Any positive number preceded by a negative sign is equal to a negative number, indicating the opposite number, and the negative number is less than zero.
Positive number definition:
Numbers greater than 0 are called positive numbers. Positive numbers are usually preceded by a "+"symbol, which can usually be omitted.
There are countless kinds of positive numbers, including positive integers, positive fractions and positive irrational numbers.
Geometric meaning of positive numbers:
The points representing positive numbers on the number axis are all on the right of 0 on the number axis.
Positive numbers are positive real numbers, including positive integers and positive fractions (including positive decimals). And positive integers are only a small part of positive numbers.
Positive numbers do not include 0, and anything greater than 0 is positive.
Negative number:
A mathematical term for a real number less than 0, such as? 3。
On the number axis, negative numbers are all on the left of 0, there is no maximum and minimum negative number, and all negative numbers are smaller than natural numbers.
Negative numbers are marked with a minus sign (that is, equivalent to a minus sign) "-",such as? 2,? 5.33,? 45,? 0.6 and so on. The minus sign before a negative number equals the absolute number of a negative number. The absolute value of -2 is 2, that of -5.33 is 5.33, that of -45 is 45, and that of -0.6 is 0.6.
Negative numbers are antonyms of positive absolute values. Any positive number preceded by a negative sign is equal to a negative number.
The score can also be negative, such as -2/5.
0 is neither positive nor negative.
We use positive numbers to indicate temperatures above zero and negative numbers to indicate temperatures below zero.
In the thermometer (axis), the number to the right of 0 is positive, and the number to the left of 0 is negative.
Add:
Negative number 1+ negative number 2 =-| negative number 1+ negative number 2|= negative number
Negative number+positive number = the sign takes the sign of the addend with larger absolute value, and the numerical value takes the addend with larger absolute value minus the addend with smaller absolute value.
Subtraction:
Negative number 1- negative number 2= negative number 1 | negative number 2| = negative number 1 plus the reciprocal of negative number 2, and then calculate by adding negative number to positive number.
Negative number-positive number =-| positive number+negative number | = negative number The subtraction of two numbers with different signs is equal to the sum of their absolute values.
Multiplication:
Negative 1× negative 2=| negative 1× negative 2| = positive.
Negative x positive =-| positive x negative | = negative.
Department:
Negative number 1÷ negative number 2=| negative number 1÷ negative number 2| = positive number.
Negative number/positive number =-| Negative number/positive number | = negative number
Generally speaking, being divided by the same number equals to a positive number, and being divided by different numbers equals to a negative number.
People often encounter various quantities with opposite meanings in their lives. For example, there are surpluses and deficits in bookkeeping; When calculating the rice stored in the granary, sometimes you should remember the grain and sometimes you should remember the valley. For convenience, people think that numbers have opposite meanings. So people introduced the concepts of positive number and negative number, and recorded the excess money as positive number of grain and the loss of money and grain as negative number. It can be seen that both positive and negative numbers are produced in production practice.
According to historical records, as early as 2000 years ago, China had the concept of positive and negative numbers and mastered the arithmetic of positive and negative numbers. When people calculate, they use some small bamboo sticks to put out various figures to calculate. For example, 356 is placed in |||, 3056 is placed in, and so on. These small bamboo sticks are called "computing chips" and can also be made of bones and ivory.
Liu Hui was a scholar during the Three Kingdoms period in China, and he made great contributions to the establishment of the concept of negative numbers. Liu Hui first gave the definitions of positive numbers and negative numbers. He said: "Today's gains and losses are the opposite, and positive and negative numbers should be named." In other words, in the process of calculation, positive numbers and negative numbers should be used to distinguish.
Liu Hui gave the method of distinguishing positive and negative numbers for the first time. He said: "The front is red and the negative is black; Otherwise, the number of the red pendulum represents a positive number, and the number of the Hei Bang pendulum represents a negative number; You can also use a stick with an oblique pendulum to represent negative numbers, and a stick with a positive pendulum to represent positive numbers.
In Nine Chapters Arithmetic, a famous mathematical monograph in ancient China (written in the first century A.D.), the law of addition and subtraction of positive and negative numbers was put forward for the first time: "The theory of positive and negative numbers: the same name is divided, different names are beneficial, positive and negative; Its synonyms are divided, and the same name is beneficial. [2] There is nothing positive and nothing negative. " Here, the name is a number, except subtraction, mutual benefit and division are the absolute values of two numbers, and nothing is zero.
In the present words: "the addition and subtraction of positive and negative numbers is: the subtraction of two numbers with the same sign equals the subtraction of their absolute values, and the subtraction of two numbers with different signs equals the addition of their absolute values." Zero minus a positive number is a negative number, and zero minus a positive number. The addition of two numbers with different signs equals the subtraction of their absolute values, and the addition of two numbers with the same sign equals the addition of their absolute values. Zero plus positive number equals positive number, and zero plus negative number equals negative number. "
This statement about the arithmetic of positive and negative numbers is completely correct and completely in line with the current law! The introduction of negative numbers is one of the outstanding contributions of Chinese mathematicians.
The habit of using numbers of different colors to represent positive and negative numbers has been preserved until now. At present, red is generally used to represent negative numbers. The newspaper reports that a country's economy is in deficit, which shows that its expenditure is greater than its income and it has incurred financial losses.
Negative numbers are antonyms of positive numbers. In real life, we often use positive numbers and negative numbers to represent two quantities with opposite meanings. In summer, the temperature in Wuhan is as high as 42℃, and you will feel that Wuhan is really like a stove. The minus sign of the temperature in Harbin in winter is -32℃, which makes you feel the cold in winter in the north.
In the current textbooks for primary and secondary schools, the introduction of negative numbers is through arithmetic operation: a negative number can be obtained by subtracting a larger number from a smaller number. This introduction method can have an intuitive understanding of negative numbers in special problem scenarios. In ancient mathematics, in the process of solving algebraic equations, negative numbers are often produced. The algebraic study of ancient Babylon found that the Babylonians did not put forward the concept of negative root when solving equations, that is, they did not use or find the concept of negative root. In the works of Diophantine, a Greek scholar in the 3rd century, only the positive root of the equation was given. However, in China's traditional mathematics, negative numbers and related arithmetic were formed earlier.
In addition to the positive and negative operation methods defined in Nine Chapters Arithmetic, Liu Hong (AD 206) at the end of the Eastern Han Dynasty and Yang Hui (126 1) in the Song Dynasty also discussed the addition and subtraction principles of positive and negative numbers, all of which were completely consistent with those mentioned in Nine Chapters Arithmetic. In particular, in Yuan Dynasty, Zhu Shijie gave not only the rules of addition and subtraction of positive and negative numbers with the same sign but different signs, but also the rules of multiplication and division of positive and negative numbers. In his algorithm enlightenment, negative numbers were recognized and recognized abroad, much later than in China. In India, it was not until AD 628 that the mathematician Yarlung Zangbo realized that negative numbers can be the root of quadratic equations. In Europe, Qiu Kai, the most successful French mathematician in the14th century, described negative numbers as absurd numbers. It was not until the17th century that the Dutchman Jirar (1629) first realized and used negative numbers to solve geometric problems.
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.