Negative numbers are numbers with a minus sign (−), for example −1, −2, −3. Reads like: minus one, minus two, minus three.
Application example negative numbers is a thermometer that shows the temperature of the body, air, soil or water. In winter, when it is very cold outside, the temperature can be negative (or, as people say, “minus”).
For example, −10 degrees cold:
The ordinary numbers that we looked at earlier, such as 1, 2, 3, are called positive. Positive numbers are numbers with a plus sign (+).
When writing positive numbers, the + sign is not written down, which is why we see the numbers 1, 2, 3 that are familiar to us. But we should keep in mind that these positive numbers look like this: +1, +2, +3.
Lesson contentThis is a straight line on which all numbers are located: both negative and positive. As follows:
The numbers shown here are from −5 to 5. In fact, the coordinate line is infinite. The figure shows only a small fragment of it.
Numbers on the coordinate line are marked as dots. In the figure, the thick black dot is the origin. The countdown starts from zero. Negative numbers are marked to the left of the origin, and positive numbers to the right.
The coordinate line continues indefinitely on both sides. Infinity in mathematics is symbolized by the symbol ∞. The negative direction will be indicated by the symbol −∞, and the positive direction by the symbol +∞. Then we can say that all numbers from minus infinity to plus infinity are located on the coordinate line:
Each point on the coordinate line has its own name and coordinate. Name is any Latin letter. Coordinate is a number that shows the position of a point on this line. Simply put, a coordinate is the very number that we want to mark on the coordinate line.
For example, point A(2) reads as "point A with coordinate 2" and will be denoted on the coordinate line as follows:
Here A is the name of the point, 2 is the coordinate of the point A.
Example 2. Point B(4) reads as "point B with coordinate 4"
Here B is the name of the point, 4 is the coordinate of the point B.
Example 3. Point M(−3) reads as "point M with coordinate minus three" and will be denoted on the coordinate line as follows:
Here M is the name of the point, −3 is the coordinate of point M .
Points can be designated by any letters. But it is generally accepted to denote them in capital Latin letters. Moreover, the beginning of the report, which is otherwise called origin usually denoted by the capital Latin letter O
It is easy to notice that negative numbers lie to the left relative to the origin, and positive numbers lie to the right.
There are phrases such as “the further to the left, the less” And "the further to the right, the more". You probably already guessed what we are talking about. With each step to the left, the number will decrease downwards. And with each step to the right the number will increase. An arrow pointing to the right indicates a positive reference direction.
Comparing negative and positive numbers
Rule 1. Any negative number is less than any positive number.
For example, let's compare two numbers: −5 and 3. Minus five less than three, despite the fact that five strikes the eye first of all as a number greater than three.
This is due to the fact that −5 is a negative number, and 3 is positive. On the coordinate line you can see where the numbers −5 and 3 are located
It can be seen that −5 lies to the left, and 3 to the right. And we said that “the further to the left, the less” . And the rule says that any negative number is less than any positive number. It follows that
−5 < 3
"Minus five is less than three"
Rule 2. Of two negative numbers, the one that is located to the left on the coordinate line is smaller.
For example, let's compare the numbers −4 and −1. Minus four less, than minus one.
This is again due to the fact that on the coordinate line −4 is located to the left than −1
It can be seen that −4 lies to the left, and −1 to the right. And we said that “the further to the left, the less” . And the rule says that of two negative numbers, the one that is located to the left on the coordinate line is smaller. It follows that
Minus four is less than minus one
Rule 3. Zero is greater than any negative number.
For example, let's compare 0 and −3. Zero more than minus three. This is due to the fact that on the coordinate line 0 is located more to the right than −3
It can be seen that 0 lies to the right, and −3 to the left. And we said that "the further to the right, the more" . And the rule says that zero is greater than any negative number. It follows that
Zero is greater than minus three
Rule 4. Zero is less than any positive number.
For example, let's compare 0 and 4. Zero less, than 4. This is in principle clear and true. But we will try to see this with our own eyes, again on the coordinate line:
It can be seen that on the coordinate line 0 is located to the left, and 4 to the right. And we said that “the further to the left, the less” . And the rule says that zero is less than any positive number. It follows that
Zero is less than four
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Positive and negative numbers
Coordinate line
Let's go straight. Let's mark point 0 (zero) on it and take this point as the starting point.
We indicate with an arrow the direction of movement in a straight line to the right from the origin of coordinates. In this direction from point 0 we will plot positive numbers.
That is, numbers that are already known to us, except zero, are called positive.
Sometimes positive numbers are written with a “+” sign. For example, "+8".
For brevity, the “+” sign before a positive number is usually omitted and instead of “+8” they simply write 8.
Therefore, “+3” and “3” are the same number, only designated differently.
Let's choose some segment whose length we take as one and move it several times to the right from point 0. At the end of the first segment the number 1 is written, at the end of the second - the number 2, etc. 
Putting the unit segment to the left from the origin we get negative numbers: -1; -2; etc.
Negative numbers used to denote various quantities, such as: temperature (below zero), flow - that is, negative income, depth - negative height, and others.
As can be seen from the figure, negative numbers are numbers already known to us, only with a minus sign: -8; -5.25, etc.
- The number 0 is neither positive nor negative.
The number axis is usually positioned horizontally or vertically.
If the coordinate line is located vertically, then the direction up from the origin is usually considered positive, and the direction down from the origin is negative.
The arrow indicates the positive direction.
The straight line marked:
. origin (point 0);
. unit segment;
. the arrow indicates the positive direction;
called coordinate line
or number axis.
Opposite numbers on a coordinate line
Let us mark two points A and B on the coordinate line, which are located at the same distance from point 0 on the right and left, respectively.
In this case, the lengths of the segments OA and OB are the same.
This means that the coordinates of points A and B differ only in sign. 
Points A and B are also said to be symmetrical about the origin.
The coordinate of point A is positive “+2”, the coordinate of point B has a minus sign “-2”.
A (+2), B (-2).
- Numbers that differ only in sign are called opposite numbers. The corresponding points of the numerical (coordinate) axis are symmetrical relative to the origin.
Every number has only one opposite number. Only the number 0 does not have an opposite, but we can say that it is the opposite of itself.
The notation "-a" means the opposite number of "a". Remember that a letter can hide either a positive number or a negative number.
Example:
-3 is the opposite number of 3.
We write it as an expression:
-3 = -(+3)
Example:
-(-6) is the opposite number to the negative number -6. So -(-6) is a positive number 6.
We write it as an expression:
-(-6) = 6
Adding Negative Numbers
The addition of positive and negative numbers can be analyzed using the number line.
It is convenient to perform the addition of small modulo numbers on a coordinate line, mentally imagining how the point denoting the number moves along the number axis.
Let's take some number, for example, 3. Let's denote it on the number axis by point A.
Let's add the positive number 2 to the number. This will mean that point A must be moved two unit segments in the positive direction, that is, to the right. As a result, we get point B with coordinate 5.
3 + (+ 2) = 5
In order to add a negative number (- 5) to a positive number, for example, 3, point A must be moved 5 units of length in the negative direction, that is, to the left.
In this case, the coordinate of point B is - 2.
So, the order of adding rational numbers using the number line will be as follows:
. mark a point A on the coordinate line with a coordinate equal to the first term;
. move it a distance equal to the modulus of the second term in the direction that corresponds to the sign in front of the second number (plus - move to the right, minus - to the left);
. the point B obtained on the axis will have a coordinate that will be equal to the sum of these numbers.
Example.
- 2 + (- 6) =
Moving from point - 2 to the left (since there is a minus sign in front of 6), we get - 8.
- 2 + (- 6) = - 8
Adding numbers with the same signs
Adding rational numbers can be easier if you use the concept of modulus.
Let us need to add numbers that have the same signs.
To do this, we discard the signs of the numbers and take the modules of these numbers. Let's add the modules and put the sign in front of the sum that was common to these numbers.
Example. 
An example of adding negative numbers.
(- 3,2) + (- 4,3) = - (3,2 + 4,3) = - 7,5
- To add numbers of the same sign, you need to add their modules and put in front of the sum the sign that was before the terms.
Adding numbers with different signs
If the numbers have different signs, then we act somewhat differently than when adding numbers with the same signs.
. We discard the signs in front of the numbers, that is, we take their modules.
. From the larger module we subtract the smaller one.
. Before the difference we put the sign that was in the number with a larger module.
An example of adding a negative and a positive number.
0,3 + (- 0,8) = - (0,8 - 0,3) = - 0,5
An example of adding mixed numbers.
To add numbers of different signs you need:
. subtract the smaller module from the larger module;
. Before the resulting difference, put the sign of the number with the larger modulus.
Subtracting Negative Numbers
As you know, subtraction is the opposite of addition.
If a and b are positive numbers, then subtracting the number b from the number a means finding a number c that, when added to the number b, gives the number a.
a - b = c or c + b = a
The definition of subtraction holds true for all rational numbers. That is subtracting positive and negative numbers can be replaced by addition.
- To subtract another from one number, you need to add the opposite number to the one being subtracted.
Or, in another way, we can say that subtracting the number b is the same as addition, but with the opposite number to b.
a - b = a + (- b)
Example.
6 - 8 = 6 + (- 8) = - 2
Example.
0 - 2 = 0 + (- 2) = - 2
- It is worth remembering the expressions below.
- 0 - a = - a
- a - 0 = a
- a - a = 0
Rules for subtracting negative numbers
As can be seen from the examples above, subtracting a number b is an addition with a number opposite to b.
This rule holds true not only when subtracting a smaller number from a larger number, but also allows you to subtract a larger number from a smaller number, that is, you can always find the difference of two numbers.
The difference can be a positive number, a negative number, or a zero number.
Examples of subtracting negative and positive numbers.
. - 3 - (+ 4) = - 3 + (- 4) = - 7
. - 6 - (- 7) = - 6 + (+ 7) = 1
. 5 - (- 3) = 5 + (+ 3) = 8
It is convenient to remember the sign rule, which allows you to reduce the number of parentheses.
The plus sign does not change the sign of the number, so if there is a plus in front of the parenthesis, the sign in the parentheses does not change.
+ (+ a) = + a
+ (- a) = - a
The minus sign in front of the parentheses reverses the sign of the number in the parentheses.
- (+ a) = - a
- (- a) = + a
From the equalities it is clear that if there are identical signs before and inside the brackets, then we get “+”, and if the signs are different, then we get “-”.
(- 6) + (+ 2) - (- 10) - (- 1) + (- 7) = - 6 + 2 + 10 + 1 - 7 = - 13 + 13 = 0
The sign rule also applies if the brackets contain not just one number, but an algebraic sum of numbers.
a - (- b + c) + (d - k + n) = a + b - c + d - k + n
Please note that if there are several numbers in brackets and there is a minus sign in front of the brackets, then the signs in front of all the numbers in these brackets must change.
To remember the rule of signs, you can create a table for determining the signs of a number.
Sign rule for numbers
Or learn a simple rule.
- Two negatives make an affirmative,
- Plus times minus equals minus.
Multiplying Negative Numbers
Using the concept of the modulus of a number, we formulate the rules for multiplying positive and negative numbers.
Multiplying numbers with the same signs
The first case that you may encounter is the multiplication of numbers with the same signs.
To multiply two numbers with the same signs:
. multiply the modules of numbers;
. put a “+” sign in front of the resulting product (when writing the answer, the “plus” sign before the first number on the left can be omitted).
Examples of multiplying negative and positive numbers.
. (- 3) . (- 6) = + 18 = 18
. 2 . 3 = 6
Multiplying numbers with different signs
The second possible case is the multiplication of numbers with different signs.
To multiply two numbers with different signs:
. multiply the modules of numbers;
. Place a “-” sign in front of the resulting work.
Examples of multiplying negative and positive numbers.
. (- 0,3) . 0,5 = - 1,5
. 1,2 . (- 7) = - 8,4
Rules for multiplication signs
Remembering the sign rule for multiplication is very simple. This rule coincides with the rule for opening parentheses.
- Two negatives make an affirmative,
- Plus times minus equals minus.
In “long” examples, in which there is only a multiplication action, the sign of the product can be determined by the number of negative factors.
At even number of negative factors, the result will be positive, and with odd quantity - negative.
Example.
(- 6) . (- 3) . (- 4) . (- 2) . 12 . (- 1) =
There are five negative factors in the example. This means that the sign of the result will be “minus”.
Now let's calculate the product of the moduli, not paying attention to the signs.
6 . 3 . 4 . 2 . 12 . 1 = 1728
The end result of multiplying the original numbers will be:
(- 6) . (- 3) . (- 4) . (- 2) . 12 . (- 1) = - 1728
Multiplying by zero and one
If among the factors there is a number zero or positive one, then the multiplication is performed according to known rules.
. 0 . a = 0
. a. 0 = 0
. a. 1 = a
Examples:
. 0 . (- 3) = 0
. 0,4 . 1 = 0,4
Negative one (- 1) plays a special role when multiplying rational numbers.
- When multiplied by (- 1), the number is reversed.
In literal expression, this property can be written:
a. (- 1) = (- 1) . a = - a
When adding, subtracting and multiplying rational numbers together, the order of operations established for positive numbers and zero is maintained.
An example of multiplying negative and positive numbers.
Dividing negative numbers
It's easy to understand how to divide negative numbers by remembering that division is the inverse of multiplication.
If a and b are positive numbers, then dividing the number a by the number b means finding a number c that, when multiplied by b, gives the number a.
This definition of division applies to any rational numbers as long as the divisors are non-zero.
Therefore, for example, dividing the number (- 15) by the number 5 means finding a number that, when multiplied by the number 5, gives the number (- 15). This number will be (- 3), since
(- 3) . 5 = - 15
Means
(- 15) : 5 = - 3
Examples of dividing rational numbers.
1. 10: 5 = 2, since 2 . 5 = 10
2. (- 4) : (- 2) = 2, since 2 . (- 2) = - 4
3. (- 18) : 3 = - 6, since (- 6) . 3 = - 18
4. 12: (- 4) = - 3, since (- 3) . (- 4) = 12
From the examples it is clear that the quotient of two numbers with the same signs is a positive number (examples 1, 2), and the quotient of two numbers with different signs is a negative number (examples 3,4).
Rules for dividing negative numbers
To find the modulus of a quotient, you need to divide the modulus of the dividend by the modulus of the divisor.
So, to divide two numbers with the same signs, you need to:
. Place a “+” sign in front of the result.
Examples of dividing numbers with the same signs:
. (- 9) : (- 3) = + 3
. 6: 3 = 2
To divide two numbers with different signs, you need to:
. divide the module of the dividend by the module of the divisor;
. Place a “-” sign in front of the result.
Examples of dividing numbers with different signs:
. (- 5) : 2 = - 2,5
. 28: (- 2) = - 14
You can also use the following table to determine the quotient sign.
Rule of signs for division
When calculating “long” expressions in which only multiplication and division appear, it is very convenient to use the sign rule. For example, to calculate a fraction
Please note that the numerator has 2 minus signs, which when multiplied will give a plus. There are also three minus signs in the denominator, which when multiplied will give a minus sign. Therefore, in the end the result will turn out with a minus sign.
Reducing a fraction (further actions with the modules of numbers) is performed in the same way as before:
- The quotient of zero divided by a number other than zero is zero.
- 0: a = 0, a ≠ 0
- You CANNOT divide by zero!
All previously known rules of division by one also apply to the set of rational numbers.
. a: 1 = a
. a: (- 1) = - a
. a: a = 1
, where a is any rational number.
The relationships between the results of multiplication and division, known for positive numbers, remain the same for all rational numbers (except zero):
. if a . b = c; a = c: b; b = c: a;
. if a: b = c; a = c. b; b = a: c
These dependencies are used to find the unknown factor, dividend and divisor (when solving equations), as well as to check the results of multiplication and division.
An example of finding the unknown.
x. (- 5) = 10
x = 10: (- 5)
x = - 2
Minus sign in fractions
Divide the number (- 5) by 6 and the number 5 by (- 6).
We remind you that the line in the notation of an ordinary fraction is the same division sign, and we write the quotient of each of these actions in the form of a negative fraction.
Thus, the minus sign in a fraction can be:
. before a fraction;
. in the numerator;
. in the denominator. 
- When writing negative fractions, the minus sign can be placed in front of the fraction, transferred from the numerator to the denominator, or from the denominator to the numerator.
This is often used when working with fractions, making calculations easier.
Example. Please note that after placing the minus sign in front of the bracket, we subtract the smaller one from the larger module according to the rules for adding numbers with different signs. 
Using the described property of sign transfer in fractions, you can act without finding out which of the given fractions has a greater modulus.
Lesson
mathematicians
in 6th grade.
The ancient Greek scientist Pythagoras said: “Numbers rule the world.”
You and I live in this world of numbers, and during our school years we learn to work with different numbers.
Updating knowledge
№ 1
Andrey caught a cold, and in the evening his temperature increased from 36.6º to 2.3º. But in the morning he felt better and his temperature dropped by 1.8º. What was Andrey's temperature?
And in the evening? B) in the morning?
Updating knowledge
№ 2
- What is shown in the picture?
- What is the O point called?
- What is the name of segment OA?
- What does the arrow show?
Continue with offers
- The coordinate ray is...
- The starting point is designated -…
- Positive direction-...
- A unit segment is called...
- The coordinates of points A, K, P are respectively equal to -...
- With the help of a coordinate ray you can...
Updating knowledge
Organize information into three columns
Less than zero
Equal to zero
Above zero
1. The company's losses amounted to 1,000,000 rubles, and a few years later the company made a profit of 500,000 rubles.
2. In summer, the average air temperature is 25 ºС warm, and in winter – 20 ºС cold.
3. Sea level.
4. Death Valley is located 86 m below sea level and 57 ºС heat was recorded here.
5. The thermometer scale consists of two parts - red and blue.
6. As you climb Mount Elbrus, whose height is 5,642 m above sea level, the temperature can drop to 30 ºС below zero.
7. For a long time, some numbers were called “debt”, “shortage”, and others “property”.
8. Zero mark on the thermometer scale.
Positive
negative
numbers
Generated results
Subject: form an idea of negative numbers, introduce the concept of a negative number, a positive number, numbers with different signs.
Personal: to generate interest in studying the topic and the desire to apply acquired knowledge and skills.
Metasubject: to form initial ideas about the ideas and methods of mathematics as a universal language of science, a means of modeling phenomena and processes.
When presenting new material,
you need to fill out the table
Theoretical material
I understand/don’t understand (+ / -)
1. Numbers greater than zero are called positive.
Question for the teacher
2. Numbers less than zero are called negative.
3. Numbers with a “+” sign are called positive.
4. Numbers with the “-” sign are called negative.
5. The number 0 is neither positive nor negative.
The world around us is so complex and diverse. Natural and fractional numbers are sometimes not enough to measure some quantities and describe many events.
Guys, what time of year is it now?
How is the weather different in summer and winter?
How did you know it was cold outside?
Using what device?
Let's look at a thermometer.
What is shown on the thermometer?
How are the numbers arranged?
Historical reference
The concept of negative numbers arose in practice a very long time ago, and when solving problems where a larger number had to be subtracted from a smaller number. The Egyptians, Babylonians, as well as the ancient Greeks did not know negative numbers and the mathematicians of that time used a counting board to carry out calculations. And since there were no plus and minus signs, they marked positive numbers on this board with red counting sticks, and negative numbers with blue ones. And for a long time negative numbers were called words that meant debt, shortage, and positive numbers were interpreted as property.
The ancient Greek scientist Diophantus did not recognize negative numbers at all, and if when solving he got a negative root, he discarded it as inaccessible.
Historical reference
Ancient Indian mathematicians had a completely different attitude towards negative numbers: they recognized the existence of negative numbers, but treated them with some distrust, considering them peculiar, not entirely real.
Europeans did not approve of them for a long time, because the interpretation of property and debt caused bewilderment and doubt. Indeed, you can add and subtract property - debt, but how to multiply and divide? It was incomprehensible and unrealistic.
Negative numbers received general recognition in the first half of the 19th century. A theory was created according to which we are now studying negative numbers.
Coordinate line
Let's go straight. Let's mark point 0 (zero) on it and take this point as the starting point.
We indicate with an arrow the direction of movement in a straight line to the right from the origin of coordinates. In this direction from point 0 we will plot positive numbers.
Putting the unit segment to the left from the origin we get negative numbers: -1; -2; etc.
Coordinate line
The number 0 is neither positive nor negative.
The straight line marked:
Origin (point 0);
Unit segment;
The arrow indicates the positive direction;
called coordinate line or number axis.
REMEMBER!
Numbers that differ only in sign are called opposite numbers. The corresponding points of the numerical (coordinate) axis are symmetrical relative to the origin.
Every number has a unique opposite number. Only the number 0 does not have an opposite, but we can say that it is the opposite of itself.
Record "-a" means the opposite number "a". Remember that a letter can hide either a positive number or a negative number.
5 is the opposite number to 5.
We write it as an expression:
REMEMBER!
If one number is positive and the other is negative, then such numbers are said to be
what are they have different signs.
If both numbers are positive or both numbers are negative, then they have identical signs.
Primary consolidation
new material
Which of the numbers
7; 23; -89; ⅜; - 4⅔; -5,4; 9⅞; 0; 10; -14;
A) are positive;
B) are negative;
C) are neither positive nor negative;
D) natural numbers;
Write down the information from the Hydrometeorological Center using the “+” and “-” signs:
a) 18º heat; c) 12º below zero;
b) 7º frost; d) 16º above zero.
a) + 18; b) – 7; at 12 ; d) + 16 or 16
Write six negative fractions with a denominator of 5.
№ 1
Repetition
There are 150 maples growing in the park, oaks account for 2/15 of the number of maples, birches account for 23/34 of the number of oaks, and linden trees account for 20/87 of the total number of maples, oaks and birches.
How many of these trees are there in the park?
№ 2
Repetition
Lesson summary
- What numbers did you meet today?
- What symbol is used to represent negative numbers? Positive numbers?
- What number is zero?
- Which two numbers are said to have different signs? Same signs?
Homework
questions 1 – 3,
Now we'll figure it out positive and negative numbers. First, we will give definitions, introduce notation, and then give examples of positive and negative numbers. We will also dwell on the semantic load that positive and negative numbers carry.
Page navigation.
Positive and Negative Numbers - Definitions and Examples
Give identifying positive and negative numbers will help us. For convenience, we will assume that it is located horizontally and directed from left to right.
Definition.
Numbers that correspond to points of the coordinate line lying to the right of the origin are called positive.
Definition.
The numbers that correspond to the points of the coordinate line lying to the left of the origin are called negative.
The number zero, which corresponds to the origin, is neither a positive nor a negative number.
From the definition of negative and positive numbers it follows that the set of all negative numbers is the set of numbers opposite all positive numbers (if necessary, see the article opposite numbers). Therefore, negative numbers are always written with a minus sign.
Now, knowing the definitions of positive and negative numbers, we can easily give examples of positive and negative numbers. Examples of positive numbers are integers 5, 792 and 101,330, and indeed any natural number is positive. Examples of positive rational numbers are the numbers , 4.67 and 0,(12)=0.121212... , and the negative ones are the numbers , −11 , −51.51 and −3,(3) . As examples of positive irrational numbers we can give the number pi, the number e, and the infinite non-periodic decimal fraction 809.030030003..., and examples of negative irrational numbers are the numbers minus pi, minus e and the number equal to. It should be noted that in the last example it is not at all obvious that the value of the expression is a negative number. To find out for sure, you need to get the value of this expression in the form of a decimal fraction, and we will tell you how to do this in the article comparison of real numbers.
Sometimes positive numbers are preceded by a plus sign, just as negative numbers are preceded by a minus sign. In these cases, you should know that +5=5, 
and so on. That is, +5 and 5, etc. - this is the same number, but designated differently. Moreover, you can come across definitions of positive and negative numbers based on the plus or minus sign.
Definition.
Numbers with a plus sign are called positive, and with a minus sign – negative.
There is another definition of positive and negative numbers based on comparison of numbers. To give this definition, it is enough just to remember that the point on the coordinate line corresponding to the larger number lies to the right of the point corresponding to the smaller number.
Definition.
Positive numbers are numbers that are greater than zero, and negative numbers are numbers less than zero.
Thus, zero sort of separates positive numbers from negative ones.
Of course, we should also dwell on the rules for reading positive and negative numbers. If a number is written with a + or − sign, then pronounce the name of the sign, after which the number is pronounced. For example, +8 is read as plus eight, and - as minus one point two fifths. The names of the signs + and − are not declined by case. An example of correct pronunciation is the phrase “a equals minus three” (not minus three).
Interpretation of positive and negative numbers
We have been describing positive and negative numbers for quite some time. However, it would be nice to know what meaning they carry? Let's look at this issue.
Positive numbers can be interpreted as an arrival, as an increase, as an increase in some value, and the like. Negative numbers, in turn, mean exactly the opposite - expense, deficiency, debt, reduction of some value, etc. Let's understand this with examples.
We can say that we have 3 items. Here the positive number 3 indicates the number of items we have. How can you interpret the negative number −3? For example, the number −3 could mean that we have to give someone 3 items that we don't even have in stock. Similarly, we can say that at the cash register we were given 3.45 thousand rubles. That is, the number 3.45 is associated with our arrival. In turn, a negative number -3.45 will indicate a decrease in money in the cash register that issued this money to us. That is, −3.45 is the expense. Another example: a temperature increase of 17.3 degrees can be described with a positive number of +17.3, and a temperature decrease of 2.4 can be described with a negative number, as a temperature change of -2.4 degrees.
Positive and negative numbers are often used to describe the values of certain quantities in various measuring instruments. The most accessible example is a device for measuring temperatures - a thermometer - with a scale on which both positive and negative numbers are written. Often negative numbers are depicted in blue (it symbolizes snow, ice, and at temperatures below zero degrees Celsius, water begins to freeze), and positive numbers are written in red (the color of fire, the sun, at temperatures above zero degrees Celsius, ice begins to melt). Writing positive and negative numbers in red and blue is also used in other cases when you need to highlight the sign of the numbers.
Bibliography.
- Vilenkin N.Ya. and others. Mathematics. 6th grade: textbook for general education institutions.