Definition of negative numbers
Negative number is a concept used in mathematics to represent numbers less than zero. In the real number system, negative numbers can be expressed as positive numbers preceded by a negative sign-,such as-1, -2, -3, etc.
Properties of negative numbers
Negative numbers have some special properties. On the one hand, the result of adding two negative numbers is negative, such as-3+(-4) =-7; On the other hand, the result of multiplying a negative number by a positive number is also negative, such as -2×3=-6.
Application of negative numbers
Negative numbers are widely used in real life and various disciplines. In economics, negative numbers can indicate liabilities or losses; In physics, negative numbers can indicate the direction to the left or down; In a thermometer, a negative number indicates that the temperature is below freezing point, etc.
The number axis representation of negative numbers
The number axis is a commonly used tool to represent numbers, and negative numbers can also be represented by the number axis. On the number axis, negative numbers are to the left of zero. The smaller the value, the farther away from zero. For example,-1 is closer to zero than -0.5.
Operation of negative numbers
There are some special rules for the operation of negative numbers. For example, two negative numbers can be added by removing the negative sign, adding their absolute values and adding the negative sign; When a negative number is multiplied by a positive number, you can first remove the negative sign, then multiply it by its absolute value, and finally add the negative sign.
Absolute value of negative number
The absolute value is the non-negative representation of a number, and the absolute value of a negative number is the value minus the negative sign. For example, |-3|=3, |-7|=7 and so on. The absolute value of a negative number indicates the distance between the number and zero.
Square root of negative number
The square root of a negative number is not defined in the real number range. Because the square of any number is non-negative, negative numbers have no real square root. But in the field of complex numbers, negative numbers have square roots, such as √(- 1)=i (imaginary unit).
Expand knowledge:
Negative numbers first appeared in Shu Shu Jiu Zhang in the Southern Song Dynasty in China, and were introduced to Europe in16th century. The concept of negative number has played an important role in promoting the development and application of mathematics. Negative numbers can be used to solve many practical problems, such as altitude, temperature change, voltage direction and so on. They have important applications in mathematical models, physics, engineering and economics.
Negative numbers can also be used to represent debts or arrears, such as a negative balance in a bank account. This is common in business transactions and finance. The concept of negative numbers provides a basis for the development of abstract algebra and number theory.