1. The property of dividing two equal natural numbers:
If a natural number is divided by its equal number, the result is one.
It remains to give a couple of examples. The quotient of the natural number 405 divided by its equal number 405 is 1; The result of dividing 73 by 73 is also 1.
2. Property of dividing a natural number by one:
The result of dividing a given natural number by one is that natural number.
Let us write down the formulated property of division in literal form: a: 1 = a.
Let's give examples. The quotient of the natural number 23 divided by 1 is the number 23, and the result of dividing the natural number 10,388 by one is the number 10,388.
3. Division of natural numbers does not have the commutative property.
If the dividend and the divisor are equal natural numbers, then due to the property of dividing equal natural numbers, discussed in the first paragraph of this article, we can swap them. In this case, the result of division will be the same natural number 1.
In other words, if the dividend and the divisor are equal natural numbers, then in this case division has the commutative property. 5: 5 = 1 and 5: 5 = 1
In other cases, when the dividend and the divisor are not equal natural numbers, the commutative property of division does not apply.
So, in general, division of natural numbers does NOT have the commutative property.
Using letters, the last statement is written as a: b ≠ b: a, where a and b are some natural numbers, and a ≠ b.
4. The property of dividing the sum of two natural numbers by a natural number:
dividing the sum of two natural numbers by a given natural number is the same as adding the quotients of dividing each term by a given natural number.
Let's write this property of division using letters. Let a, b and c be natural numbers such that a can be divided by c and b can be divided by c, then (a + b) : c = a: c + b: c. On the right side of the written equality, division is performed first, followed by addition.
Let us give an example that confirms the validity of the property of dividing the sum of two natural numbers by a given natural number. Let us show that the equality (18 + 36) : 6 = 18: 6 + 36: 6 is correct. First, let's calculate the value of the expression from the left side of the equality. Since 18 + 36 = 54, then (18 + 36) : 6 = 54: 6. From the multiplication table of natural numbers we find 54: 6 = 9. We proceed to calculating the value of the expression 18:6+36:6. From the multiplication table we have 18: 6 = 3 and 36: 6 = 6, therefore 18: 6 + 36: 6 = 3 + 6 = 9. Therefore, the equality (18 + 36) : 6 = 18: 6 + 36: 6 is correct .
5. The property of dividing the difference of two natural numbers by a natural number:
dividing the difference of two numbers by a given number is the same as subtracting from the quotient of the minuend and the given number the quotient of the subtrahend and the given number.
Using letters, this property of division can be written as follows: (a - b) : c = a: c - b: c, where a, b and c are natural numbers such that a is greater than or equal to b, and also both a and b can be divided by c.
As an example confirming the property of division under consideration, we will show the validity of the equality (45 - 25) : 5 = 45: 5 - 25: 5. Since 45 - 25 = 20 (if necessary, study the material in the article subtracting natural numbers), then (45 - 25) : 5 = 20: 5. Using the multiplication table, we find that the resulting quotient is equal to 4. Now let’s calculate the value of the expression 45: 5 - 25: 5, which is on the right side of the equality. From the multiplication table we have 45: 5 = 9 and 25: 5 = 5, then 45: 5 - 25: 5 = 9 - 5 = 4. Therefore, the equality (45 - 25) : 5 = 45: 5 - 25: 5 is true .
6. The property of dividing the product of two natural numbers by a natural number:
the result of dividing the product of two natural numbers by a given natural number that is equal to one of the factors is equal to the other factor.
Here is the literal form of this division property: (a · b) : a = b or (a · b) : b = a, where a and b are some natural numbers.
Although mathematics seems difficult to most people, it is far from true. Many mathematical operations are quite easy to understand, especially if you know the rules and formulas. So, knowing the multiplication table, you can quickly multiply in your head. The main thing is to constantly train and not forget the rules of multiplication. The same can be said about division.
Let's look at the division of integers, fractions and negatives. Let's remember the basic rules, techniques and methods.
Division operation
Let's start, perhaps, with the very definition and name of the numbers that participate in this operation. This will greatly facilitate further presentation and perception of information.
Division is one of the four basic mathematical operations. Its study begins in elementary school. It is then that the children are shown the first example of dividing a number by a number and the rules are explained.
The operation involves two numbers: the dividend and the divisor. The first is the number that is being divided, the second is the number that is being divided by. The result of division is the quotient.
There are several notations for writing this operation: “:”, “/” and a horizontal bar - writing in the form of a fraction, when the dividend is at the top, and the divisor is below, below the line.
Rules
When studying a particular mathematical operation, the teacher is obliged to introduce students to the basic rules that they should know. True, they are not always remembered as well as we would like. That's why we decided to refresh your memory a little on the four fundamental rules.
Basic rules for dividing numbers that you should always remember:
1. You cannot divide by zero. This rule should be remembered first.
2. You can divide zero by any number, but the result will always be zero.
3. If a number is divided by one, we get the same number.
4. If a number is divided by itself, we get one.
As you can see, the rules are quite simple and easy to remember. Although some may forget such a simple rule as impossibility or confuse the division of zero by a number with it.
per number
One of the most useful rules is a sign that determines the possibility of dividing a natural number by another without a remainder. Thus, the signs of divisibility by 2, 3, 5, 6, 9, 10 are distinguished. Let us consider them in more detail. They make it much easier to perform operations on numbers. We also give an example for each rule of dividing a number by a number.
These rules-signs are quite widely used by mathematicians.
Test for divisibility by 2
The easiest sign to remember. A number that ends in an even digit (2, 4, 6, 8) or 0 is always divisible by two. Quite easy to remember and use. So, the number 236 ends in an even digit, which means it is divisible by two.
Let's check: 236:2 = 118. Indeed, 236 is divisible by 2 without a remainder.
This rule is best known not only to adults, but also to children.
Test for divisibility by 3
How to correctly divide numbers by 3? Remember the following rule.
A number is divisible by 3 if the sum of its digits is a multiple of three. For example, let's take the number 381. The sum of all digits will be 12. This is three, which means it is divisible by 3 without a remainder.
Let's also check this example. 381: 3 = 127, then everything is correct.
Divisibility test for numbers by 5
Everything is simple here too. You can divide by 5 without a remainder only those numbers that end in 5 or 0. For example, let’s take numbers such as 705 or 800. The first ends in 5, the second in zero, therefore they are both divisible by 5. This is one one of the simplest rules that allows you to quickly divide by a single-digit number 5.
Let's check this sign using the following examples: 405:5 = 81; 600:5 = 120. As you can see, the sign works.
Divisibility by 6
If you want to find out whether a number is divisible by 6, then you first need to find out whether it is divisible by 2, and then by 3. If so, then the number can be divided by 6 without a remainder. For example, the number 216 is divisible by 2 , since it ends with an even digit, and with 3, since the sum of the digits is 9.
Let's check: 216:6 = 36. The example shows that this sign is valid.
Divisibility by 9
Let's also talk about how to divide numbers by 9. The sum of digits whose divisible by 9 is divided by this number. Similar to the rule of dividing by 3. For example, the number 918. Let's add all the digits and get 18 - a number that is a multiple of 9. So, it divisible by 9 without a remainder.
Let's solve this example to check: 918:9 = 102.
Divisibility by 10
One last sign to know. Only those numbers that end in 0 are divisible by 10. This pattern is quite simple and easy to remember. So, 500:10 = 50.
That's all the main signs. By remembering them, you can make your life easier. Of course, there are other numbers for which there are signs of divisibility, but we have highlighted only the main ones.
Division table
In mathematics, there is not only a multiplication table, but also a division table. Once you learn it, you can easily perform operations. Essentially, a division table is a reverse multiplication table. Compiling it yourself is not difficult. To do this, you should rewrite each line from the multiplication table in this way:
1. Put the product of the number in first place.
2. Put a division sign and write down the second factor from the table.
3. After the equal sign, write down the first factor.
For example, take the following line from the multiplication table: 2*3= 6. Now we rewrite it according to the algorithm and get: 6 ÷ 3 = 2.
Quite often, children are asked to create a table on their own, thus developing their memory and attention.
If you don’t have time to write it, you can use the one presented in the article.
Types of division
Let's talk a little about the types of division.
Let's start with the fact that we can distinguish between division of integers and fractions. Moreover, in the first case we can talk about operations with integers and decimals, and in the second - only about fractional numbers. In this case, a fraction can be either the dividend or the divisor, or both at the same time. This is due to the fact that operations on fractions are different from operations on integers.
Based on the numbers that participate in the operation, two types of division can be distinguished: into single-digit numbers and into multi-digit ones. The simplest is division by a single digit number. Here you will not need to carry out cumbersome calculations. In addition, a division table can be a good help. Dividing by other - two-, three-digit numbers - is harder.
Let's look at examples for these types of division:
14:7 = 2 (division by a single digit number).
240:12 = 20 (division by a two-digit number).
45387: 123 = 369 (division by a three-digit number).
The last one can be distinguished by division, which involves positive and negative numbers. When working with the latter, you should know the rules by which a result is assigned a positive or negative value.
When dividing numbers with different signs (the dividend is a positive number, the divisor is negative, or vice versa), we get a negative number. When dividing numbers with the same sign (both the dividend and the divisor are positive or vice versa), we get a positive number.
For clarity, consider the following examples:
Division of fractions
So, we have looked at the basic rules, given an example of dividing a number by a number, now let’s talk about how to correctly perform the same operations with fractions.
Although dividing fractions may seem like a lot of work at first, working with them is actually not that difficult. Dividing a fraction is done in much the same way as multiplying, but with one difference.
In order to divide a fraction, you must first multiply the numerator of the dividend by the denominator of the divisor and record the resulting result as the numerator of the quotient. Then multiply the denominator of the dividend by the numerator of the divisor and write the result as the denominator of the quotient.
It can be done simpler. Rewrite the divisor fraction by swapping the numerator with the denominator, and then multiply the resulting numbers.
For example, let's divide two fractions: 4/5:3/9. First, let's turn the divisor over and get 9/3. Now let's multiply the fractions: 4/5 * 9/3 = 36/15.
As you can see, everything is quite easy and no more difficult than dividing by a single-digit number. The examples are not easy to solve if you do not forget this rule.
conclusions
Division is one of the mathematical operations that every child learns in elementary school. There are certain rules that you should know, techniques that make this operation easier. Division can be with or without a remainder; there can be division of negative and fractional numbers.
It is quite easy to remember the features of this mathematical operation. We have discussed the most important points, looked at more than one example of dividing a number by a number, and even talked about how to work with fractions.
If you want to improve your knowledge of mathematics, we advise you to remember these simple rules. In addition, we can advise you to develop memory and mental arithmetic skills by doing mathematical dictations or simply trying to verbally calculate the quotient of two random numbers. Believe me, these skills will never be superfluous.
Let's consider the concept of division in the problem:
There were 12 apples in the basket. Six children sorted the apples. Each child got the same number of apples. How many apples does each child have?
Solution:
We need 12 apples to divide among six children. Let's write down problem 12:6 mathematically.
Or you can say it differently. What number must the number 6 be multiplied by to get the number 12? Let's write the problem in the form of an equation. We don’t know the number of apples, so let’s denote them as the variable x.
To find the unknown x we need 12:6=2
Answer: 2 apples for each child.
Let's take a closer look at the example 12:6=2:
The number 12 is called divisible. This is the number that is being divided.
The number 6 is called divider. This is the number that is divided by.
And the result of dividing the number 2 is called private. The quotient shows how many times the dividend is greater than the divisor.
In literal form, the division looks like this:
a:b=c
a– divisible,
b- divider,
c– private.
So what is division?
Division- this is the inverse action of one factor, we can find another factor.
Division is checked by multiplication, that is:
a:
b=
c, check with⋅b=
a
18:9=2, check 2⋅9=18
Unknown multiplier.
Let's consider the problem:
Each package contains 3 pieces of Christmas balls. To decorate the Christmas tree we need 30 balls. How many packages of Christmas balls do we need?
Solution:
x – unknown number of packages of balls.
3 – pieces in one package of balloons.
30 – total balls.
x⋅3=30 we need to take 3 so many times to get a total of 30. x is an unknown factor. That is, To find the unknown you need to divide the product by the known factor.
x=30:3
x=10.
Answer: 10 packs of balloons.
Unknown dividend.
Let's consider the problem:
Each package contains 6 colored pencils. There are 3 packs in total. How many pencils were there in total before they were put into packages?
Solution:
x – total pencils,
6 pencils in each package,
3 – packs of pencils.
Let's write the equation of the problem in division form.
x:6=3
x is the unknown dividend. To find the unknown dividend, you need to multiply the quotient by the divisor.
x=3⋅6
x=18
Answer: 18 pencils.
Unknown divisor.
Let's look at the problem:
There were 15 balls in the store. During the day, 5 customers came to the store. Buyers bought an equal number of balloons. How many balloons did each customer buy?
Solution:
x – the number of balls that one buyer bought,
5 – number of buyers,
15 – number of balls.
Let's write the equation of the problem in division form:
15:x=5
x – in this equation is an unknown divisor. To find the unknown divisor, we divide the dividend by the quotient.
x=15:5
x=3
Answer: 3 balls for each buyer.
Properties of dividing a natural number by one.
Division rule:
Any number divided by 1 results in the same number.
7:1=7
a:1=
a
Properties of dividing a natural number by zero.
Let's look at an example: 6:2=3, you can check whether we divided correctly by multiplying 2⋅3=6.
If we are 3:0, then we will not be able to check, because any number multiplied by zero will be zero. Therefore, recording 3:0 makes no sense.
Division rule:
You cannot divide by zero.
Properties of dividing zero by a natural number.
0:3=0 this entry makes sense. If we divide anything into three parts, we get nothing.
0:
a=0
Division rule:
When dividing 0 by any natural number not equal to zero, the result will always be 0.
The property of dividing identical numbers.
3:3=1
a:
a=1
Division rule:
When dividing any number by itself that is not equal to zero, the result will be 1.
Questions on the topic “Division”:
In the entry a:b=c, what is quotient here?
Answer: a:b and c.
What is private?
Answer: the quotient shows how many times the dividend is greater than the divisor.
At what value of m is the entry 0⋅m=5?
Answer: when multiplied by zero, the answer will always be 0. The entry does not make sense.
Is there such an n such that 0⋅n=0?
Answer: Yes, the entry makes sense. Any number multiplied by 0 will result in 0, so n is any number.
Example #1:
Find the value of the expression: a) 0:41 b) 41:41 c) 41:1
Answer: a) 0:41=0 b) 41:41=1 c) 41:1=41
Example #2:
For what values of variables is the equality true: a) x:6=8 b) 54:x=9
a) x – in this example is divisible. To find the dividend, you need to multiply the quotient by the divisor.
x – unknown dividend,
6 – divisor,
8 – quotient.
x=8⋅6
x=48
b) 54 – dividend,
x is a divisor,
9 – quotient.
To find an unknown divisor, you need to divide the dividend by the quotient.
x=54:9
x=6
Task #1:
Sasha has 15 marks, and Misha has 45 marks. How many times more stamps does Misha have than Sasha?
Solution:
The problem can be solved in two ways. First way:
15+15+15=45
It takes 3 numbers 15 to get 45, therefore, Misha has 3 times more marks than Sasha.
Second way:
45:15=3
Answer: Misha has 3 times more stamps than Sasha.
Division is an arithmetic operation inverse to multiplication, through which one finds out how many times one number is contained in another.
The number being divided is called divisible, the number being divided by is called divider, the result of division is called private.
Just as multiplication replaces repeated addition, division replaces repeated subtraction. For example, dividing the number 10 by 2 means finding out how many times the number 2 is contained in 10:
10 - 2 - 2 - 2 - 2 - 2 = 0
By repeating the operation of subtracting 2 from 10, we find that 2 is contained in 10 five times. This can be easily checked by adding 2 times five or multiplying 2 by 5:
10 = 2 + 2 + 2 + 2 + 2 = 2 5
To record division, use the sign: (colon), ÷ (obelus) or / (slash). It is placed between the dividend and the divisor, with the dividend written to the left of the division sign and the divisor to the right. For example, writing 10: 5 means that the number 10 is divisible by the number 5. To the right of the division record, put an = (equals) sign, after which the result of the division is written. Thus, the complete division notation looks like this:
This entry reads like this: the quotient of ten and five equals two, or ten divided by five equals two.
Division can also be considered as the action by which one number is divided into as many equal parts as there are units in another number (by which it is divided). This determines how many units are contained in each individual part.
For example, we have 10 apples, dividing 10 by 2 we get two equal parts, each containing 5 apples:
Checking division
To check division, you can multiply the quotient by the divisor (or vice versa). If the result of multiplication is a number equal to the dividend, then the division is correct.
Consider the expression:
where 12 is the dividend, 4 is the divisor, and 3 is the quotient. Now let's check the division by multiplying the quotient by the divisor:
or divisor by quotient:
Division can also be checked by division; to do this, you need to divide the dividend by the quotient. If the result of division is a number equal to the divisor, then the division is performed correctly:
The main property of the private
The quotient has one important property:
The quotient will not change if the dividend and divisor are multiplied or divided by the same natural number.
For example,
32: 4 = 8, (32 3) : (4 3) = 96: 12 = 8 32: 4 = 8, (32: 2) : (4: 2) = 16: 2 = 8
Dividing a number by itself and one
For any natural number a the following equalities are true:
a : 1 = a
a : a = 1
Number 0 in division
When zero is divided by any natural number, the result is zero:
0: a = 0
You cannot divide by zero.
Let's look at why you can't divide by zero. If the dividend is not zero, but any other number, for example 4, then dividing it by zero would mean finding a number that, when multiplied by zero, results in the number 4. But there is no such number, because any number, when multiplied by zero, gives again zero.
If the dividend is also equal to zero, then division is possible, but any number can serve as a quotient, because in this case any number after multiplication by the divisor (0) gives us the dividend (i.e., 0 again). Thus, division, although possible, does not lead to a single definite result.
Division of natural numbers
A lesson in the integrated application of knowledge and methods of action
based on the system-activity teaching method
5th grade
Full name Zhukova Nadezhda Nikolaevna
Place of work : MAOU secondary school No. 6 Pestovo
Job title : mathematic teacher
Topic Division of natural numbers
(training session on the integrated application of knowledge and methods of action)
Target: creating conditions for improving knowledge and skillsand skills in dividing natural numbers and methods of action in modified conditionsand non-standard situations
UDD:
Subject
They simulate a situation, illustrating the arithmetic operation and the progress of its execution, select an algorithm for solving a non-standard problem, and solve equations based on the relationship between the components and the result of the arithmetic operation.
Metasubject
Regulatory : determine the goal of educational activity, implement the means to achieve it.
Cognitive : Convey content in compressed or expanded form.
Communication: they know how to express their point of view, trying to substantiate it, giving arguments.
Personal:
They explain to themselves their individual immediate goals of self-development, give a positive self-assessment of the result of educational activities, understand the reasons for the success of educational activities, and show cognitive interest in studying the subject.
During the classes
1. Organizational moment.
In work we use addition,
Honor and honor to the addition!
Let's add patience to skills,
And the amount will bring success.
Don't forget subtraction.
So that the day is not wasted,
From the sum of efforts and knowledge
We will subtract idleness and laziness!
Multiplication will help in work,
For the work to be useful,
Let's multiply hard work a hundredfold
Our deeds will increase.
Division serves in practice,
It will always help us.
Who shares the difficulties equally?
Share the successes of labor!
Any of the following will help:
They bring us good luck.
And that’s why we’re together in life
Science and labor are advancing.
II. Formulating the topic and objectives of the lesson
Did you like the poem? What did you like about it?
(students' answers)
You said it very well. The lines we read fit very well with our lesson today. Remember a poem you heard and try to determine topic of the lesson.
(Division of natural numbers) (slide 1) . Write down the date and topic of the lesson in your notebook.
Today is the first lesson on the topic “Dividing numbers”? What else are you not good at and what would you like to learn? (students' answers)
So, today we will improve our division skills, learn to justify our decisions, find errors and correct them, evaluate our work and the work of our classmates.
III. Preparation for active educational and cognitive activities
- Motivation for schoolchildren's learning
Humanity has been learning division for the longest time. To this day, the saying “Division is a difficult thing” has been preserved in Italy. This is difficult both from the point of view of mathematics, and technically, and morally. Not every person is given the ability to divide and share.
In the Middle Ages, a person who mastered division received the title “doctor of the abacus”
Abacus is an abacus.
At first there was no sign for the division action. This action was written in words.
And Indian mathematicians wrote division with the first letter of the name of the action.
The colon sign for division came into use in 1684 thanks to the German mathematician Gottfried Wilhelm Leibniz.
Division is also indicated by an oblique or horizontal line. This sign was first used by the Italian scientist Fibonacci.
- How do we divide multi-digit numbers? (Corner)
Do you remember what components are called when divided?(slide 2)
- Do you know that the components of division: dividend, divisor, quotient were first introduced in Russia by Magnitsky. Who is this and what was the real name of this scientist? Prepare answers to these questions for the next lesson.
2) Updating students’ basic knowledge
- Graphic dictation
1. Division is an action by which another factor is found from a product and one of the factors.
2. Division has a commutative property.
3.To find the dividend, you need to multiply the quotient by the divisor.
4. You can divide by any number.
5.To find the divisor, you need to divide the dividend by the quotient.
6. An equality with a letter whose value must be found is called an equation
(Designation: yes; - no) (slide 3)
KEY: (slide 4)
B) Individual work of students using cards.
(simultaneously with dictation)
- Prove that the number 4 is the root of the equation 44: x + 9 = 20.
- Solution . If x=4 then 44:4+9=20
11+9=20
20=20, that's right.
2. Calculate: a) 16224: 52 = (312) d) 13725: 45 = (305)
B) 4230:18 = (235) d) 54756: 39 = (1404)
c) 9800: 28= (350)
3. Solve the equation: 124: (y – 5) = 31
Answer: y=9
4. Two students work using cards: solve 3 tasks each and ask each other theory questions
c) Collective verification of individual work (slide 5)
(Students ask the answering questions about theory)
- Application of knowledge and methods of action
A) Independent work with self-test(Slides 6 -7)
Select and solve only those examples in which the quotient has three digits:
Option 1 Option 2
A)2888: 76 = (38) a)2491:93= (47)
B)6539:13 = (503) b)5698: 14= (407)
B) 5712: 28 = (204) c) 9792: 32 = (306)
B) Physical education minute.
They stood up together and stretched.
Hands on the belt, turned around.
Right, left, once, twice,
They turned their heads.
We stood on our toes,
The back was held with a string
Now, sit down quietly,
We haven't done everything yet.
B) Work in pairs (slide 8)
(during work in pairs, if necessary, the teacher gives consultations)
No. 484 (textbook, page 76)
X cm is the length of one of the sides of the octagon
4x+4 4 =24
4x+16=24
4x=24-16
4x=8
X=2
2 cm is the length of one of the sides of the octagon
Solve equations:
a) 96: x = 8 b) x: 60 = 14 c) 19 * x = 76
D) Work in groups
Before you start completing tasks, read the rules for working in groups
Group I (1st row)
Rules for working in groups
Correct mistakes:
A)9100:10=91; a) 9100:10 = 910
B)5427: 27=21; b) 5427: 27 = 201
B)474747: 47=101; c) 474 747: 47 = 10101
D)42·11=442. d) 42 11 = 462
Group II (2nd row)
Rules for working in groups
- Actively participate in collaboration.
- Listen carefully to your interlocutor.
- Do not interrupt your friend until he finishes his story.
- Express your point of view on this issue, while being polite.
- Don't laugh at other people's shortcomings and mistakes, but tactfully point them out.
Check if the task was completed correctly. Offer your solution
Find the value of the expression x:19 +95 if x =1995.
Solution.
If x=1995, then x:19 +95 = 1995:19 +95=15+95=110
(1995: 19 + 95 = 200)
Group III (3rd row)
Rules for working in groups
- Actively participate in collaboration.
- Listen carefully to your interlocutor.
- Do not interrupt your friend until he finishes his story.
- Express your point of view on this issue, while being polite.
- Don't laugh at other people's shortcomings and mistakes, but tactfully point them out.
Prove that an error was made in solving the equation.
Solve the equation.
124: (y-5) =31
U-5 = 124·31 y – 5 =124: 31
U-5 = 3844 y – 5 = 4
Y = 3844+ 5 y = 4+ 5
Y = 3849 y = 9
Answer: 3849 Answer: 9
D) Mutual check of work in pairs
Students exchange notebooks and check each other's work, highlight errors with a simple pencil and put a mark
E) Group report on the work done
(Slides 5-7)
The slide shows the task for each group. The group leader explains the mistake made and writes the solution proposed by the group on the board.
V. Monitoring student knowledge
Individual testing “Moment of Truth”
Test on the topic “Division”
Option 1
1.Find the quotient of 2876 and 1.
a) 1; b) 2876; c) 2875; d) your answer_______________
2.Find the root of equation 96: x =8
a) 88; b) 12; c) 768; d) your answer ________________
3 .Find the quotient of 3900 and 13.
a) 300; b) 3913; c) 30; d) your answer_______________
4 .One box contains 48 pencils, and the other contains 4 times less. How many pencils are there in two boxes?
a) 192; b) 60; c) 240; d) your answer________________
5. Find two numbers if one of them is 3 times larger than the other, and their
Their sum is 32.
a) 20 and 12; b) 18 and 14; c)26 and 6; d) your answer_________
Test on the topic “Division”
Last name, first name___________________________________________
Option 2
Underline the correct answer or write down your answer.
1 .Find the quotient of 2563 and 1.
a) 1; b) 2563; c) 2564; d) your answer_______________
2. Find the root of Equation 105: x = 3
a) 104; b) 35; c) 315; d) your answer ________________
3 .Find the quotient of 7800 and 13.
a)600; b) 7813; c) 60; d) your answer_______________
4 . In one tub the beekeeper had 24 kg. honey, and in the other 2 times more. How many kilograms of honey did the beekeeper have in two tubs?
a) 12; b) 72; c) 48; d) your answer_______________
5. Find two numbers if one of them is 4 times less than the other, and
Their difference is 27
A) 39 and 12; b) 32 and 8; c) 2 and 29; d) your answer_____________
Test verification key
Option 1
Job number | |||||
9; 36 |
VI. Lesson summary. Homework.
House. Exercise. P.12, No. 520,523,528 (essay).
So, our lesson has come to an end. I would like to interview you about the results of your work.
Continue the sentences:
I am... satisfied/not satisfied with my work in class
I managed …
It was difficult...
The lesson material was... useful/useless for me
What does mathematics teach?