus, addition of infinite non-periodic decimal fractions is reduced to the addition of final decimal fractions.

Let's consider the solution of an example.

Example.

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

Solution.

Let's round the added decimal fractions to hundredths (we won't 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 it remains to add the final decimal fractions:.

Answer:

4,358…+11,11002244…≈15,47 .

In conclusion of this paragraph, we say that the addition of positive decimal fractions is characterized by all the properties of addition of natural numbers. That is, the combination property of addition allows you to unambiguously determine the addition of three and more decimal fractions, and the displacement property of addition allows you to rearrange the folded decimal fractions in places.

Column addition of decimal fractions

It is quite convenient to carry out the addition of final decimal fractions in a column. This method allows you to do without converting the added decimal fractions into fractions.

To execute column addition of decimal fractions, necessary:

write one fraction under the other so that the same digits are under each other, and the comma under the comma (for convenience, you can equalize the number of decimal places by attributing a certain number of zeros to one of the fractions on the right);
further, ignoring the commas, perform the addition in the same way as the addition of a column of natural numbers is performed;
put the decimal point in the resulting sum so that it is under the decimal points of the terms.

For clarity, consider an example of column addition of decimal fractions.

Example.

Add the decimal fractions 30.265 to 1,055.02597.

Solution.

Let's add the decimal fractions in a column.

First, let's equalize the number of decimal places in the added fractions. To do this, you need to add two zeros to the right in the fraction 30.265, and you get the fraction 30.26500 equal to it.

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

We carry out addition according to the rules of column addition, ignoring the commas:

It remains only to put a decimal point in the resulting number, after which the addition of decimal fractions in a column takes on a complete form:

Answer:

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

Adding decimal fractions with natural numbers

We will immediately announce rule for adding decimal fractions with natural numbers: to add the decimal 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 6, if you add the natural number 48 to it, we get the number 54. So 6.36 + 48 = 54.36.

Answer:

6,36+48=54,36 .

Adding Decimal Fractions with Fractions and Mixed Numbers

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

Example.

Add the decimal 0.45 to the fraction 3/8.

Solution.

Replace decimal 0.45 with an ordinary fraction:. After that, 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 obtained common fraction can be converted to decimal.

Adding decimal fractions is made according to the rules of addition to the column.

Decimal fractions are added in a column, like natural numbers, ignoring the commas.

In the final result, a comma is placed under the commas as in the original fractions.

Note! If in leading decimal fractions different number signs (digits) after the decimal point, then to the fraction in which there are fewer decimal places, you need to add the required number of zeros to equalize the number of decimal places in the fractions.

If there are not enough digits of the fractional part to the right of the addend or the reduced one, then on the right in the fractional part, you can add as many zeros (increase the digit capacity of the fractional part) as there are digits in the other addend or the reduced one.

Let's look at an example. Determine the sum of decimal fractions:

0,678 + 13,7 =

We equalize the number of decimal places in decimal fractions. Add 2 zeros to the right to the decimal 13,7 :

0,678 + 13,700 =

We write down the answer:

0,678 + 13,7 = 14,378

Basic rules for adding decimal fractions:

Equalize the number of decimal places.
Write decimal fractions under each other in such a way that the commas are under each other.
Perform the addition of decimal fractions, ignoring the commas, according to the rules for adding in a column of natural numbers.
Put a comma under the commas in response.

In written addition and subtraction of decimal fractions, the comma that separates the integer part from the fractional part must be located in the terms and the sum in one column (the comma under the comma from the condition record until the end of the calculation).

For example.Adding decimal fractions to a string:

243,625 + 24,026 = 200 + 40 + 3 + 0,6 + 0,02 + 0,005 + 20 + 4 + 0,02 + 0,006 = 200 + (40 + 20) + (3 + 4)+ 0,6 + (0,02 + 0,02) + (0,005 + 0,006) = 200 + 60 + 7 + 0,6 + 0,04 + 0,011 = 200 + 60 + 7 + 0,6 + (0,04 + 0,01) + 0,001 = 200 + 60 + 7 + 0,6 + 0,05 + 0,001 = 267,651.

Chapter 2 FRACTIONAL NUMBERS AND ACTIONS WITH THEM

§ 37. Addition and subtraction of decimal fractions

Decimal fractions are written in the same way 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" - under each other so that the digits of the same name are under each other. Thus, the comma will be below the comma. Next, we perform the action as with natural numbers, ignoring the commas. In the sum (or difference), we put a comma under the commas of the addends (or commas of the decreasing and the subtractor).

Example 1.37.982 + 4.473.

Explanation. 2 thousandths plus 3 thousandths equals 5 thousandths. 8 acres plus 7 acres is equal to 15 acres, or 1 tenth and 5 acres. We write down 5 acres, and we memorize 1 tenth, etc.

Example 2. 42.8 - 37.515.

Explanation. Since the decreasing and the subtracted have a different number of decimal places, it is possible to assign the required number of zeros to the decreasing one. Figure out on your own how the example is done.

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

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

First level

1228. Calculate (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. Numbers:

1230. Calculate (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. Numbers:

1232. Numbers:

1233. One car had 2.7 tons of sand, and the other - 3.2 tons. How much sand was there on two cars?

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 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 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 many flying carpet flew in the second hour?

1239.1) Multiply 7.2831 by 2.423.

2) Decrease the number 5.372 by 4.47.

Average 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. How is it more convenient 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 metal pipe 7.92 m long, they cut off 1.17 m first, and then another 3.42 m. What is the length of the remaining pipe?

1247. Apples together with the box weigh 25.6 kg. How many kilograms do apples weigh if an empty box weighs 1.13 kg?

1248. Find the Length of the Polyline ABC if AB = 4.7 cm, and BC is 2.3 cm less than AB.

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

1250. Numbers:

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 the boat in still water is 17.2 km / h, and the speed of the current is 2.7 km / h. Find the boat speed upstream and upstream.

1254. Fill in the table:

Own speed, km / h	Speed currents, km / h	Downstream speed, km / h	Speed upstream, 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 in centimeters the sides of the quadrilateral shown in Figure 257 and find its perimeter.

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

1258. Point B was designated on the segment AC (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 AB is longer than the 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 lateral 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.

Enough 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 one 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 contained 5.13 kg less apples than the first and second combined. How many kilograms of apples were in three boxes together?

1265. On the first day, tourists covered 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 such numbers in the cells so that correctly executed examples are formed:

1270. Simplify the expression:

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

1271. Simplify the expression:

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

1272. Find the regularity and write down the three numbers of 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 - (c - 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) (c - 8.42) + 3.14 = 5.9;

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

1275. Find the value of the 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 the 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 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 the freight train is 52.4 km / h, the speed of the passenger train is 69.5 km / h. Determine whether these trains are moving away or approaching 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 catches up with the freight one;

1280. The speed of the first cyclist is 18.2 km / h, and the speed of the second is 16.7 km / h. Determine whether the cyclists are moving away or approaching and 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 overtakes the second;

3) from one point in opposite directions;

4) from one point in one direction.

1281. Calculate, the answer is rounded to the nearest hundredth:

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

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

1282. Calculate, having written these values in centners:

1) 8 q - 319 kg;

2) 9 q 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, having written 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 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. There are 109.6 kg of tomatoes in three boxes. In the first and second boxes together 69.9 kg, and in the second and third 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. Replace the asterisks with the signs "+" and "-" so that the equality is fulfilled:

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 UAH 1.7, Dale got UAH 1.2. less than Chip. How much money did Dale have first?

1291. Two brigades pave the highway and move 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 were left before their meeting. How long was the section of the highway that needed to be asphalted?

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) decrease the decreasing by 7.1;

2) increase the decreasing by 8.3;

3) increase the deductible by 4.7;

4) decrease the deductible by 4.19?

1294. The difference between the two numbers is 8.325. What is the new difference if the decreasing one is increased by 13.2 and the deductible is increased by 5.7?

1295. How will the difference change if:

1) increase the decreasing by 0.8, and the deducted by 0.5;

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

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

4) decrease the decreasing by 4.2, and increase the deductible by 2.1?

Repetition exercises

1296. Compare the values of expressions without performing any 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. The dining room has two types of first courses, 3 types of second and 2 types of third courses. How many ways can you choose a three-course meal in this dining room?

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

1299. Write down the largest decimal fraction:

1) with one decimal place, less than 10;

2) with two decimal places, less than 5.

1300. Write down the smallest decimal fraction:

1) with one decimal place, more than 6;

2) with two decimal places, greater than 17.

Home independent work № 7

2. Which of the inequalities is correct:

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 down the decimal fraction 4.0701 with a mixed number:

5. Which of the rounding to the nearest hundredth is 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 = 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 are the largest natural number that does not exceed 7.0809:

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

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

A) 5; B) 0; AT 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 for a so that the 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.

Tasks for testing knowledge No. 7 (§34 - §37)

1. Compare decimal fractions:

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

2. Perform the addition:

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

3. Subtract:

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 it in kilometers and write it down in decimal:

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 current speed is 1.9 km / h. Find the boat speed upstream and upstream.

7. On the first day, 7.3 tons of vegetables were brought to the warehouse, which is 2.6 tons more than on the second, 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 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 inequalities 0.7< n < 4,2 и 2,7 < n < 8,9 одновременно являются правильными?