Subtraction of decimal fractions from a natural number. Actions with decimal fractions

Arithmetic computational actions like addition and subtraction decimal fractions required to receive the desired result by fractional numbers. The special importance of these operations is that in many areas of human activity, measures of many entities are presented decimal fractions. Therefore, to implement certain actions with many subjects material world Required to fold or subtract exactly decimal fractions. It should be noted that in practice these operations are used almost everywhere.

Procedures addition and subtraction of decimal fractions In terms of its mathematical essence, it is practically exactly the same as similar operations for integer numbers. When it is embedded, the value of each discharge of one number must be recorded under the value of a similar discharge of another number.

Submits to the following rules:

First, it is necessary to adjust the number of signs that are arranged after the comma;

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

Implement the procedure subtract decimal fractions In full accordance with those rules that act to subtract integers. It does not need to pay any attention to the comma;

After receiving a response, the comma in it needs to be put strictly under those available in the initial numbers.

Operation additions of decimal fractions It is carried out in accordance with the same rules and algorithm, which are described above for subtraction procedure.

An example of addition decimal fractions

Two whole two tenths plus one hundreds plus fourteen whole ninety five hundredths equals seventeen as many sixteen hundredths.

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

Examples of addition and subtraction of decimal fractions

Mathematical operations additions and subtract decimal fractions In practice, it is used extremely wide, and they often concern many objects of the environment of the material world. Below is several examples of such calculations.

Example 1.

According to design and estimate documentation, for the construction of a small production facility Ten more than five tenth of cubic meters of concrete is required. Using modern technologies building buildings, contractors without prejudice to qualitative characteristics The facilities managed to use only nine more than nine ten cubic meters of concrete for all works. Size of savings is:

Ten as many as five tenths minus nine more than nine tenths equal to zero as many as six tenth of the cubic meter of concrete.

10.5 - 9.9 \u003d 0.6 m 3

Example 2.

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

Eight more than two tenths liter minus seven whole five tenths of liters equal to zero as many as seven tenths liters per hundred kilometers of run in city traffic mode.

8.2 - 7.5 \u003d 0.7l

Operations of addition and deduction of decimal fractions are used extremely widely, and their implementation is no problem. In modern mathematics, these procedures are practically perfectly worked out, and they almost all speak well since school bench.

In this lesson, we will look at each of these operations separately.

Design of lesson

Addition of decimal fractions

As we know, the decimal fraction has a whole and fractional part. With the addition of decimal fractions, integers and fractional parts are detached separately.

For example, lay decimal fractions 3.2 and 5.3. Decimals more conveniently folded in a column.

We prepare first these two fractions in the column, while the whole parts must be under whole, and fractional under fractional. At school this requirement is called "Comma dressed".

We write the fraction in the column so that the comma is filled:

We begin to add fractional parts: 2 + 3 \u003d 5. We write on the top five in the fractional part of our answer:

Now we fold entire parts: 3 + 5 \u003d 8. Record the eight in the whole part of our answer:

Now separate the semicolons the whole part of the fractional. To do this, again, we observe the rule "Comma dressed":

Received an answer 8.5. It means expressions 3,2 + 5,3 equals 8.5

In fact, not everything is so simple, as it seems at first glance. Here, too, there are their underwater stones, which we will talk about.

Discharges in decimal fractions

In decimal fractions, as in ordinary numbers, there are their discharges. These are discharges of the tenths, the discharge of hundredths, the discharges of thousands. At the same time, the discharge begins after the comma.

The first digit after the comma is responsible for the discharge of the tenths, the second digit after the comma for the discharge of hundredths, the third digit after the comma for the discharge of thousands.

Discharges in decimal fractions keep some useful information. In particular, they report how much in decimal fractions of the tenths, hundredths and thousands of units.

For example, consider the decimal fraction 0,345

The position where the triple is called discharge of tenths

The position where the four is called discharge of hundredths

Position where the fide is called the discharge of thousands

Let's look at this picture. We see that in the discharge of the tenths there is a triple. This suggests that in the decimal fraction 0.345 contains three tenths.

If we fold the fractions, and then we get the original decimal fraction 0,345

It can be seen that at first we got the answer, but transferred it to the decimal fraction and got 0.345.

In addition, decimal fractions are complied with the same principles and rules as when the usual numbers are addition. The addition of decimal fractions occurs in discharges: the tenths are folded with tenth parts, hundredths with hundredths, thousandths with thousands.

Therefore, when adding decimal fractions, you need to comply with the rule "Comma dressed". The comma dive ensures that the very order in which the tenths add up with tits, hundredths with hundredths, thousands of thousands.

Example 1. Find the value of expression 1.5 + 3.4

First of all, we fold fractional parts 5 + 4 \u003d 9. We write down the nine in the fractional part of our answer:

Now we fold entire parts 1 + 3 \u003d 4. Record the fourth in the whole part of our answer:

Now separate the semicolons the whole part of the fractional. To do this, again, we comply with the "comma dive" rule:

Received an answer 4.9. So the value of the expression is 1.5 + 3.4 is 4.9

Example 2. Find an expression value: 3.51 + 1.22

We write in the column This expression, following the "comma dive" rule

First of all, we fold the fractional part, namely the hundredths of the 1 + 2 \u003d 3. We write down the top three in the hundredth of our answer:

Now we fold the tenths of 5 + 2 \u003d 7. We write a seven in the tenth of our answer:

Now we fold entire parts 3 + 1 \u003d 4. We write down the fourth in the whole part of our answer:

Separate the semicolons, the whole part of the fractional, observing the "comma-filled" rule:

Received the answer 4.73. So the value of expression 3.51 + 1,22 is 4.73

3,51 + 1,22 = 4,73

As in conventional numbers, with the addition of decimal fractions can occur. In this case, one digit is written in response, and the rest are transferred to the next discharge.

Example 3. Find an expression value 2.65 + 3,27

We write in the column This expression:

We fold the cells 5 + 7 \u003d 12. The number 12 does not fit in a hundredth of our response. Therefore, in the cell of the part, we write the number 2, and the unit is transferred to the next discharge:

Now we fold the tenths of 6 + 2 \u003d 8 plus a unit that got from the previous operation, we get 9. Record number 9 in the tenth of our answer:

Now we fold entire parts 2 + 3 \u003d 5. Record 5 in the whole part of our answer:

Received 5.92. So the value of the expression 2.65 + 3,27 is 5.92

2,65 + 3,27 = 5,92

Example 4. Find an expression value 9.5 + 2.8

We write in the column this expression

We fold fractional parts 5 + 8 \u003d 13. The number 13 does not fit in the fractional part of our answer, so first write the number 3, and the unit is transferred to the next discharge, more precisely carry it to the integer part:

Now we fold entire parts 9 + 2 \u003d 11 plus a unit that got from the previous operation, we get 12. Record number 12 in the whole part of our answer:

Separate the semicolons the whole part of fractional:

Received 12.3. Means the value of expression 9.5 + 2.8 is 12.3

9,5 + 2,8 = 12,3

When decaying decimal fractions, the number of digits after the comma in both fractions should be the same. If the numbers are missing, then these places in the fractional part are filled with zeros.

Example 5.. Find an expression value: 12,725 + 1.7

Before recording this expression in the column, we will make the number of numbers after the comma in both fractions the same. In the decimal fraction 12.725 after the semicolons, three digits, and in the fraction 1.7 only one. So in the fraction 1.7 at the end you need to add two zero. Then we get a fraction of 1,700. Now you can write this expression in the column and start computing:

We fold the thousands of parts 5 + 0 \u003d 5. Write the figure 5 in the thousandth part of our answer:

We fold the cellular parts 2 + 0 \u003d 2. Write on the number 2 in the hundredth of our answer:

We fold the tenths 7 + 7 \u003d 14. The number 14 does not fit in the tenth of our response. Therefore, first write the number 4, and the unit is transferred to the next discharge:

Now we fold entire parts 12 + 1 \u003d 13 plus a unit that got from the previous operation, we obtain 14. Record number 14 in the whole part of our answer:

Separate the semicolons the whole part of fractional:

Received the answer 14,425. So the value of expression 12,725 + 1,700 is 14,425

12,725+ 1,700 = 14,425

Subtraction decimal fractions

When subtracting decimal fractions, it is necessary to comply with the same rules as when adding: "comma dilated" and "equal number of numbers after a comma."

Example 1. Find the value of the expression 2.5 - 2.2

We record this expression in the column, following the comma duty rule:

Calculate the fractional part 5-2 \u003d 3. Write on the figure 3 in the tenth of our answer:

Calculate the whole part 2-2 \u003d 0. Record zero in the whole part of our answer:

Separate the semicolons the whole part of fractional:

Received 0.3. So the value of expression 2.5 - 2.2 is 0.3

2,5 − 2,2 = 0,3

Example 2. Find an expression value 7,353 - 3.1

In this expression, a different number of numbers after the comma. In the fraction 7.353 after the semicolons, three digits, and in the fraction 3.1 only one. So in the fraction 3.1 at the end you need to add two zero to make the number of numbers in both fractions the same. Then we get 3,100.

Now you can write this expression in the column and calculate it:

Received 4.253 response. Means the value of expression 7,353 - 3.1 is 4.253

7,353 — 3,1 = 4,253

As in conventional numbers, sometimes they will have to occupy a unit from a neighboring discharge, if the subtraction becomes impossible.

Example 3. Find an expression value 3.46 - 2.39

We subtract the hundredth parts 6-9. From the number 6 not to subtract the number 9. Therefore, you need to take a unit from a neighboring discharge. Having taught the unit in the neighboring discharge number 6 refers to the number 16. Now you can calculate the cells of the cells 16-9 \u003d 7. We write down a seven in a hundredth of our answer:

Now we will deduct the tenths. Since we took in the discharge of the tenths of one unit, then the figure that was located there decreased by one unit. In other words, in the discharge of the tenths no longer digit 4, and the figure 3. I calculate the tenths 3-3 \u003d 0. Write zero in the tenth of our answer:

Now we will deduct the whole parts 3-2 \u003d 1. We write down the unit in the whole part of our answer:

Separate the semicolons the whole part of fractional:

Received the answer 1.07. So the value of expression 3,46-2.39 is 1.07

3,46−2,39=1,07

Example 4.. Find an expression value 3-1.2

In this example, a decimal fraction is deducted from an integer. We write this expression by the column so that whole part Decimal fraction 1,23 turned out to be at number 3

Now we will make the number of numbers after the comma are the same. For this, after the number 3, we will put a comma and add one zero:

Now we will deduct the tenths: 0-2. From zero not subtract number 2. Therefore, you need to take a unit from a neighboring discharge. Taking a unit in a neighboring discharge, 0 refers to the number 10. Now you can calculate the tenths 10-2 \u003d 8. Write the eight in the tenth of our answer:

Now deduct the whole parts. Previously, the number 3 was located in the whole, but we took it one unit. As a result, it appealed to the number 2. Therefore, from 2, we subtract 1. 2-1 \u003d 1. We write down the unit in the whole part of our answer:

Separate the semicolons the whole part of fractional:

Received an answer 1.8. Means the value of expression 3-1,2 is 1.8

Multiplying decimal fractions

Multiplying decimal fractions is simple and even fascinating. In order to multiply decimal fractions, you need to multiply them as conventional numbers, not paying attention to the commas.

Having received the answer, it is necessary to separate the comma to the whole part of the fractional. To do this, it is necessary to calculate the number of numbers after the comma in both fractions, then in response to count the right of the same number and put a comma.

Example 1. Find the value of the expression 2.5 × 1.5

Move these decimal fractions as ordinary numbers, not paying attention to the commas. In order not to pay attention to commas, it is possible to present that they are generally absent:

We received 375. In this regard, it is necessary to separate the semicolons from the fractional. To do this, it is necessary to calculate the number of digits after the comma in fractions 2.5 and 1.5. In the first fraction after the semicolons, one digit, in the second fraction, too alone. Total two digits.

Returning to the number 375 and begin to move right to left. We need to count two digits to the right and put a comma:

Received the answer 3.75. Means the value of the expression 2.5 × 1.5 is 3.75

2.5 × 1 5 \u003d 3.75

Example 2. Find an expression value 12.85 × 2.7

Alternate these decimal fractions, not paying attention to the commas:

We received 34695. In this regard, it is necessary to separate the comma to the whole part of the fractional. To do this, it is necessary to calculate the number of digits after the comma in the fractions of 12.85 and 2.7. In the fraction 12.85 after the semicolons, two digits, in the fraction 2.7 one digit - total three digits.

Returning to the number 34695 and begin to move right to left. We need to count three digits to the right and put a comma:

Received the answer 34.695. Means the value of expression 12.85 × 2.7 is 34,695

12.85 × 2,7 \u003d 34,695

Multiplication of decimal fraction on the usual number

Sometimes there are situations when you need to multiply the decimal fraction to the usual number.

In order to multiply the decimal fraction and the usual number, you need to multiply them, not paying attention to the comma in the decimal fraction. Having received the answer, it is necessary to separate the comma to the whole part of the fractional. To do this, it is necessary to calculate the number of numbers after the comma in the decimal fraction, then in response to refer to the right of the same number and put the comma.

For example, multiply 2.54 to 2

We multiply the decimal fraction 2.54 to the usual number 2, not paying attention to the comma:

They received the number 508. In this regard, it is necessary to separate the semicolons the whole part of the fractional. To do this, it is necessary to calculate the number of numbers after the comma in the fraction 2.54. In the fraction 2.54 after the semicolons two digits.

Returning to the number 508 and begin to move right to left. We need to count two digits to the right and put a comma:

Received 5.08. Means the value of the expression 2.54 × 2 is 5.08

2.54 × 2 \u003d 5.08

Multiplying decimal fractions by 10, 100, 1000

The multiplication of decimal fractions by 10, 100 or 1000 is performed in the same way as the multiplication of decimal fractions into conventional numbers. You need to perform multiplication, not paying attention to the comma in the decimal fraction, then in response to separate the whole part of the fractional, squeezing the right of the same number as the numbers were after the semicolons in the decimal fraction.

For example, multiply 2.88 to 10

Multiply decimal fraction 2.88 by 10, not paying attention to the comma in decimal fraction:

Received 2880. In this regard, it is necessary to separate the comma to the whole part of the fractional. To do this, it is necessary to calculate the number of numbers after the semicolon in the fraction 2.88. We see that in the fraction 2.88 after the semicolons two digits.

Returning to the number 2880 and begin to move right to left. We need to count two digits to the right and put a comma:

Received the answer 28.80. We will throw the last zero - we get 28.8. Means the value of the expression 2.88 × 10 is 28.8

2.88 × 10 \u003d 28.8

There is a second way of multiplying decimal fractions by 10, 100, 1000. This method is much easier and more convenient. It lies in the fact that the comma in the decimal fraction moves to the right to so many numbers as zeros in the multiplier.

For example, we solve the previous example of 2.88 × 10 in this way. Do not lead to any calculations, we immediately look at the multiplier 10. We are interested in how much zeros in it. We see that in it one zero. Now in the fraction 2,88 move the comma to the right to one digit, we get 28.8.

2.88 × 10 \u003d 28.8

Let's try to multiply 2.88 per 100. We immediately look at the multiplier 100. We are interested in how much zeros in it. We see that in it two zero. Now in the twist 2,88 move the comma to the right into two digits, we get 288

2.88 × 100 \u003d 288

Let's try to multiply 2.88 per 1000. We immediately look at the factor of 1000. We are interested in how much zeros in it. We see that in it three zero. Now in the twist 2,88 move the comma to the right to three digits. There are no third digits there, so we finish another zero. As a result, we get 2880.

2.88 × 1000 \u003d 2880

Multiplying decimal fractions by 0.1 0.01 and 0.001

The multiplication of decimal fractions by 0.1, 0.01 and 0.001 occurs in the same way as the multiplication of the decimal fraction for a decimal fraction. It is necessary to multiply the fractions as conventional numbers, and in response to put a comma, counting so much the numbers on the right, how many digits after a comma in both fractions.

For example, multiply 3.25 to 0.1

We multiply these fractions, as ordinary numbers, not paying attention to the commas:

Received 325. In this regard, it is necessary to separate the semicolons from the fractional. To do this, it is necessary to calculate the number of numbers after the comma in the frauds 3.25 and 0.1. In the fraction 3.25 after the semicolons, two digits, in the fraction 0.1 one digit. Total three numbers.

We return to the number 325 and begin to move right to left. We need to count three digits to the right and put a comma. After counting the three digits, we discover that the numbers are over. In this case, you need to add one zero and put a comma:

Received 0.325. So the value of expression is 3.25 × 0.1 is 0.325

3.25 × 0.1 \u003d 0.325

There is a second method of multiplication of decimal fractions by 0.1, 0.01 and 0.001. This method is much easier and more convenient. It lies in the fact that the comma in decimal fraction moves to the left of so many numbers as zeros in the multiplier.

For example, we solve the previous example of 3.25 × 0.1 in this way. Do not lead to any calculations immediately look at the multiplier of 0.1. We are interested in how much zeros in it. We see that in it one zero. Now in the fraction 3,25 move the comma left to one digit. After moving the comma on one digit to the left, we see that there are no more numbers before the triple. In this case, add one zero and put the comma. As a result, we get 0.325

3.25 × 0.1 \u003d 0.325

Let's try to multiply 3.25 by 0.01. We immediately look at the multiplier of 0.01. We are interested in how much zeros in it. We see that in it two zero. Now in the fraction 3,25 move the comma to the left into two digits, we get 0.0325

3.25 × 0,01 \u003d 0,0325

Let's try to multiply 3.25 by 0.001. We immediately look at the multiplier of 0.001. We are interested in how much zeros in it. We see that in it three zero. Now in the fraction 3,25 move the comma to the left of three digits, we get 0.00325

3.25 × 0.001 \u003d 0.00325

It is impossible to confuse the multiplication of decimal fractions by 0.1, 0.001 and 0.001 with multiplication by 10, 100, 1000. Typical error Most people.

When multiplying 10, 100, 1000, the comma is transferred to the right to the same number how many zeros in the multiplier.

And with multiplication by 0.1, 0.01 and 0.001, the comma is transferred to the left for the same number how many zeros in the multiplier.

If at first it is difficult to remember, you can use the first method in which multiplication is performed as with conventional numbers. In response, it will be necessary to separate the whole part of the fractional, counting the right of the same number as numbers after the comma in both fractions.

Dividing a smaller number to more. Advanced level.

In one of the previous lessons, we said that when dividing a smaller number, the fraction was greater, in the numerator of which is divisible, and in the denominator - a divider.

For example, to divide one apple for two, you need to write 1 in the numerator (one apple), and write 2 in the denominator (two friends). As a result, we will get a fraction. So each friend will get on the apple. In other words, half of the apple. Fraction is the answer to the task "How to divide one apple for two"

It turns out that it is possible to solve this problem and further if divided 1 at 2. After all, a fractional feature in any fraction means division, which means that this division is allowed. But how? We are accustomed to the fact that Delimi is always more divisor. And here, on the contrary, a divided less divider.

Everything will become clear if you remember that the fraction means crushing, division, separation. And therefore, the unit can be fragmented as many parts, and not only into two parts.

When dividing a smaller number, a decimal fraction is greater, in which the whole part will be 0 (zero). The fractional part can be any.

So, we divide 1 to 2. I will solve this example:

The unit is simply not divided into two units. If you ask a question "How many twists in unity" , then the answer will be 0. Therefore, in private, write 0 and put the comma:

Now, as usual, we multiply the private on the divider to pull out the residue:

The moment came when the unit can be crushed into two parts. To do this, to the right of the received units add another zero:

Received 10. We divide 10 to 2, we get 5. Write on the top five in the fractional part of our answer:

Now pull out the last residue to complete the calculation. Multiply 5 to 2, we get 10

Received 0.5. So the fraction is equal to 0.5

Half of the apple can be recorded and with a decimal fraction 0.5. If you fold these two halves (0.5 and 0.5), we again get the original one-piece apple:

This moment can also be understood if you represent how 1 cm is divided into two parts. If 1 centimeter is divided into 2 parts, then it turns out 0.5 cm

Example 2. Find an expression value 4: 5

How many tops in the fourth? Not at all. We write in private 0 and put the comma:

We multiply 0 to 5, we get 0. Record zero under the fourth. Immediately deduct this zero from the divide:

Now let's start crushing (divide) the fourth on 5 parts. To do this, to the right of 4 add zero and divide 40 to 5, we get 8. Write the eight in private.

Complete an example, multiplying 8 to 5, and receiving 40:

Received 0.8. So the value of expression 4: 5 is 0.8

Example 3. Find an expression value 5: 125

How many numbers 125 in the five? Not at all. We write 0 in private and put a comma:

We multiply 0 to 5, we get 0. Write 0 under the top five. Immediately subtract 0 from the top five

Now let's start crushing (divide) the top five5 parts. To do this, to the right of this five watering zero:

Delim 50 to 125. How many numbers 125 are among 50? Not at all. So in private again write 0

Multiply 0 to 125, we get 0. We write this zero under 50. Immediately deduct 0 out of 50

Now we divide the number 50 to 125 parts. To do this, to the right of 50, we write another zero:

We divide 500 to 125. How many numbers 125 are among 500. Among the 500 four numbers 125. Write the fourth in private:

Complete an example, multiplying 4 to 125, and receiving 500

Received 0.04. So the value of expression 5: 125 is 0.04

Division of numbers without residue

So, we put a comma in private after the unit, thereby pointing out that the division of integral parts is over and we proceed to the fractional part:

I add zero to the residue 4

Now we divide 40 to 5, we get 8. Record eight in private:

40-40 \u003d 0. Received 0 in the remainder. So division is fully completed. When dividing 9 on 5, a decimal fraction is obtained 1.8:

9: 5 = 1,8

Example 2.. Split 84 by 5 without a residue

At first we divide 84 to 5 as usual with the residue:

Received in private 16 and another 4 in the remainder. Now we divide this residue by 5. We put in a private comma, and I add 4 to the residue 4

Now we divide 40 to 5, we get 8. We write to the eight in the private after the comma:

and complete the example, checking whether there is still the residue:

Decimal decimal fraction on the usual number

Decimal fraction, as we know consists of a whole and fractional part. When dividing decimal fractions to the usual number, first of all, it is necessary:

• split the whole part of the decimal fraction on this number;
• after the whole part is divided, you need to immediately put a comma in a private immediately and continue the calculation as in the usual division.

For example, we divide 4.8 to 2

We write this example to the corner:

Now we divide the whole part on 2. Four divided into two will be two. We write down the two in private and immediately put the comma:

Now I multiply the private on the divider and see whether there is a belt from division:

4-4 \u003d 0. The residue is zero. Zero not yet written, because the solution is not completed. Next, continue to calculate as in the usual division. Demolish 8 and divide it on 2

8: 2 \u003d 4. Record the fourth in private and immediately multiply it on the divider:

Received a response 2.4. The value of 4.8: 2 expression is 2.4

Example 2. Find an expression value 8,43: 3

We divide 8 to 3, we get 2. Immediately put the comma after twos:

Now I multiply the private on the divider of 2 × 3 \u003d 6. We write a six-eight seventh and find the residue:

We divide 24 to 3, we get 8. Record the eight in private. Immediately multiply it on the divider to find the balance of division:

24-24 \u003d 0. The residue is zero. Zero not yet written. We demolish the last three of the divide and divide to 3, we get 1. Immediately multiply 1 to 3 to complete this example:

Received the answer 2.81. Means the value of expression 8.43: 3 is 2.81

Decimal decimal fraction for decimal fraction

To divide the decimal fraction to the decimal fraction, it is necessary to transfer comma to the right to the same number in a divider, and then they are after the comma in the divider, and then make division to the usual number.

For example, we divide 5.95 by 1.7

We write this expression

Now in divide and in the divider, we will move the comma to the right to the same number as they are after the comma in the divider. In the divider after a comma one digit. So we must in divide and in the divider move the comma to the right to one digit. Transfer:

After transferring the comma to the right to one digit, the decimal fraction 5,95 turned into a shot 59.5. And the decimal fraction 1.7 after the transfer of the comma to the right to one digit appealed to the usual number 17. And how to share the decimal fraction to the usual number we already know. Further computation is not much difficult:

The comma is transferred to the right to facilitate division. This is allowed due to the fact that when multiplying or dividing the divide and divider on the same number, the private does not change. What does it mean?

This is one of interesting features division. It is called the property of private. Consider the expression 9: 3 \u003d 3. If in this expression, the divider and divider multiply or divided into one and the same number, then the private 3 will not change.

Let's multiply divide and divider for 2, and let's see what happens from this:

(9 × 2): (3 × 2) \u003d 18: 6 \u003d 3

As can be seen from the example, the private has not changed.

The same thing happens when we transfer the comma in Delim and in the divider. In the previous example, where we divided 5.91 by 1.7, we were transferred in divide and divider to the comma on one digit to the right. After the transfer of the comma, the shot 5.91 was transformed into a fraction 59.1 and the fraction 1.7 was transformed into a normal number 17.

In fact, in this process, multiplication took place at 10. That's how it looked:

5.91 × 10 \u003d 59.1

Therefore, on the number of numbers after the comma in the divider, it depends on what the divider and divider will be multiplied. In other words, on the number of numbers after a comma in the divider, it will depend on how many numbers in the division and in the comma divider will be transferred to the right.

Decimal decimal fraction 10, 100, 1000

The division of decimal fractions on 10, 100, or 1000 is carried out in the same way as. For example, we split 2.1 to 10. I will solve this example:

But there is a second way. He is more easy. The essence of this method is that the comma in division is transferred to the left of so many numbers as zeros in the divider.

I decide the previous example in this way. 2.1: 10. We look at the divider. We are interested in how much zeros in it. We see that there is one zero. So in Delima 2.1 you need to move the comma to the left per digit. We transfer the comma to the left to one digit and see that there are no more numbers left. In this case, in front of the digit, add another zero. In the end we get 0.21

Let's try to divide 2.1 per 100. Among the 100 two zero. So in Delim 2.1 it is necessary to transfer the comma to the left into two digits:

2,1: 100 = 0,021

Let us try to divide 2.1 per 1000. Among 1000 three zero. So in Delima 2.1 it is necessary to transfer the comma to the left of three digits:

2,1: 1000 = 0,0021

Decision decimal fraction 0.1, 0,01 and 0.001

Decision decimal fraction 0.1, 0.01, and 0.001 is carried out in the same way as. In Delim and in the divider, you need to transfer the comma to the right to so many numbers as they are after the comma in the divider.

For example, we divide 6.3 to 0.1. First of all, we will transfer commas in divide and in the divider to the right on the same number as they are after the comma in the divider. In the divider after a comma one digit. So we transfer commas in divide and in the divider to the right to one digit.

After transferring the comma to the right to one digit, the decimal fraction 6.3 turns into a normal number 63, and the decimal fraction 0.1 after transferring the comma to the right to one digit turns into one. And divided 63 to 1 is very simple:

So the value of expression 6.3: 0,1 is 63

But there is a second way. He is more easy. The essence of this method is that the comma in division is transferred to the right to so many numbers as zeros in the divider.

I decide the previous example in this way. 6.3: 0.1. We look at the divider. We are interested in how much zeros in it. We see that there is one zero. So in divide 6.3 you need to transfer the comma to the right to one digit. We carry the comma to the right to one digit and get 63

Let us try to divide 6.3 to 0.01. In the divider 0.01 two zero. So in divide 6.3 it is necessary to transfer the comma to the right into two digits. But in division after the comma, only one digit. In this case, at the end you need to add one more zero. As a result, we get 630

Let's try to divide 6.3 to 0.001. In the divider 0.001 three zero. So in divide 6.3 it is necessary to transfer the comma to the right to three digits:

6,3: 0,001 = 6300

Tasks for self-decisions

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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.

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.

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?