Numbers. Subtraction of natural numbers
difference of integers non-negative numbers a andb is the number of elements in the complement of a set B to a set A, provided thatn(A)= a, n(B)= b, BA, i.e. but -b = n(A B). This is due to the fact that A \u003d B (AB), i.e.n(A)= n(B) + n(A B).
Let's prove it. Since according to the condition IN- own subset of the set BUT, then they can be represented as in Fig. 3.
Subtraction of natural (non-negative integer) numbers is defined as the inverse operation of addition: but -b = c () b + c = a.
Difference AB shaded in this figure. We see that the sets IN And AB do not intersect and their union is equal to BUT. Therefore, the number of elements in the set BUT can be found using the formula n(A)=n(B) + n(AB), whence, by definition of subtraction as an operation inverse to addition, we obtain n(AB) = but -b.
A similar interpretation is given to the subtraction of zero, as well as the subtraction but from but. Because A=A AA=, then but - 0= a And a - a = 0.
Difference but -b non-negative integers exist if and only if .
The action by which the difference is found but -b, is called subtraction, number but- reduced, b- subtractable.
Using the definitions, we will show that 8 - 5 = 3 . Let two sets be given such that n(A) = 8, n(B) = 5. And let the multitude IN is a subset of the set BUT. For example, A ={a, s, d, f, g, h, j, k} , B={a, s, d, f, g} .
Find the complement of the set IN to many A: AB ={h, j, k). We get that n(AB) = 3.
Consequently , 8 - 5 = 3.
The relationship between subtraction of numbers and subtraction of sets allows us to justify the choice of action when solving text problems. Let's find out why the following problem is solved using subtraction and solve it: “7 trees grew at the school, 3 of them were birches, the rest were lindens. How many lindens grew near the school?
Let us present the condition of the problem visually, depicting each tree planted near the school in a circle (Fig. 4). Among them there are 3 birches - in the figure we will highlight them with hatching. Then the rest of the trees - not the shaded circles - are lindens. That is, there are as many of them as there will be subtract 3 from 7 , i.e. . 4.
The problem considers three sets: the set BUT all trees, many IN- birches, which is a subset BUT, and set FROM lip - it is the complement of the set IN before BUT. The task is to find the number of elements in this addition.
By condition n(A) = 7, n(B)= 3 and BA. Let be A ={a, b, c, d, e, f, g} , B={a, b, c} . Find the complement of the set BUT before IN: AB={d, e, f, g) And n(AB) = 4.
Means, n(C) = n(AB) = n(A) - n(B)= 7 - 3 = 4.
Consequently, 4 lindens grew near the school.
The considered approach to the addition and subtraction of non-negative integers allows us to interpret various rules from the set-theoretic positions.
Rule for subtracting a number from a sum: to subtract a number from the sum, it is enough to subtract this number from one of the terms and add another term to the result obtained, i.e. at ace we have that (a+b)-c=(a-c)+b; at bc we have that (a+b)-c=a+(b-c); at ac And bc any of these formulas can be used.
Let us find out the meaning of this rule: Let A, B, C are sets such that n(A)=a, n(B)=b And AB= , SA(Fig.5).
It is easy to prove with the help of Euler circles that the equality holds for these sets.
The right side of the equality looks like:
The left side of the equality has the form: Therefore (a + b) - c = (a - c) + b,at provided that a>c.
Rule for subtracting a sum from a number : to subtract the sum of numbers from a number, it is enough to subtract from this number successively each term one after the other, i.e. provided that a b+c, we have but - (b + c) = (a - b) - c.
Let's find out the meaning of this rule. For these sets, the equality holds.
Then we get that the right side of the equality has the form:. The left side of the equality has the form: .
Consequently (a + b) - c = (a - c) + b, at provided that a>c.
The rule for subtracting the difference from a number:
to subtract from but difference b-c, it is enough to add the subtrahend to this number from and subtract the minuend from the result b; at a > b it is possible to subtract the reduced b from the number a and add the subtracted c to the result obtained, i.e. but - (b - c) = (a + c) - b = (a - b) + c.
Means, A(BC) = .
Consequently, n(A(BC)) = n( ) And but - (b - c) = (a + c) - b.
The rule for subtracting a number from the difference: to subtract the third number from the difference of two numbers, it is enough to subtract the sum of two other numbers from the reduced one, i.e. (but -b) - c = a - (b + c). It is proved similarly to the rule for subtracting a sum from a number.
Example. What are the ways to find the difference: a) 15 - (5 + 6); b) (12 + 6) - 2?
Solution. a) We use the rule for subtracting the sum from a number: 15 - (5 + 6) \u003d (15 - 5) - 6 \u003d 10 - 6 \u003d 4.
Or 15 - (5 + 6) = (15 - 6) - 5 = 9 - 4 = 4.
Or 15 - (5 + 6) = 15 - 11= 4 .
b) We use the rule for subtracting a number from the sum: (12 + 6) - 2 = (12 - 2) + 6 = 10 + 6 = 16.
Or (12 + 6) - 2 = 12 + (6 - 2) = 12 + 4 = 16 .
Or (12 + 6) - 2 = 18 - 2 = 16.
These rules simplify calculations and are widely used in primary course mathematics.
subtraction), the inverse of addition. Denoted with a minus sign "-". This is an action by which the sum and one of the terms can be used to find the second term.The number to be subtracted from is called minuend, and the number to be subtracted is subtrahend. The result of subtraction operations is called difference.
Let us know: the sum of 2 numbers c And b equals a, so the difference a−c will b, and the difference a−b will c.
It is most convenient to subtract using the “in a column” method.
subtraction table.
For easier and faster mastering of the subtraction process, view and memorize the subtraction table up to ten for grade 2:
Properties of subtraction of natural numbers.
- Subtraction, as a process, does NOT have the commutative property: a−b≠b−a.
- The difference of identical numbers is equal to zero: a−a=0.
- Subtracting the sum of 2 integers from an integer: a−(b+c)=(a−b)−c.
- Subtracting a number from the sum of 2 numbers: (a+b)−c=(a−c)+b=a+(b−c).
- distribution property multiplication versus subtraction: a (b−c)=a b−a c and (a−b) c=a c−b c.
- And all other properties of subtraction of integers (natural numbers).
Let's consider some of them:
The property of subtracting two equal natural numbers.
Difference of 2 identical natural numbers equals zero.
a−a=0,
where a- any natural number.
Subtraction of natural numbers does NOT have the commutative property.
From the property described above, it can be seen that for 2 identical natural numbers, the commutative property of subtraction works. In all other cases (if the minuend ≠ the subtrahend), the subtraction of natural numbers does not have a commutative property. Or, to put it another way, the minuend and the subtrahend are not interchanged.
When the minuend is greater than the subtrahend and we decide to swap them, then we will subtract from the natural number, which is less, the natural number, which is greater. This system does not correspond to the essence of the subtraction of natural numbers.
If a And b unequal natural numbers a−b≠b−a. For example, 45−21≠21−45.
The property of subtracting the sum of two numbers from a natural number.
To subtract from the indicated natural number the required sum of 2 natural numbers is the same, if the 1st term of the required sum is subtracted from the indicated natural number, then the 2nd term is subtracted from the calculated difference.
It can be expressed in letters like this:
a−(b+c)=(a−b)−c,
where a, b And c- natural numbers, the conditions must be met a>b+c or a=b+c.
The property of subtracting a natural number from the sum of two numbers.
Subtracting a natural number from the sum of 2 numbers is the same as subtracting a number from one of the terms, and then adding the difference and the other term. The subtracted number can NOT be greater than the term from which this number is subtracted.
Let be a, b And c- integers. So if a more or equal c, equality (a+b)−c=(a−c)+b will be true, and if b more or equal c, then: (a+b)−c=a+(b−c). When and a And b more or equal c, so both last equalities hold, and they can be written like this:
(a+b)−c=(a−c)+b= a+(b−c).
For a full analysis of the topic of the article, we introduce terms and definitions, denote the meaning of the subtraction action and derive a rule according to which the subtraction action can lead to the addition action. Let's look at practical examples. And also consider the action of subtraction in a geometric interpretation - on the coordinate line.
In general, the basic terms used to describe the operation of subtraction are the same for any type of number.
Yandex.RTB R-A-339285-1 Definition 1
Minuend is the integer to be subtracted from.
Subtrahend is the integer to be subtracted.
Difference is the result of the subtraction operation performed.
To indicate the action itself, a minus sign is used, placed between the minuend and the subtrahend. All the constituent parts of the action mentioned above are written in the form of equality. That is, if integers a and b are given, and when subtracting from the first second, the number c is obtained, the subtraction action will be written as follows: a - b \u003d c.
An expression of the form a - b will also be denoted as a difference, as well as the very final value of this expression.
The meaning of integer subtraction
In the topic of subtracting natural numbers, the relationship between the operations of addition and subtraction was established, which made it possible to define subtraction as a search for one of the terms by a known sum and the second term. We assume that the subtraction of integers has the same meaning: the second term is determined by a given sum and one of the terms.
The indicated meaning of the action of subtracting integers makes it possible to assert that c - b \u003d a and c - a \u003d b, if a + b \u003d c, where a, b, c are integers.
Consider simple examples to reinforce the theory:
Let we know that - 5 + 11 \u003d 6, then the difference is 6 - 11 \u003d - 5;
Suppose it is known that - 13 + (- 5) \u003d - 18, then - 18 - (- 5) \u003d - 13, and - 18 - (- 13) \u003d - 5.
Integer Subtraction Rule
The above meaning of the action of subtraction does not mean for us specific way calculate the difference. Those. we can assert that one of the known terms is the result of subtracting another known term from the sum. But, if one of the terms turns out to be unknown, then we cannot know what the difference between the sum and the known term will be. Therefore, to perform the subtraction action, we need the integer subtraction rule:
Definition 1
In order to determine the difference between two numbers, it is necessary to add to the minuend the number opposite to the subtracted one, i.e. a - b = a + (- b) , where a and b are integers; b and – b are opposite numbers.
Let us prove the indicated subtraction rule, i.e. Let us prove the validity of the equality indicated in the rule. To do this, according to the meaning of subtracting integers, we add to a + (- b) subtracted b and make sure that we get a reduced a as a result, i.e. check the validity of the equality (a + (- b)) + b = a . Based on the properties of addition of integers, we can write a chain of equalities: (a + (- b)) + b = a + ((- b) + b) = a + 0 = a , it will be the proof of the rule for subtracting integers.
Consider the application of the rule for subtracting integers on specific examples.
Subtraction of a positive integer, examples
Example 1It is necessary to subtract from the integer 15 the positive integer 45 .
Solution
According to the rule, in order to subtract a positive integer 45 from a given number 15, you need to add the number - 45 to the reduced 15, i.e. opposite to the given 45 . Thus, the desired difference will be equal to the sum of the integers 15 and - 45 . Having calculated the required sum of numbers with opposite signs, we get the number - 30. Those. the result of subtracting the number 45 from the number 15 will be the number - 30. Let's write the whole solution in one line: 15 - 45 = 15 + (- 45) = - 30 .
Answer: 15 - 45 = - 30.
Example 2
It is necessary to subtract from the negative integer - 150 the positive integer 25 .
Solution
According to the rule, let's add to the decreasing number - 150 the number - 25 (that is, the opposite of the given subtracted 25). Find the sum of negative integers: - 150 + (- 25) = - 175 . Thus, the desired difference is equal to. We write the whole solution like this: - 150 - 25 \u003d - 150 + (- 25) \u003d - 175.
Answer: - 150 - 25 = - 175.
Zero Subtraction Examples
The integer subtraction rule makes it possible to derive the principle of subtracting zero from an integer - subtracting zero from any integer does not change this number, i.e. a - 0 = a, where a is an arbitrary integer.
Let's explain. According to the subtraction rule, the subtraction of zero is the addition to the minuend of a number opposite to zero. Zero is a number opposite to itself, i.e. subtracting zero is the same as adding zero. Based on the related property of addition, adding zero to any integer does not change that number. In this way,
a - 0 = a + (- 0) = a + 0 = a .
Consider simple examples of subtracting zero from various integers. For example, the difference 61 - 0 is 61 . If you subtract zero from a negative integer - 874, then you get - 874. If we subtract zero from zero, we get zero.
Subtraction of a negative integer, examples
Example 3It is necessary to subtract an integer from an integer 0 a negative number - 324 .
Solution
According to the subtraction rule, the determination of the difference 0 - (- 324) must be made by adding to the decreasing number 0 the number opposite to the subtracted one - 324. Then: 0 - (- 324) = 0 + 324 = 324
Answer: 0 - (- 324) = 324
Example 4
Determine the difference - 6 - (- 13) .
Solution
Let's subtract from a negative integer - 6 a negative integer - 13 . To do this, we calculate the sum of two numbers: the reduced one - 6 and the number 13 (that is, the opposite of the given subtrahend - 13). We get: - 6 - (- 13) \u003d - 6 + 13 \u003d 7.
Answer: - 6 - (- 13) = 7 .
Subtraction of equal integers
If the given minuend and subtrahend are equal, then their difference will be equal to zero, i.e. a - a = 0 , where a is any integer.
Let's explain. According to the rule for subtracting integers a - a = a + (- a) = 0, which means: in order to subtract an integer equal to it, you need to add to this number a number that is opposite to it, which will result in zero.
For example, the difference of equal integers - 54 and - 54 is equal to zero; performing the action of subtracting the number 513 from the number 513, we get zero; subtracting zero from zero, we also get zero.
Checking the result of subtracting integers
The necessary verification is performed using the addition action. To do this, we add the subtrahend to the resulting difference: as a result, we should get a number equal to the one being reduced.
Example 5
An integer - 112 was subtracted from an integer - 300 , and the difference - 186 was obtained. Was the subtraction correct?
Solution
Let's check according to the above principle. Let's add the subtrahend to the given difference: - 186 + (- 112) \u003d - 298. We received a number different from the given reduced, therefore, an error was made when calculating the difference.
Answer: No, the subtraction was done incorrectly.
In conclusion, consider the geometric interpretation of the action of subtracting integers. Let's draw a horizontal coordinate line directed to the right:
Above, we derived the rule for performing the subtraction action, according to it: a - b \u003d a + (- b), then the geometric interpretation of the subtraction of numbers a and b will coincide with geometric sense addition of integers a and - b. It follows from this that to subtract an integer b from an integer a, it is necessary:
Move from the point with coordinate a by b unit segments to the left, if b is a positive number;
Move from the point with coordinate a to | b | (the modulus of the number b) unit segments to the right, if b is a negative number;
Stay at the point with coordinate a if b = 0 .
Consider an example using a graphic image:
Let it be necessary to subtract from an integer - 2 a positive integer 2 . To do this, according to the above scheme, move to the left by 2 single segment, thus getting to the point with coordinate - 4 , i.e. - 2 - 2 = - 4 .
Another example: we subtract from the integer 2 a negative integer - 3 . Then, according to the scheme, move to the right by | - 3 | = 3 unit segments, thus getting to the point with coordinate 5 . We get the equality: 2 - (- 3) = 5 and an illustration to it:
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Sections: Primary School
Class: 2
Basic goals:
1) to form an idea about the property of subtracting a sum from a number, the ability to use this property to rationalize calculations;
2) train the skills of oral counting, the ability to independently analyze and solve complex problems;
3) cultivate accuracy.
Demo material:
1) the image of Dunno. <Рисунок1 >
2) cards with the statement: wish - bark - success - hov.
3) hourglass.
4) the standard for subtracting the sum from a number.
a-(b+c) = (a-b)-c = (a-c)-b
5) the standard of the order of actions. a-(b+c)
6) sample for self-test for step 6:
7) sample for self-examination for the 7th stage.
1) 45 -15 = 30 (m) - left with Denis
2) 30 - 13 =17 (m)
Answer: Denis has 17 stamps left.
Handout:
1) a beige card with an individual task for stage 2 for each student:
2) a green card with an individual task for stage 5.
3) independent work for stage 6.
4) traffic lights: red, yellow, green.
During the classes:
I. Self-determination to learning activities.
1) motivate to activity in the lesson through the introduction of a fairy-tale character;
2) determine the content of the lesson: subtracting the amount from the number.
Organization educational process at stage I.
What did you do in the last lesson? (Addition properties)
What properties of addition have been repeated? (displacement and associative)
Why do we need to know the properties of addition? (It is more convenient to solve examples)
Today we have a fairy-tale hero Dunno .<Рисунок1 >
He has prepared many interesting assignments and will watch how we work in the lesson. Ready?
II. Actualization of knowledge and fixation of difficulties in activities.
1) train mental operation - generalization;
2) repeat the rules of the order of actions in expressions with brackets;
3) to organize the difficulty in individual activity and its fixation by students in loud speech.
Organization of the educational process at stage II.
1) Oral account.
Look at the blackboard and do the actions orally. <Приложение 1 >
If we fulfill them correctly, then we will read the wish that Dunno encrypted for us:
(Add 19 to 27, you get 46;
Subtract 24 from 46 to get 22;
Add 38 to 22 to get 60;
Subtract 5 from 60 to get 55)
Increase 55 by 200. (200+55=255)
Give a description of the number 255. (255 is a three-digit number, contains two hundred, five tens and five ones. The previous number is 254, the next is 256, the sum of the bit terms is 200+50+5, the sum of the digits is 12).
Express the number 255 in different units of account. (255=2s 5d 5ed = 25d 5ed = 2s 55ed)
Express 255 cm in different units. (255=2m 5dm 5cm=25dm 5cm=2m 55cm)
2) Repetition of the rule of order of actions in expressions with brackets. <Приложение 2 >
How are expressions similar? (By action components, same order of actions)
How are the expressions different? (Various deductibles)
How are subtrahends represented? (The subtrahends are represented by the sum of two numbers)
What did we repeat when we found the meanings of expressions? (Procedure).
Why repeat the procedure?
Where can we repeat the order of operations rule? (In the textbook or standards <Приложение 3 > )
3) Individual task.
Take a pen and a piece of beige paper. <Приложение 4 >
Now let's take a look at some examples. At my command, stop your decision.
Attention! Started! …
Raise your hand, who solved all the examples?
Raise your hand, who solved one example?
Suggest the standard by which you solved the examples. (We do not know the standard).
Who has not solved the examples?
III. Identification of the causes of the difficulty and setting the goal of the activity.
1) identify and fix the place and cause of the difficulty;
2) agree on the purpose and topic of the lesson.
Organization of the educational process at stage III.
Repeat, what was the task?
Why was there a problem? (Little time, no suitable property)
What to do? (Children's guess). Set the sheets aside.
Try to formulate the purpose of the lesson.
Formulate the topic of the lesson.
Lesson topic: Subtracting a sum from a number. Speak the topic of the lesson to yourself, in an undertone. (The topic of the lesson is written on the board)
IV. Construction of the project of an exit from difficulty.
1) to organize the construction by children of a new mode of action, using a leading dialogue;
2) fix new way actions are symbolic in speech.
Organization of the educational process at stage IV.
Look and read the expression: 87 - (7 + 15).
Which term is more convenient to subtract first? (It is more convenient to subtract the first term - 7)
We subtracted the first term, and we need to subtract two terms. What need to do? (Subtract the second term)
The teacher writes on the blackboard. <Приложение5 >
Look, I will replace the number 87 with the letter a, the number 7 with the letter b, the number 15 with the letter c, we get equality. <Приложение 6 >
Let's see. Read the expression: 87 - (15 + 7)
What is more convenient to subtract the term from the number 87? (It is more convenient to subtract the second term 7)
The teacher writes on the blackboard.
We have subtracted the second term, and we need to subtract two terms. What need to do? (Subtract the first term)
The teacher writes on the blackboard. <Приложение 7 >
Let's see. I will replace the number 87 with the letter a, the number 7 with the letter b, the number 15 with the letter c, we get equality. <Приложение 8 >
Find out how you can subtract the sum from the number. (Children's answers are heard)
Where can we check if we have drawn the right conclusions? (In the textbook)
Open your textbook to page 44. Read the rule. <Приложение 9 >
V. Primary consolidation in external speech.
Purpose: to create conditions for fixing the studied mode of action in external speech.
Organization of the educational process at stage V.
Who will repeat the rule?
Why was there a problem? (We couldn't decide quickly)
And now can we?
What helped us? (The rule for subtracting a sum from a number)
Take a green sheet and, at my command, solve the examples. <Приложение10 >
Attention! Started! Stop!
front poll.
How much did it turn out in the first example?
Who so raise your hand.
Who has a mistake?
How much did it turn out in the second example?
Who so raise your hand.
Who has a mistake?
How did you decide? Where is the mistake? What is the reason?
Can you say that you have learned to solve? (Yes)
What helped? (We know the rule, the speed of the solution has increased)
Where can we apply the new technique? (When solving problems, examples).
At home, solve on page 44, task number 4, for a new rule. Come up with and write down your example. (The task is written on the board). <Приложение11 >
Who will remember the rule?
VI. Independent work with self check.
1) organize independent implementation by students typical tasks to a new mode of action with self-examination according to the model;
2) organize self-assessment by children of the correctness of the task.
Organization of the educational process at stage VI.
And now Dunno will look at how we learned to apply the new rule.
Independent work. <Приложение12 >
Why do we do our own work? (Find out difficulties and overcome them, test your strength)
What are the ways to subtract a sum from a number? (It is convenient to subtract one term, and then another)
Take a leaf white color. On my command, we begin to decide.
Started...Stop.
Take a simple pencil and check with the sample. <Приложение13 >
Who so, put "+".
Whoever has an error, put “-”.
Raise your hand, who did it?
Raise your hand, who's got a bug? Where did the difficulty arise? (Computational reception)
You did a wonderful job.
What did you learn in the lesson? (learned a convenient way to subtract the amount from a number)
Make a conclusion. (children's answers)
Fizminutka.
VII. Inclusion in the system of knowledge and repetition.
Purpose: to repeat the solution of the problem, to find a convenient way to solve it.
Organization of the educational process at stage VII.
Where can you apply the learned rules? (When solving problems, examples)
Look and read problem #3 to yourself.
Conduct a task analysis. (It is known in the problem that Denis had 45 stamps. He gave Petya 15 stamps, and Kolya 13 stamps. We need to find out how many stamps he has left.
To answer the question of the problem, it is necessary to subtract the number of stamps that Denis gave to Petya and Kolya from the total number of stamps. We cannot immediately answer the question of the problem, since we do not know how many stamps Denis gave Petya and Kolya in total. And we can find out by adding the number of stamps that he gave to Petya to the number of stamps that he gave to Kolya).
In case of difficulty in analyzing the problem, the teacher helps with the questions that are presented below:
What is known about the problem?
What do you need to know?
How to answer the question of the task?
Can we immediately answer the question of the problem? Why?
Can we find out? How?
Tell a plan for solving the problem. (In the first step, we will find out how many stamps Denis gave in total, then we will answer the question of the problem). <Приложение 14 >
Who solved the problem differently? (To answer the question of the problem, it is necessary to subtract the number of stamps that Denis gave to Petya from the total number of stamps, and then the number of stamps that he gave to Kolya)
Tell the plan for solving the problem in the second way. (The first step is to find out how many stamps Denis has left after he gave Petya, and then we find out how many stamps he has left after he gave Kolya 13 stamps and answer the question of the problem). <Приложение15 >
What is the best way to solve the problem? Why? (Second, it is more convenient to subtract one part from the whole, and then another part)
Write down the solution of the problem in a convenient way. Sample self-test. <Приложение16 >
VIII. Reflection of activity.
1) fix in speech a new method of action studied in the lesson: subtracting the amount from a number;
2) fix the difficulties that remain, and ways to overcome them;
3) evaluate their own activities in the lesson, coordinate homework.
Organization of the educational process at stage VIII.
So, today in the lesson, one more rule was added to our knowledge, remember it. (Today in the lesson we learned how to subtract the amount from a number. To subtract the amount from a number, you can first subtract one term and then another)
Who is having trouble?
Have you managed to overcome them? How?
What else needs to be worked on?
Evaluation by the teacher for the work in the lesson.
Homework: p.44, No. 4. Come up with and solve your own example on a new topic.
Literature
1) Textbook “Mathematics Grade 2, Part 2”; L.G. Peterson. Publishing house "Yuventa", 2008.
3) L.G. Peterson, I.G. Lipatnikova "Oral exercises in mathematics lessons Grade 2". M.: “School 2000…”
The concept of subtraction is best understood with an example. You decide to drink tea with sweets. There were 10 candies in the vase. You ate 3 candies. How many candies are left in the vase? If we subtract 3 from 10, then 7 sweets will remain in the vase. Let's write the problem mathematically:
Let's take a closer look at the entry:
10 is the number from which we subtract or which we reduce, therefore it is called reduced.
3 is the number we are subtracting. Therefore it is called deductible.
7 is the result of subtraction or is also called difference. The difference shows how much the first number (10) is greater than the second number (3) or how much the second number (3) is less than the first number (10).
If you are in doubt whether you have found the difference correctly, you need to do verification. Add the second number to the difference: 7+3=10
When subtracting l, the minuend cannot be less than the subtrahend.
We draw a conclusion from what has been said. Subtraction- this is an action with the help of which the second term is found by the sum and one of the terms.
In literal form, this expression will look like this:
a -b=c
a - reduced,
b - subtracted,
c is the difference.
Properties of subtracting a sum from a number.
13 — (3 + 4)=13 — 7=6
13 — 3 — 4 = 10 — 4=6
The example can be solved in two ways. The first way is to find the sum of numbers (3 + 4), and then subtract from total number(13). The second way is to subtract the first term (3) from the total number (13), and then subtract the second term (4) from the resulting difference.
In literal form, the property for subtracting the sum from a number will look like this:
a - (b + c) = a - b - c
The property of subtracting a number from a sum.
(7 + 3) — 2 = 10 — 2 = 8
7 + (3 — 2) = 7 + 1 = 8
(7 — 2) + 3 = 5 + 3 = 8
To subtract a number from the sum, you can subtract this number from one term, and then add the second term to the result of the difference. Under the condition, the term will be greater than the subtracted number.
In literal form, the property for subtracting a number from a sum will look like this:
(7 + 3) — 2 = 7 + (3 — 2)
(a +b) —c=a + (b - c), provided b > c
(7 + 3) — 2=(7 — 2) + 3
(a + b) - c \u003d (a - c) + b, provided a > c
Subtraction property with zero.
10 — 0 = 10
a - 0 = a
If you subtract zero from the number then it will be the same number.
10 — 10 = 0
a -a = 0
If you subtract the same number from a number then it will be zero.
Related questions:
In the example 35 - 22 = 13, name the minuend, the subtrahend and the difference.
Answer: 35 - reduced, 22 - subtracted, 13 - difference.
If the numbers are the same, what is their difference?
Answer: zero.
Do a subtraction check 24 - 16 = 8?
Answer: 16 + 8 = 24
Subtraction table for natural numbers from 1 to 10.
Examples for tasks on the topic "Subtraction of natural numbers."
Example #1:
Insert the missing number: a) 20 - ... = 20 b) 14 - ... + 5 = 14
Answer: a) 0 b) 5
Example #2:
Is it possible to subtract: a) 0 - 3 b) 56 - 12 c) 3 - 0 d) 576 - 576 e) 8732 - 8734
Answer: a) no b) 56 - 12 = 44 c) 3 - 0 = 3 d) 576 - 576 = 0 e) no
Example #3:
Read the expression: 20 - 8
Answer: “Subtract eight from twenty” or “Subtract eight from twenty.” Pronounce words correctly
