How did the negative become positive, and why did the negative become positive?

Find a point on the positive half axis on the number line, for example, (point, negative once is to symmetricate this point once to the negative half axis to the left of the origin, and then negative once is to symmetricate again and return to the original positive half axis or that positive number.

The rule of multiplication operation "negative negative is positive" is only a prescript, and the law of operation of numbers is originally prescribed, not derived. Specify the algorithm first, and then study whether the algorithm is true.

The rules of operation cannot be arbitrary, but depend on the properties of the number system itself. For example, in order to reflect a certain quantitative relationship of objective reality, so as to solve relevant practical problems.

Every child grows up listening to stories. So, they should have more interest and enthusiasm for the story. And for students. They will be impressed by strong concepts, such as good and bad, good and evil, etc.

In the 7th century AD, the Indian mathematician Brahmayup-ta had a clear concept of positive and negative numbers, and his four rules of operation: "Multiply positive and negative numbers to get negative, multiply two negative numbers to get positive, and two positive numbers to get positive." ”

Until the 18th century, some Western mathematicians considered the "negative negative to positive" algorithm a fallacy. Even in the 19th century, there were some mathematicians in England who did not accept negative numbers, such as the English mathematician Frende (1757-1841), who criticized those algebraists who talked about "negative negative positive", arguing that negative numbers were counterintuitive, and that "only those who like to talk and hate serious thinking support the use of such numbers." ”

In fact, until the middle of the 19th century, the operation of negative and negative positive was not correctly explained in algebra textbooks, and the French writer Stendhal (1783-1843) had been troubled by this law for a long time when he was a student, and his two mathematics teachers, Mr. Dupiy and Chabele, failed to give him a convincing explanation.

Stendhal became distrustful of mathematics and its teachers, saying, "Are my two teachers lying to me or is mathematics itself a game?" Obviously, in order to reduce the difficulty of students in learning the multiplication of negative numbers, it is not advisable to use the rigid "prescribed" method to directly introduce the law of negative and negative positive.

The following is an introduction method to help students understand.

The explanations for the reasons why negative and negative are positive in mathematical multiplication are:

1. American mathematics historian and mathematics educator M. Klein solved the problem of "two negative numbers multiplying positively" through the debt model

One person owes $5 per day and $15 after 3 days on a given date ($0). If a $5 house is recorded as -5, then "$5 a day in debt for 3 days" can be expressed mathematically: 3 (-5) = -15.

If the same person owes $5 a day, then 3 days ago on the given date ($0), his property is $15 more than the property on the given date. If we use -3 for 3 days ago and -5 for each day of debt, then 3 days ago his financial situation is expressed as (-3) (5) = 15.

2. Opposite number model:

Therefore, if you replace a factor with its opposite, the resulting product is the opposite of the original product, so (-5) (3) = 15.

Negative numbers are a mathematical term, numbers smaller than 0 are called negative numbers, and negative numbers and positive numbers represent quantities with opposite meanings. Negative numbers are marked with a minus sign" and a positive number, such as 2, which represents the opposite of 2.

As a result, any positive number preceded by a negative sign becomes a negative number. A negative number is the opposite of its absolute value. On the number axis, negative numbers are on the left side of 0, and the earliest record of negative numbers is the ancient mathematical work "Nine Chapters of Arithmetic" in China.

It is specified in the calculation"Positive is red, negative is black", that is, the red arithmetic chip is used to represent a positive number, and the black number is a negative number. The two negative numbers are compared to the size, and the absolute value is larger than the smaller.

Hello. Now let's imagine it.

1, 5 10 can be seen as earning ten five dollars.

2,-5 10 can be seen as being fined ten times five dollars.

3,-5 -10 can be seen as being fined ten times for five yuan but escaping the fine, can you see that you have earned 50 yuan in disguise?

Hello, because according to the mathematical theorem, the negative sign indicates the sign of a negative number or a negative pole. Writing"－"Same as the minus sign, but a negative sign before a number or an algebraic formula, denoted by "-", indicates a number smaller than zero or the opposite of a number.

A negative sign is added to precede a negative number to indicate the opposite of this negative number, so negative negative is positive.

Isn't this a rule, because negative positive gets negative, positive positive gets positive, so negative negative gets positive. (Normal omitted is not written).

Can I say that it is because the extremes of things must be reversed?

It's a theorem, there's no why.

Because of the regulations. So do you want to ask why 1+1=2?

There are two ways to turn a batch of negative numbers into positive numbers, one is to find all the negative signs and replace all the negative signs with empty ones in batches.

Another type of scrambling is to select all the numbers in the cell and then multiply -1 selectively into the selected range.

However, the second method has a drawback, when there is a positive number in the cell you selected, it will become a negative number due to multiplying -1, resulting in.

1. Open Excel** and select the area where you want to turn negative numbers into positive numbers.

2. Use the search shortcut key Ctrl+F to open the search box.

3. Click "Replace Options" in the search box and enter the input box of "-Replace with" in the input box of "Find content", and do not enter any content.

4. Click "Replace All" to turn all negative signs into empty.

It was given by the mathematician Zhu Shijie at the end of the 13th century. In "The Enlightenment of Arithmetic" (1299), Zhu Shijie proposed: "Ming multiplication and division, multiplication with the same name is positive, and multiplication with different names is negative".

Solution: Negative negative to positive means that the product of negative numbers multiplied by negative numbers is positive, and the product of negative numbers multiplied by positive numbers is negative.

Negative multiplication can also be understood very intuitively from the perspective of the number axis, for example, multiplying by -1 is equivalent to moving the points on the number line from one side of the origin to the other, and keeping the distance from the origin unchanged, which is also equivalent to making the entire number axis rotate 180 degrees along the origin.

With the introduction of negative numbers, we want this correspondence to remain, and this requires us to extend the number axis infinitely to the left. At this time, moving 2 units to the right should reach the point corresponding to the number 2, and we talked about moving 2 units to the right is also moving 2 units to the left, so the point corresponding to 2 is to the left of the origin, and the distance from the origin is 2.

The points on the number line correspond exactly to real numbers (including negative, 0, and positive numbers), and as in the previous section, the more points to the right, the larger the number it corresponds to.