A negative number is a number less than 0.

For example:-5,6, 10

Negative number, the larger the number, the smaller the value.

Negative number calculation

Addition, subtraction, multiplication and division of negative numbers and integers: negative number 1+ negative number 2=-(| negative number 1|+| negative number 2|)

Negative+positive = | positive |-| negative |

Negative 1- negative 2=| negative 1 |- negative 2|

Negative number-positive number =-(| positive number |+| negative number |)

Negative number 1* negative number 2=| negative number 1|*| negative number 2|

Negative number * positive number =-| positive number | *| negative number |

Negative number 1\ negative number 2=| negative number1||| negative number 2|

Negative number/positive number =-| negative number || positive number

|| refers to the absolute value.

2. Knowledge points about negative numbers

Knowledge point 1 The introduction of negative numbers is based on actual needs. With the development of society, the natural numbers, fractions and decimals in primary school can no longer meet the actual needs, such as some quantities with opposite meanings: income, 200 yuan expenditure 100 yuan, zero plus MINUS 6, etc. They not only have opposite meanings, but also represent a number. How to express them? We define the quantity of one meaning as positive and the quantity of another opposite meaning as negative, thus producing positive numbers and negative numbers.

When positive numbers and negative numbers are used to represent quantities with opposite meanings, which meaning is positive can be chosen at will, but it is customary to stipulate that "forward, upward, income, temperature above zero" is positive and "backward, downward, expenditure, temperature below zero" is negative. Knowledge point 2 The concepts of positive and negative numbers, such as 3,1.5,58, are called positive numbers. The number of primary school students is positive except 0, and the positive number is greater than 0.

Numbers such as -3,-1.5 and -584 with a "-"in front of a positive number are called negative numbers. Negative number is less than 0.

Zero is neither positive nor negative, and zero is the dividing line between positive and negative numbers. Note: (1) For emphasis, positive numbers can sometimes be preceded by "+"(pronounced as positive numbers), such as 3, 1.5, or +3,+1.5,+.

(2) The concepts of positive numbers and negative numbers cannot be simply understood as follows: numbers with "+"sign are positive numbers and numbers with "-"sign are negative numbers. For example, must -a be negative? The answer is not necessarily.

Because the letter a can represent any number, if a represents a positive number, then -a is a negative number; If a stands for 0, -a is still 0; When a stands for negative number, -a is not negative (in this case, -a is positive). I hope it helps you. Thank you.

3. Want to know negative numbers?

The world is made up of many contradictory things. If we want to know and transform the world, we must start with these contradictory things. The same is true of mathematical research. Odd and even, positive and negative, left and right, one with the crowd, straight and curved, dynamic and static, etc. , a combination of opposing concepts, contains the simplest philosophical thought of unity of opposites and development. How to infiltrate these ideas into students through our math class?

At the beginning, a set of opposites is introduced, and the number "4" cannot express two quantities with opposite meanings. What should I do? Students use their existing life experience to solve contradictions. Before counting, they use different symbols to represent two quantities with opposite meanings, so that contradictions can be unified under the symbol thought and students can feel the role of symbols.

In class, use five positive numbers and five negative numbers written by students at will to guide students to observe that the integers (except 0), fractions and decimals they have learned before are all positive numbers. Put a negative sign in front of these numbers to lead to a negative number * * *, so as to grasp the connection between negative numbers and numbers learned in the past and feel the development of numbers.

The reading teaching of this course is also very distinctive, so pay attention to giving reading new connotation. For example, if students are allowed to talk about their feelings in combination with their own experiences after reading Antarctic Temperature and Boiling Temperature of Water, it will give students more opportunities to experience numbers. "Too cold" and "too hot", lifeless numbers greatly enrich students' experience, and their sense of numbers has also been well cultivated. For another example, let students deepen their understanding of negative numbers in reading. Let the students read aloud in pairs: 1,-1 ... Let the students feel that negative numbers and positive numbers are corresponding in reading, and understand that negative numbers * * * and positive numbers * * * are equally infinite; Orderly guide students to read positive or negative numbers, 1, 2, 3, 4, 5,-1, -2, -3, -4, -5, so that students can feel that the larger the number after the negative sign, the smaller the value, understand the relationship between negative numbers, 0 and positive numbers, and complete the preliminary construction of the logarithmic structure in primary schools.

4. Knowledge about positive numbers and negative numbers

1. The concepts of positive numbers and negative numbers cannot be simply understood as follows: numbers with "+"sign are positive numbers and numbers with "-"sign are negative numbers. For example: "-a" must be a negative number? The answer is not necessarily. Because the letter a can represent any number. If a represents a positive number, it is a negative number; When a stands for 0, even if a negative sign is added before 0, it is still 0, and 0 means positive or negative; When a represents a negative number, "-a" is not a negative number, but a positive number.

2. After introducing negative numbers, the range of numbers is expanded to rational numbers, and the extensions of odd numbers and even numbers are also expanded from natural numbers to integers. Integers can also be divided into odd and even numbers. Numbers divisible by 2 are even numbers, such as …-6, -4, -2, 0, 2, 4, 6…, and numbers divisible by 2 are odd numbers, such as …-5, -4.

3. There are five kinds of subdivision of numbers: positive integer, positive fraction, 0, negative integer and negative fraction, but when studying problems, rational numbers are usually divided into positive number, 0 and negative number for discussion.

4. Generally, positive numbers and 0 are collectively referred to as non-negative numbers, negative numbers and 0 are collectively referred to as non-positive numbers, and positive numbers and 0 are collectively referred to as non-negative integers; Negative integers and 0 are collectively referred to as non-positive integers.

negative number

China introduced the concept of negative numbers and the addition and subtraction of positive and negative numbers in the chapters of Nine Arithmetic and Equation. In some problems, the number sold is positive (because of income) and the number bought is negative (because of payment); The surplus money is positive, and the lack of money is negative. In the calculation of grain, the addition is positive and the subtraction is negative. The terms "positive" and "negative" have been used to this day.

In the chapter "Equation", the law of adding positive and negative numbers introduced is called "addition and subtraction operation". The law of multiplication and division of positive and negative numbers appeared relatively late. Zhu Shijie described the law of addition and subtraction of positive and negative numbers with "Ming addition and subtraction" in "Arithmetic Enlightenment" written in, with eight items, which are more clear than "Nine Chapters Arithmetic". There is a saying in Ming Dynasty's Multiplication and Division that "the multiplication of the same name is positive and the multiplication of different names is negative", that is, (A) * (B) =+AB, (A) * (B) =-AB. This law of positive and negative multiplication is the earliest record in China. At the end of Song Dynasty, Ye Li also used oblique strokes to represent negative numbers. The introduction of the concept of negative number is one of the most outstanding creations of China's ancient mathematics.

Unlike China's ancient mathematicians, western mathematicians are more concerned about the rationality of the existence of negative numbers. In the 16 and 17 centuries, most mathematicians in Europe did not admit that negative numbers were numbers. Pascal thinks that subtracting 4 from 0 is sheer nonsense. Pascal's friend Ahrend put forward an interesting argument against negative numbers. He said (-1):1=1:(-1), then how can the ratio of smaller numbers to larger numbers be equal to the ratio of larger numbers to smaller numbers? Until 17 12, even Leibniz admitted that this statement was reasonable. Wally, a British mathematician, acknowledged negative numbers and thought that negative numbers were less than zero and greater than infinity (1655). He explained it this way: Because of a>0, Augustus de Morgan, a famous British mathematician, still thinks that negative numbers are fictitious in 183 1. He used the following example to illustrate this point: "My father is 56 years old and my son is 29 years old. When will the father be twice as big as his son? " Simultaneous equation 56+x=2(29+x) is solved, and x=-2 is obtained. He called the solution absurd. Of course, in Europe in the18th century, not many people refused negative numbers. With the establishment of integer theory in19th century, the logical rationality of negative numbers was really established.

The first Indian to put forward negative numbers was Brahmagupta, about 628 (about 598-665). He put forward the arithmetic of negative numbers and marked them with dots or circles to represent negative numbers. The Italian mathematician Fibonacci (1 170- 1250) first put forward the concept of negative numbers in Europe. When solving a profit problem, he said: I will prove that this problem cannot be solved unless I admit that this person can be in debt. /kloc-Shukai in the 0/5th century (1445? - 15 10? ) and Steve in the 6th century (1553) both found negative numbers, but both described them as absurd numbers. Cardan (1545) gave the negative root of the equation, but he described it as a "pseudo number". Vedas knew that negative numbers existed, but he didn't want them at all. Descartes partially accepted negative numbers. He called the negative root of the equation a false root because it was smaller than "nothing".

5. Knowledge about negative numbers

In the history of mathematics development, it took more than 1000 years for negative numbers to be officially recognized. There is a related legend, but it can't be verified, but it is an acknowledged fact that China was the first country to use negative numbers. Liu Hui, an outstanding mathematician in ancient China, commented on China's ancient mathematical masterpiece Nine Chapters Arithmetic: "The gains and losses of the two calculations are opposite, and the pros and cons should be named."

He refers to the case where zero is the minuend. "Nothing is positive and nothing is negative." According to the same explanation, it means that zero plus is positive and zero plus negative is negative.

Later, Zhu Shijie, a mathematician in Yuan Dynasty, made new progress in the operation of positive and negative numbers in his book "The Enlightenment of Arithmetic" (1299). He rewrote the statement in "Nine Chapters of Arithmetic" as follows: "If the same name is subtracted from the same name, and the different names are added, the positive is not added, and the negative is not added; If you subtract synonyms, you add the same name. Nothing is right and nothing is negative. " After that, India and some European countries successively introduced negative numbers!

6. People's Education Edition sixth grade negative knowledge, comprehensive.

Unit 1 Unit 1 "negative" error-prone knowledge summary, practice "negative" error-prone knowledge summary and practice, summarize the definition of negative knowledge, and learn that all numbers (except 0) are positive, but positive "+"can be omitted! Definition of negation: adding "-"in front of it means negation.

3. Negative numbers must be preceded by "-".If they are "-"(possibly unsigned "+"), they are positive numbers (except 0). 4,0 is neither positive nor negative, it is the dividing line between positive and negative numbers.

Exercise: 1, the following requirements are 511.25,-7,3,3.05438+0.

-5, 0,2, -0.03 3 2 7 positive number 2, the relative negative number below the written number is not positive, and the number form is 317,7,3,2+0.33.

5 3 19 2. The negative number of negative effect is arbitrarily defined in the positive direction. As shown in figure 2, negative numbers are used to represent quantities and the opposite positive meanings.

First, select 3 represented by a positive number or a negative number to view the predetermined positive direction. 4. Generally, it contains negative derogatory commendatory words expressed as positive numbers and quantities.

Example: 5+5℃-5℃-above 5℃. The income is 2000 yuan, 2000 yuan; 500 yuan -500 yuan said.

Practice: 1, +20%, a year-on-year increase of 20%-20% What? One night, at 0: 00 in the morning, the temperature in Huangshan dropped by 7 degrees Celsius at 2 degrees Celsius. When the normal water level of Huangshan Mountain is 0 tonight, the water level is higher than the normal water level, and it is recorded as 0.3 meters below the normal water level of _ _ _ _ _ _ _ _ _ _. The normal water level is 5m, and the normal water level is recorded as 2.5m, below 6.3m ..

Centigrade. 4. In the answer that meets the requirements: A student demonstrates that the teacher's requirements are positive development.

(1) The second step is to move forward _ _ _ _ _ _ _ _ _ _ _. (2) Take a step back, which means _ _ _ _ _ _ _ _ _ _ _.

(3) "How about recording step by step?" Should he go? Record as -4 steps? 5, the answer GMT, Tokyo 1 hour early,+1; Seven hours later, Paris time, recorded as -7. Beijing time is the standard time in other time zones.

Sydney time: _ _ _ _ _ _ _ _ London time: _ _ _ _ _ _ 6, the question of authenticity (1) can be regarded as positive or negative ((2) altitude-155m. (3) If the profit is 65,438+0,000 yuan, it can be recorded as a loss of 2 million yuan-2 million yuan ((4) The temperature is 0℃()BR/ >) and the above seven common negative numbers (1): the significance of negative numbers in topographic maps of China. You can see that China has the highest mountain in the world-Mount Everest. The chart is marked with 8848, and the map is marked with the northwest of Turpan Basin 155 meters. You can talk about 8848 meters and 155 meters. What did you say?/Sorry? Whose standards are these two heights? (2) Revenue and expenditure: 2,600; (3 million) education expenditure; (3 million) Entertainment expenditure: 500 yuan (). (3) What does elevator-3rd floor mean? According to World Health Organization standards? At the beginning of school, I went to East and West. Xiao Ming went to +50 meters and 100 meters away from the school. The distance between Xiao Ming and the school is ().

9. Food packaging often says: "If the net weight is 500.5g, the standard food quality is (). In fact, it does not cover more than () at all, at least not less than (). Negative reading and writing, reading method: read "negative" before writing, practice "-"before writing: 16 degrees Celsius or above, zero to minus 3 degrees Celsius, axis 1, axis element: a positive direction (as shown by the arrow), at the origin (on scale 0), unit length (scale).

2. Positive development direction: according to the meaning of the question, it is positive, generally upward or right. 3. Place of origin: the location with the number 0. Generally speaking, the number is certain. If you need the origin to represent positive and negative numbers, it is almost equal to the fact that the 1 line leaves more positive numbers than negative numbers in the middle of the origin; Negation is more positive than correct origin.

As shown in Figure 4, unit length: the size is determined by the distance between scales indicating the size. If the quantity is large, the distance can be appropriately smaller, and if the quantity is small, the distance can be appropriately larger. The unit length does not necessarily represent each scale.

For example, the positive direction of writing: (writing: () or ()) reading: reading:-4br/> -3 unit length -2-1, and the number axis represents the number 1, which already represents the number of axes corresponding to the scale: the number of product points. 22 Non-integer: the decimal places are further subdivided, for example, the segment between 0 and 1 needs to be divided into three equal parts.

33 is negative: a negative number is a positive number around 0. Example: 3.5 3 and 4, middle, and -3.5 -3 and -4.

Practice: 1, axis number 1 1.75 -4 3 4 0 -3.2 2, write the following AB -8 -6 -4 -2? D 0 2 4 F 6 8 G 10 6, according to the relative size of the left axis 1, 0 is negative, and the number to the right of 0 is positive; All positive factors are greater than negative factors; All negative numbers are less than positive numbers, and the greater the number of axes, the smaller the number to the left; 3, the size is negative, regardless of the negative sign, but the number of decimal parts; 4,0 is greater than all negative numbers, that is, at least not all positive numbers. Practice: 1, scale comparison -6.5 -6.6 1.5 4 7 0 9 7 -9.8 2 negative 038-0.05350.5-2.751.65438+2.75-0./kloc-0

①5, 2,-1, -4, (), ()) ②- 10, -5, 0, 5, 10, (), (For the first unit, please fill in the space below how to read the temperature displayed by the thermometer in buildings below the second floor. Record, becoming the deepest Mariana Trench in the world. At the end of the year, the deepest part exceeded the sea level 1 1034 meters, and the record was () meters.

) layer. 5。

The change record of reservoir water level. A rise of 7 meters is 7 centimeters, and the remaining 4 records will be said.

The green school that rises 7+7 cm goes 80 meters to the east, records 80 meters, goes west 100 meters, and then records the distance from her school (). You know, if the freezing temperature of water in life is lower than the boiling temperature of water (℃). Two judgments.

7. What do negative numbers mainly learn?

Compared with positive numbers, negative numbers are neither positive nor negative with 0 as the dividing line. Real numbers include positive and negative numbers and 0. With the number axis 0 as the boundary, the negative number on the left and the positive number on the right are infinite and can be said to be symmetrical.

Such as the common 1, 0. 1, 2.

Is a positive number,+1, +0. 1, +2 are all positive numbers, and the preceding+sign can be omitted. A negative number is a numeric value preceded by a "-"sign. In basic operations, two negative numbers are multiplied by a positive number, and a negative number is multiplied by a negative number, so is division. In addition and subtraction, negative numbers can be taken as subtraction numbers.

Even numbers of negative numbers are multiplied by positive numbers and odd numbers are multiplied by negative numbers. In addition and subtraction, a negative number can be calculated by subtracting a number -4=0-4. If -4+2=2-4=-2, 2 minus 4 is not enough, then a negative sign can be added. I don't know if you can understand. Simply put, a negative number is a number less than 0.

8. Information about negative numbers ~

Negative numbers refer to numbers less than zero, such as-1, -2. 1, -0.5, etc. It has the opposite meaning to a positive number.

Nine Chapters Arithmetic is one of the most important classical works of China's ancient mathematics. According to the current research, the book was written at the latest in BC 1 century, but some of its mathematical contents can also be traced back to the Zhou Dynasty. "Nine Chapters Arithmetic" takes the form of problem sets. The book contains 246 questions, which are divided into Tian Fang, Su Mi, Decline, Shao Guang, Shang Gong and Both Loss.

The introduction and use of negative numbers is an outstanding contribution of Nine Chapters Arithmetic. In the "equation skills" of the nine chapters of arithmetic, when elements are eliminated by multiplication and direct division (that is, equations cannot be solved by addition, subtraction and elimination), there may be cases where the subtrahend is greater than the minuend. So it is necessary to introduce negative numbers. The equation chapter of "Nine Chapters Arithmetic" puts forward "addition and subtraction" under groups;

Sweep with the same name, different names are mutually beneficial, positive and negative.

Its synonyms are divided into two parts, the same name is beneficial, and the different names are not positive, but negative.

This is actually the addition and subtraction algorithm of positive and negative numbers and zero. "Same name" and "different name" refer to the same number and different numbers respectively; "Mutual benefit" and "division" refer to the addition and subtraction of the absolute values of two numbers respectively.

The first four sentences are the subtraction rules of positive number, negative number and zero, which are translated into the current language as follows: two numbers with the same symbol are subtracted and the absolute value is taken (the absolute value of the difference); Subtract two numbers with different signs and add their absolute values (find the absolute value of the difference); Subtract a positive number from zero to get the number of members, and subtract a negative number from zero to get a positive number.

The last four sentences are the addition rules of positive numbers, negative numbers and zeros. Can it be translated into the current language?

It is not difficult to see that this is completely consistent with the addition and subtraction of rational numbers we have learned.

After Nine Chapters of Arithmetic, Liu Hui, a mathematician in Wei and Jin Dynasties, gave a natural explanation for the appearance of negative numbers: "The gains and losses of the two calculations are opposite, and the positive and negative numbers should be named", arguing that red chips represent positive numbers and black chips represent negative numbers in the calculation.

In foreign countries, the appearance and use of negative numbers were hundreds of years later than in China, and it was not until the 7th century that Indian mathematicians began to use negative numbers. In Europe, it was not until16th century that F. Viè te (1540 ~1603) refused to use negative numbers.