Subtraction. How to find the difference of an arithmetic progression: formulas and examples of solutions What does it mean to calculate the difference of numbers
For many, hard sciences like mathematics are perceived as simpler than areas that require reasoning and involve a lot of variability. However, all subjects have their own difficulties, including technical ones.
Subtraction
In order to understand what the difference is, it is necessary to understand a number of mathematical terminology. First of all, you need to find out what subtraction is.
In another way, this concept is called reduction, and by this name it is somewhat easier to understand the meaning of the process. At its core, subtraction is a mathematical operation. What kind of operations are these? As a rule, they mean certain arithmetic or logical operations. A logical question arises: what is the essence of arithmetic operations?
The concept of arithmetic appeared quite a long time ago. It originated in ancient Greek, where it was translated as “number”. Today it is a branch of mathematics that studies numbers, their relationships to each other, and properties.
So, subtraction - these are number operations related to binary. The essence of binary operations is that they use two arguments (parameters) and produce one result.
It is worth considering how to find the difference of a number. First of all, two arguments are needed, that is, two numbers. Then you need to reduce the value of the first number by the value of the second. When this operation is expressed in writing, a minus sign is used. It looks like this: a – b = c, where a is the first numerical value, b is the second, and c is the difference of the numbers.
Properties and Features
As a rule, students have much more problems with subtraction than with addition. This is partly due to the properties of these mathematical operations. Everyone knows that changing the places of the terms does not change the value of the sum. In subtraction, everything is much more complicated. If you swap the numbers, you get a completely different result. A similar property in addition and decrease is that the zero element does not change the original number.
In subtraction, everything is relatively simple if the first number is greater than the second, but in school we will also consider counterexamples. In this case, the concept of a negative number arises.
For example, if you need to subtract the number 2 from 5, then everything is not difficult. 5-2=3, so the difference of the number will be 3. However, what if you need to calculate how much two minus five is?
In expression 2-5, the difference will go into minus, that is, into a negative value. You can easily subtract a two from a two, thus getting a zero, but from a five there are still three left. Thus, the result of this expression will be negative three. That is, 2-5=-3.
Features of subtracting negative numbers
There are also situations where the second number is, in fact, less than the first, but is negative. For example, consider the expression 7-(-4). The easiest way to understand this operation is by turning the combination –(- into a regular plus. The signs even superficially resemble it. In this regard, the result of the expression, that is, the difference in numbers, will be 11.
If both numbers are negative, then the subtraction will occur as follows.
6-(-7): the minus of the first number will remain, and the combination of the two subsequent minuses will turn into a plus. Thus, you need to understand how much -6+7 will be. The difference is not difficult to find - it is equal to one.
If you need to subtract a positive number from a negative one, then the expression can be represented as a simple addition, and then add a minus to the result. For example, -3-4 (4 is a positive number) will result in -7.
Difference or subtraction of integers is directly related to the topic of addition of integers. After all, knowing the sum and one of the terms, you can find the second term. Let's look at an example:
We have 10 apples in the basket. The first time you added 2 apples to the basket, how many apples were added to the basket the second time to get 10 apples in the end?
Let us denote the variable x as the number of apples added a second time. If we add two apples to the variable x, we get 10 apples. Mathematically, the entry would look like this:
to find the variable x you need to remove 2 apples from the basket or subtract one known term 2 from the sum 10.
That is, the variable x=8.
Definition:
The difference of two integers is an integer that, when added to the subtrahend, gives the minuend.
The difference of integers a and b is denoted as a-b.
Differencea-b is the sum of the numbersa and the opposite numberb.
a-b=a+(-b)
where b and –b are opposite numbers.
Example:
5-2=5+(-2)=3
Subtracting positive integers with examples.
Example:
Subtract the number 5 from the integer 12.
Solution:
According to the difference rule, we must replace the subtrahend 5 with the opposite number, that is, -5 and perform.
Example:
Subtract 56 from the number 37.
Solution:
You need to replace the subtrahend number 56 with the opposite number, that is, the number -56, and perform the addition of integers with different signs.
37-56=37+(-56)=-21
Example:
From the number -4 you need to subtract the number 7.
Solution:
Replace the subtracted number 7 with the opposite number -7 and add from according to the rule
4-7=-4+(-7)=-11
Subtracting negative integers with examples.
Example:
Find the difference between the numbers 6 and -8.
Solution:
According to the difference rule, you need to replace the subtrahend -8 with the opposite number +8 or 8 and calculate the sum of the integers. We get:
From the whole number -14, subtract the number -10.
You need to replace the subtracted -10 with the opposite number +10 or 10 according to the rule for subtracting integers and then perform the addition.
14-(-10)=-14+10=-4
Subtracting zero from integers.
If you subtract zero from an integer, the number does not change.
Let's look at an example:
3-0=3+0=3
a-0=a
If we subtract zero from zero, we get zero.
Subtraction of identical integers.
Let's consider the problem:
Misha received 2 candies from his mother and he immediately treated his friend Sasha to two candies. How many sweets does Misha have left?
Solution:
Misha received 2 candies and gave 2 candies, mathematically it can be written like this:
Answer: Misha has 0 candies left.
That is, if you do Subtracting equal numbers results in zero.
Checking the subtraction result.
How to check if you found the difference of two integers correctly?
The answer is simple; it lies in the very definition of the difference between two integers. Need to add the difference with the subtrahend we get the minuend. The verbal formula will look like this:
Difference + Subtrahend = Minuend
Example:
19-5=14
19 is our minuend;
5 – subtrahend;
14 – difference.
Let's check:
We add the minuend to the difference; if we perform the subtraction correctly, we get the minuend.
Another example:
Check subtraction 12-23=-11
12 – reduced;
23 – subtractable;
-11 – difference.
Let's check the subtraction:
Difference + Subtrahend = Minuend
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 place 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 of them 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.
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 one of them is greater 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.
- sum - by adding 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 - Let's write the sum of numbers in brackets and put 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
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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 the concepts of sum, difference, product and quotient in mathematics in a simpler language, we can simply write them down only as phrases:
Difference in mathematics
And all these definitions are true.
Everything is 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. (
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
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