There are four basic arithmetic operations: addition, subtraction, multiplication and division. They are the basis of mathematics, with their help all other, more complex calculations are performed. Addition and subtraction are the simplest of them and are mutually opposite. But we come across terms used in addition more often in life.
We talk about the “addition of efforts” when trying together to obtain the desired result, about the “components of achieved success,” etc. The names associated with subtraction remain within the boundaries of mathematics, rarely appearing in everyday speech. Therefore, the words “subtracted”, “reduced”, “difference” are less common. The rule for finding each of these components can only be applied if you understand the meaning of these names.
Unlike many scientific terms that have Greek, Latin or Arabic origin, in this case words with Russian roots are used. So it’s not difficult to understand their meaning, which means it’s easy to remember what is meant by which term.
If you look closely at the name itself, it becomes noticeable that it has to do with the words “different”, “difference”. From this we can conclude that what is meant is an established difference between quantities.
This concept in mathematics means:
- difference between two numbers;
- it is a measure of how much more or less one quantity is than another;
- this is the result obtained when performing a subtraction - this is the definition offered by the school curriculum.
Note! If the quantities are equal to each other, then there is no difference between them. This means their difference is zero.
What are minuend and subtrahend?
As the name suggests, diminished is something that is done less. And you can make the quantity smaller by subtracting a part from it. Thus, the minuend is a number from which a part is subtracted.
Subtracted, accordingly, is the number that is subtracted from it.
| Minuend | Subtrahend | Difference | ||
| 18 | — | 11 | = | 7 |
| 14 | — | 5 | = | 9 |
| 26 | — | 22 | = | 4 |
Useful video: minuend, subtrahend, difference
Rules for finding an unknown element
Having understood the terms, it is easy to establish by what rule each of the elements of subtraction is found.
Since the difference is the result of a given arithmetic operation, it is found using this action; no other rules are required here. But they are there in case the other term of the mathematical expression is unknown.
How to find a minuend
This term, as it was found out, refers to the quantity from which a part has been subtracted. But if one was subtracted, and the other remained in the end, therefore, the number consists of these two parts. It turns out that you can find an unknown minuend by adding two known elements.
So, in this case, to find the unknown, you should add the subtrahend and the difference:
The same is true in all similar cases:
| ? | – | 5 | = | 9 |
| 9 | + | 5 | = | 14 |
| ? | – | 22 | = | 4 |
| 4 | + | 22 | = | 26 |
How to find the subtrahend
If a whole consists of two parts (in this case quantities), then subtracting one of them will result in the second. Thus, to find the unknown subtrahend, it is enough to subtract the difference from the whole instead.
Other similar examples are solved using the same rule.
| 14 | – | ? | = | 9 |
| 14 | – | 9 | = | 5 |
The article will introduce the reader to the concepts of “number difference”, “subtrahend” and “minuend”.
There are only four basic operations in arithmetic, which we call addition, multiplication, subtraction and division. Such actions are the basis of all mathematics - they allow us to carry out all calculations: both simple and the most complex. The simplest operations are addition and subtraction, which are opposite to each other. True, we also use the word “addition” in everyday life.
We may come across the phrase “putting together efforts”, for example, when we need to do some work all together. But with the term “subtraction” the situation is a little more complicated, and it is less common in conversation. We rarely hear expressions such as " minuend», « subtrahend», « difference" But in today's article we will talk about them in detail from a mathematical point of view.
What does a minuend, a subtrahend and the difference of numbers mean?
What does a minuend, a subtrahend and the difference of numbers mean? As you know, many scientific terms and expressions are taken from other languages, most often Greek and Latin. But those words that will be discussed below are of Russian origin, so it will be easier for us to parse them.
For example, what about the difference between numbers? If we pay attention to the root of the word “difference,” then we will be presented with, for example, its cognate word “difference.” And if we are talking about mathematics, then there is nothing to think about - the word “difference” means the difference between some numbers, or rather, two numbers. The difference shows us how much one value is greater than the other or, conversely, how much the second is less than the first. Strictly in mathematics, this looks like the result of subtraction.
Let's give an example right away. Let's say the barmaid carries eight pies on a tray. She gave five of them to visitors. How many pies will the barmaid have left on her tray? If you subtract 5 from 8, you get 3. Now let’s write it down mathematically:
- 8 – 5 = 3
That is, the difference between eight and five is three. Now we understand what the term “difference” is.
Attention: If two numbers are equal to each other, then there is no difference between them, it is equal to zero (8 – 8 = 0).
Now we should find out what subtrahend and minuend are. Let us again imagine the meaning of words according to their meaning. What can the number being reduced be? The minuend is the number that decreases when subtracted. Another number is subtracted from this number. What is subtrahend? The subtrahend is precisely the number that we subtract from the minuend.
Let's go back to the barmaid example. We remember how we subtracted five from eight, and we got three. We found out that three is the difference between these two numbers. Now it is no longer difficult for us to understand that 8 is a minuenda number, and 5 is a subtrahend number.
How to find the minuend and subtrahend number?
We have already figured out how to find the difference between numbers in mathematics. It's pretty simple. But can we find the minuend and subtrahend if one number is unknown? Of course we can, since we will know the other two numbers. For example, how can we find the minuend? If we know the value of the difference and the subtrahend, then the sum of these two numbers equals the minuend:
- Y – 10 = 18, where Y is the number being reduced
- So Y = 18 + 10
- 18 + 10 = 28
- Y=28
Finding the subtrahend is just as easy. If we know the difference and the minuend, then we will get the subtrahend by subtracting the difference from the minuend:
- 28 – B = 10, where B is the number to be subtracted
- So B = 28 – 10
- 28 – 10 = 18
- B=18
Video: Minuend, Subtract, Difference
Determining the sum of numbers
Sum (lat. summa- total, total number) of numbers is the result of summing these numbers: . In particular, if two numbers are added and , then
Exercise. Find the sum of numbers:
Answer.
Properties of the sum of numbers
Associativity:
Based on these properties, we can conclude that rearranging the positions of the terms does not change the sum.
Distributivity with respect to multiplication
Exercise. Find the sum of numbers in a convenient way:
Solution. By the properties of addition we have
Answer. 1)
When adding large numbers or decimal fractions, use columnar addition.
Solution. We add these numbers into a column, to do this we write them one under the other, digit under digit. In the case of decimal fractions, we focus on ensuring that the decimal point of the first number is below the decimal point of the second. Next, we add the numbers below each other, moving from right to left and writing the result under the fraction line. If the sum of the numbers in one column exceeds ten, then the number of tens is added to the numbers in the next column to the left of this column:
Answer. 1)
The addition of rational fractions is carried out according to the rule
Solution. Let's calculate the first sum using the rule of adding rational numbers
The numerator and denominator of the resulting fraction can be reduced by 2, then the answer will be
To calculate the second sum, we first transform the second term into an improper fraction, to do this we multiply the whole part by the denominator and add the resulting number to the numerator. Next, we apply the rule for adding rational fractions
Let's select the whole part of the resulting fraction; to do this, divide the numerator by the denominator with the remainder. We write the resulting quotient into the integer part, and the remainder of the division into the numerator.
Answer. 1) ; 2)
How to find the difference between numbers in mathematics
Arithmetic operations with numbers
The difference between numbers means how much more one of them is than the other.How to find the difference between quantities
Once again resorting to the school curriculum, we find a rule on how to find the difference:
Now it is clear that the difference consists of two numbers that must be known to calculate it. And how to find them, we will also use the definitions:
- Example 3. Find the subtrahend value.
- Example 5. Find the difference between rational fractions.
- Double a number is a value multiplied by two.
- Triple a number is a value multiplied by three.
- The double difference is the difference in magnitudes multiplied by two.
- A triple difference is a difference in magnitude multiplied by three.
- If the subtrahend is greater than the minuend, the difference will be negative.
- product - by multiplying factors;
- quotient - by dividing the dividend by the divisor.
- sum - the result obtained by adding numbers;
- product is the result of multiplying numbers;
- difference - subtract;
- private - to divide.
- This is subtracting one number from another.
- The minuend is a mathematical number from which it is subtracted and it decreases (becomes smaller).
- A subtrahend is a mathematical number that is subtracted from the minuend.
- To find the minuend, you need to add the difference to the subtrahend.
- To find the subtrahend, you need to subtract the difference from the minuend.
- difference - the result obtained by subtracting numbers;
- In mathematics, a difference is the result obtained by subtracting two or more numbers from each other.
- This is the quantity that is the result of subtracting two values.
- The difference shows the quantitative difference between two numbers.
- To find the difference, you need to subtract the subtrahend from the minuend.
- Example 1. Find the difference between two quantities.
- Example 2. Find the minuend.
- Example 4. Find the difference between three values.
- Example 6. Triple the difference of numbers.
- Example 7. Find the difference between values 7 and 18.
- the sum - by adding the terms;
- To introduce and develop the ability to use mathematical terms “sum”, “meaning of sum”. Improve your computing skills.
- Develop skills to compare, analyze, generalize. Develop mathematical speech and interest in mathematics.
- Develop independence, discipline, and the ability to work in a team.
- 15 2 − 2 2 = (15 − 2)(15 + 2) = 13 17 = 221
- 9a 2 − 4b 2 with 2 = (3a − 2bc)(3a + 2bc)
- Let's decompose 112 into the sum of numbers whose squares we remember well.
112 = 100 + 1 - Write the sum of the numbers in brackets and place a square above the brackets.
112 2 = (100 + 12) 2 - Let's use the formula for the square of the sum:
112 2 = (100 + 12) 2 = 100 2 + 2 100 12 + 12 2 = 10,000 + 2,400 + 144 = 12,544 - (8a + c) 2 = 64a 2 + 16ac + c 2
- Learn that “a 3” comes at the beginning.
- The two polynomials in the middle have coefficients of 3.
- Recall that any number to the zero power is 1. (a 0 = 1, b 0 = 1) . It is easy to notice that in the formula there is a decrease in the degree of “a” and an increase in the degree of “b”. You can verify this:
(a + b) 3 = a 3 b 0 + 3a 2 b 1 + 3a 1 b 2 + b 3 a 0 = a 3 + 3a 2 b + 3ab 2 + b 3 - The first bracket is the sum of two numbers.
- The second bracket is the incomplete square of the difference between the numbers. The incomplete square of the difference is the expression:
(a 2 − ab + b 2)
This square is incomplete, since in the middle, instead of the double product, there is the usual product of numbers. - a 2 + 2a + 1 = (a + 1) 2
- (ac − 4b)(ac + 4b) = a 2 c 2 − 16b 2
- Preferential pension for hazardous conditions in 2018 General information Citizens who are entitled to a preferential pension for hazardous conditions must work for at least 10 years in dangerous and harmful conditions. If there is not enough experience, access to [...]
- Law on the Protection of Consumer Rights Articles 27-31 Disputes about the protection of consumer rights are one of the most common and relevant In disputes about the protection of consumer rights, one of the parties is always the citizen purchasing or ordering goods [...]
- WHAT IS IMPORTANT TO KNOW ABOUT THE NEW PENSION LAW Subscription to news A letter to confirm your subscription has been sent to the e-mail you specified. March 15, 2018 The Pension Fund reminds that since 2018 the maternity capital program has been expanded […]
- The lawyer demands to punish the bailiff who did not let him into the courtroom. Lawyer Evgeniy Barannikov was not allowed into the courtroom to see his client, while the prosecutor was given this right. Barannikov reached the cassation court in […]
- Sample claim if consumer rights are violated when using the services of a car service When handing over a car to a car service, first of all, you need to ensure that the documents are completed correctly. According to clause 15 of the “Rules for the provision of services […]
- How to return goods to a supplier in 1C Question: How to return goods to a supplier in 1C: Accounting 8 (rev. 3.0)? Date of publication 05/11/2016 Release 3.0.43 used Return of goods not accepted for registration Return of accepted […]
- Creation of a Training Center At the moment, the creation of a training center is possible in two options: 1. Creation of a Training Center for Vocational Training (for blue-collar professions). 2. Creation of a corporate training center in the form of […]
- On moral and psychological support for the operational and official activities of the internal affairs bodies of the Russian Federation MINISTRY OF INTERNAL AFFAIRS OF THE RUSSIAN FEDERATION ORDER “11” February 2010 No. 80 On moral and psychological support […]
Solution: 17 - 7 = 10
The integer values are given: 56, 12, 4.
12 and 4 are subtracted values.
Method 1 (sequential subtraction of subtracted values):
Method 2 (subtracting two subtrahends from the sum being reduced, which in this case are called addends):
Answer: 40 is the difference of three values.
Given fractions with the same denominators, where
4/5 is a fraction to be reduced,
To complete the solution, you need to repeat the actions with fractions. That is, you need to know how to subtract fractions with the same denominator. How to handle fractions that have different denominators. They must be able to bring them to a common denominator.
Solution: 4/5 - 3/5 = (4 - 3)/5 = 1/5
How to perform such an example when you need to double or triple the difference?
2) 2 * 3 = 6. Answer: 6 is the difference between the numbers 7 and 5.
7 - reduced value;
And even though at the beginning of your journey the calculations are reduced to primitive examples, everything is ahead of you. And you will have to master a lot. We see that there are many operations with different quantities in mathematics. Therefore, in addition to the difference, it is necessary to study how to calculate the remaining results of arithmetic operations:
The basic arithmetic operations in mathematics are:
Each result of these actions also has its own name:
This is interesting: what is the modulus of a number?
Looking at Definitions, what is the difference between numbers in mathematics, this concept can be defined in several ways:
Let’s take as a basis the notation for the difference that the school curriculum offers us:
Mathematical operations with number differences
Solution: 20 - 15 = 5
Solution: 32 + 48 = 80
Answer: Subtract value 10.
More complex examples
The solution can be done in two ways.
1) 56 - 12 = 44 (here 44 is the resulting difference of the first two quantities, which in the second action will be reduced);
1) 12 + 4 = 16 (where 16 is the sum of two terms, which will be subtracted in the next operation);
Everything seems clear. Stop! Is the subtrahend greater than the minuend?
Math for blondes
At school, we were taught to calculate such operations with mathematical quantities in a column, and later - on a calculator. The calculator is also a handy aid. But, for the development of thinking, intelligence, outlook and other life qualities, we advise you to perform arithmetic operations on paper or even in your mind. The beauty of the human body is the great achievement of the modern fitness plan. But the brain is also a muscle that sometimes requires pumping. So, without delay, start thinking.
The word "difference" can have many meanings. This can also mean a difference in something, for example, opinions, views, interests. In some scientific, medical and other professional fields, this term refers to various indicators, for example, blood sugar levels, atmospheric pressure, and weather conditions. The concept of “difference” as a mathematical term also exists.
To explain in simpler language the concepts of sum, difference, product and quotient in mathematics, we can simply write them down only as phrases:
Difference in mathematics
And all these definitions are true.
All clear. But at the same time we received several more mathematical terms. What do they mean?
Based on the derived rules, we can consider illustrative examples. Mathematics is an interesting science. Here we will take only the simplest numbers to solve. Having learned to subtract them, you will learn to solve more complex values, three-digit, four-digit, integer, fractional, powers, roots, etc.
Simple examples
20 - decreasing value,
Answer: 5 - difference in values.
32 is the subtracted value.
17 is the value being reduced.
Examples 1-3 examine actions with simple integers. But in mathematics, the difference is calculated using not only two, but also several numbers, as well as integers, fractions, rational, irrational, etc.
56 - value to be reduced,
Let's use the rules again:
7 - reduced value,
5 - subtracted value.
And again there is a rule that applies to a specific case:
Answer: - 11. This negative value is the difference between two quantities, provided that the quantity being subtracted is greater than the quantity being reduced.
On the World Wide Web you can find a lot of thematic sites that will answer any question. In the same way, online calculators for every taste will help you with any mathematical calculations. All the calculations made on them are an excellent help for the hasty, incurious, and lazy. Math for Blondes is one such resource. Moreover, we all resort to it, regardless of hair color, gender and age.
This is some interesting arithmetic.
1st grade Mathematics. "Amount and value of the amount"
Goals:
Equipment: Chalk, board, cards, multimedia installation, presentation.
1. Organizing the class for a lesson.
2. Communicating the topic and objectives of the lesson:
Today in class we will discover and reveal the secrets of mathematics. So, let's go!
3. Getting to know new material.
Guys, do you like fairy tales? What about Walt Disney's fairy tales? Now I’ll read an excerpt from a fairy tale, and you try to guess who I’m talking about.
Wake up, friend Owl! - the little bunny Fatty shouted cheerfully. - A new prince has been born!
The good news instantly spread throughout the forest, and all the forest inhabitants rushed to look at the newborn fawn. They were touched as they watched him try to get up. His legs were still too weak, and he kept falling.
Who recognized him? This is, indeed, a fawn named Bambi. And then one day the time came to introduce him to the forest. From the fairy tale, we know that Bambi is inquisitive, so he was delighted with everything he saw around him.
Let us go with the fawn to the unusual “forest of mathematics”.
The fawn finds himself in a clearing and sees many flowers. But after taking a closer look, he notices that the flowers hold some kind of secret.
Help him solve this mystery.
Look and tell me what do you see? What kinds of mathematical notations can we make?
Abbreviated multiplication formulas
When calculating algebraic polynomials, to simplify calculations, use abbreviated multiplication formulas. There are seven such formulas in total. You need to know them all by heart.
It should also be remembered that instead of “a” and “b” in formulas there can be either numbers or any other algebraic polynomials.
Difference of squares
Difference of squares two numbers is equal to the product of the difference of these numbers and their sum.
a 2 − b 2 = (a − b)(a + b)
Square of the sum
The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first number and the second plus the square of the second number.
(a + b) 2 = a 2 + 2ab + b 2
Please note that with this abbreviated multiplication formula it is easy find squares of large numbers without using a calculator or long multiplication. Let's explain with an example:
Remember that the square sum formula is also valid for any algebraic polynomials.
Squared difference
The square of the difference of two numbers is equal to the square of the first number minus twice the product of the first and the second plus the square of the second number.
(a − b) 2 = a 2 − 2ab + b 2
It's also worth remembering a very useful transformation:
The formula above can be proven by simply opening the parentheses:
(a − b) 2 = a 2 −2ab + b 2 = b 2 − 2ab + a 2 = (b − a) 2
The cube of the sum of two numbers is equal to the cube of the first number plus triple the product of the square of the first number and the second plus triple the product of the first by the square of the second plus the cube of the second.
(a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3
How to remember the cube of a sum
It’s quite easy to remember this “scary”-looking formula.
Warning!
Difference cube
Difference cube two numbers is equal to the cube of the first number minus three times the product of the square of the first number and the second plus three times the product of the first number and the square of the second minus the cube of the second.
(a − b) 3 = a 3 − 3a 2 b + 3ab 2 − b 3
This formula is remembered like the previous one, but only taking into account the alternation of the “+” and “−” signs. The first term “a 3” is preceded by “+” (according to the rules of mathematics, we do not write it). This means that the next term will be preceded by “−”, then again by “+”, etc.
(a − b) 3 = + a 3 − 3a 2 b + 3ab 2 − b 3 = a 3 − 3a 2 b + 3ab 2 − b 3
Sum of cubes
Not to be confused with the sum cube!
Sum of cubes is equal to the product of the sum of two numbers and the partial square of the difference.
a 3 + b 3 = (a + b)(a 2 − ab + b 2)
The sum of cubes is the product of two brackets.
Difference of cubes
Not to be confused with the difference cube!
Difference of cubes is equal to the product of the difference of two numbers and the partial square of the sum.
a 3 − b 3 = (a − b)(a 2 + ab + b 2)
Be careful when writing down signs.
Using abbreviated multiplication formulas
It should be remembered that all the formulas given above are also used from right to left.
Many examples in textbooks are designed for you to put a polynomial back together using formulas.
You can download a table with all abbreviated multiplication formulas in the “Cribs” section.
21. Cube of sum and cube of difference. Rules
For any values of a and b, the equality is true
(a + b) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3 . (1)
(a + b) 3 = (a + b) (a 2 + 2 a b + b 2) =
A 3 + 2 a 2 b + a b 2 + a 2 b + 2 a b 2 + b 3 =
A 3 + 3 a 2 b + 3 a b 2 + b 3
Since equality (1) is true for any values of a and b,
sum cube formula. If in this formula instead of a and b
then again we get an identity.
(5 y 3 + 2 z) 3 = 125 y 9 + 150 y 6 z + 60 y 3 z 2 + 8 z 3. (2)
Therefore, the sum cube formula reads like this:
the cube of the sum of two expressions is equal to the cube of the first expression
plus triple the product of the square of the first expression and the second,
plus triple the product of the first expression and the square of the second,
plus the cube of the second expression.
(a − b) 3 = a 3 − 3 a 2 b + 3 a b 2 − b 3 . (3)
(a − b) 3 = (a − b) (a 2 − 2 a b + b 2) =
A 3 − 2 a 2 b + a b 2 − a 2 b + 2 a b 2 − b 3 =
A 3 − 3 a 2 b + 3 a b 2 − b 3
Since equality (3) is true for any values of a and b,
then it is an identity. This identity is called
difference cube formula. If in this formula instead of a and b
substitute some expressions, for example 5 y 3 and 2 z,
then again we get an identity.
(5 y 3 − 2 z) 3 = 125 y 9 − 150 y 6 z + 60 y 3 z 2 − 8 z 3 . (4)
Therefore, the difference cube formula reads like this:
the cube of the difference of two expressions is equal to the cube of the first expression
minus triple the product of the square of the first expression and the second,
plus triple the product of the first expression and the square of the second,
minus the cube of the second expression.
Problems on the topic “Cube of sum and cube of difference”
Using the sum cube or difference cube formula, transform the expression
into a polynomial of standard form and choose the correct answer.
1) = a 3 − 3 a 2 c + 3 a c 2 − c 3
2) = a 3 − 3 a 2 c + 3 a c 2 + c 3
3) = a 3 − 3 a c 2 + 3 a c 2 − c 3 Incorrect. Don't click on an empty field. (x + 2 y) 3 =
1) = x 3 + 6 x 2 y + 6 x y 2 + 4 y 3
2) = x 3 + 6 x 2 y + 12 x y 2 + 8 y 3
3) = x 3 + 6 x 2 y + 6 x y 2 + 8 y 3 Incorrect. Wrong. Wrong. Don't click on an empty field. Wrong. (3 a − 2 b) 3 =
1) = 27 a 3 − 27 a 2 b + 12 a b 2 − 8 b 3
2) = 27 a 3 − 54 a 2 b + 36 a b 2 − 8 b 3
3) = 27 a 3 − 18 a 2 b + 18 a b 2 − 8 b 3 Incorrect. Wrong. Don't click on an empty field. Wrong. (
Subtraction is an arithmetic operation inverse to addition, by means of which as many units are subtracted (subtracted) from one number as are contained in another number.
The number from which it is subtracted is called reducible, the number that indicates how many units will be subtracted from the first number is called deductible. The number resulting from subtraction is called difference(or the remainder).
Let's look at subtraction using an example. There are 9 candies on the table, if you eat 5 candies, then there will be 4 left. The number 9 is the minuend, 5 is the subtrahend, and 4 is the remainder (difference):
To write a subtraction, use the - (minus) sign. It is placed between the minuend and the subtrahend, with the minuend written to the left of the minus sign, and the subtrahend to the right. For example, the entry 9 - 5 means that the number 5 is subtracted from the number 9. To the right of the subtraction entry, put an = (equal) sign, after which the result of the subtraction is written. So the complete subtraction notation looks like this:
This entry reads like this: the difference between nine and five equals four or nine minus five equals four.
In order to obtain a natural number or 0 as a result of subtraction, the minuend must be greater than or equal to the subtrahend.
Let's consider how, using the natural series, you can perform subtraction and find the difference of two natural numbers. For example, we need to calculate the difference between the numbers 9 and 6, mark the number 9 in the natural series and count 6 numbers from it to the left. We get the number 3:
Subtraction can also be used to compare two numbers. Wanting to compare two numbers, we ask ourselves how many units one number is greater or less than the other. To find out, you need to subtract the smaller number from the larger number. For example, to find out how much 10 is less than 25 (or how much 25 is more than 10), you need to subtract 10 from 25. Then we find that 10 is less than 25 (or 25 is more than 10) by 15 units.
Subtraction check
Consider the expression
where 15 is the minuend, 7 is the subtrahend, and 8 is the difference. To find out whether the subtraction was performed correctly, you can:
- add the subtrahend with the difference, if you get the minuend, then the subtraction was performed correctly:
- subtract the difference from the minuend; if you get the subtrahend, then the subtraction was performed correctly:
In elementary school, a child is first introduced to mathematics, and his first examples are simple operations such as addition or subtraction. But sometimes it is difficult to explain to a child even such seemingly simple and familiar examples to adults. How can you learn to find the sum and difference of numbers?
What is the amount and how to find it
A sum is the result of adding two numbers (terms) between which there is a + sign. To get the sum, you need to add the second term to one term. In general, an example can be shown as follows: a + b = s, where a is the first term, b is the second term, and s is the result of adding these two terms. At the same time, you need to know that rearranging the terms does not change the sum - this is one of the very first rules in mathematics, which is taught in elementary school.To visually show your child how to add numbers, take candy or any other things. Show your child two candies, and then add two more candies to these candies. Let the child count and say that there are now four candies. Explain to him that he just added these numbers, that is, he added another number to one number and ultimately got the sum.
It is a little more difficult to explain the addition of bit terms; this topic may not be clear to a child. So, there are many categories: units, tens, thousands. Take, for example, the number 2564. If you decompose it into digits, you get: 2564 = 2000 + 500 + 60 + 4. To add, for example, the number 305 to this number, use column addition. With this addition, you need to add some digits to others, starting from the end: ones to ones, tens to tens, thousands to thousands. That is, first we add 4 and 5, then 6 and 0, after 5 and 3, and finally 2 and 0. Ultimately we get the number 2869.
How to find the difference between numbers
The difference is the result of subtracting one number from another. Unlike the sum, here we cannot use the rule “the difference does not change by rearranging the terms,” since in subtraction there is always a minuend and a subtrahend. To find the subtrahend and the difference, you first need to understand these concepts. The diminished is what we “subtract” from, that is, we remove, and the subtracted is the amount of what we return from this diminished. In general, subtraction can be written as follows: a - b = r.
Let's turn to the same candies with which we analyzed the sum of numbers. To help your child find the difference between numbers, take five candies. Let the child count and make sure there are five. Then take three candies for yourself. The child will say that there are two left. How much did they take then? Three.
As for the bit terms, here we do the same thing as with the sum, only now we do not add, but subtract. Let's take the number 6845 and subtract 4231 from it. To do this, we subtract one digit from another digit, subtracting from the end: 5-1 = 4, 4-3 = 1, 8-2 = 6, 6-4 = 2. In the answer we get 2614.
