Addition and subtraction of positive and negative numbers, what are the addition and subtraction met

The law of addition of rational numbers (positive numbers, negative numbers, and 0 are collectively referred to as rational numbers).

Add two numbers of the same sign, take the same symbol, and add the absolute values.

When the two numbers of different signs are added, the sum is 0 when the absolute values are equal; When the absolute value is unequal, take the sign of the number with the larger absolute value, and subtract the smaller absolute value from the larger absolute value.

Add a number to 0 and still get this number.

The law of subtraction of rational numbers.

Subtracting a number is equal to adding the opposite of the number.

I'm afraid you don't know absolute values, opposite numbers, number lines, so write their definitions -

Absolute value. 1 Algebraic definition of absolute values.

The absolute value of a positive number is itself; The absolute value of a negative number is its opposite; The absolute value of zero is zero.

2 Geometric definition of absolute values.

The distance from the origin of a number is represented on the number line, which is called the absolute value of the number

3.The absolute value is a non-negative number, i.e. |a|≥0.The absolute values of two numbers that are opposite to each other are equal: |a|=|－a|.

Opposite number. 1.Algebraic meaning: only two numbers with different signs are called opposites of each other, one of the numbers is called the opposite of the other, and the opposite of 0 is 0

2.Geometric significance: On both sides of the origin on the number line, two points with equal distances from the origin represent opposite numbers.

Number line. Among the two rational numbers on the number line, the number on the right is always larger than the number on the left, so the law of comparison of the size of rational numbers is: positive numbers are greater than 0, zero is greater than all negative numbers, negative numbers are less than zero, and positive numbers are greater than all negative numbers.

Examples. Addition.

The average nighttime temperature on Saturn's surface is -150, which is 27 warmer during the day than at night, so what is the average daytime temperature?

A: The average daytime temperature is -123Subtraction.

The highest mountain in the world is Mount Everest, which is about 8,844 meters above sea level, and the Turpan Basin is about -155 meters above sea level.

How many meters is the difference in height between the two places?

8999 (m).

A: The difference in height between the two places is 8,999 meters.

Mixed addition and subtraction.

A water conservancy survey team went upstream on the first day5

km, and the next day it went 5 upstream

Kilometer. On the third day, go downstream4

kilometers, and on the fourth day, they went downstream for another kilometer, and at this time the survey team was at the starting point of the **? How many kilometers apart?

5+5+(-4)+(km).

A: At this time, the survey team was upstream of the starting point, a kilometer away.

Positive numbers are added to positive numbers, and the sum is positive; For example, 3+5=8.

Negative numbers are added to negative numbers, and the sum is negative; For example, 3+5=8.

Add positive and negative numbers, and take the absolute value.

Larger symbols, absolute value subtracted.

For example, (+3)+(5)=-2;（-3）+（5）=+2。

One number minus another is equal to the opposite of one number plus another.

Explained. A positive number is a positive real number.

It includes positive integers.

Positive fractions (including positive decimals) and positive irrational numbers. Whereas, positive integers are only a small part of positive numbers.

Positive numbers do not include 0, 0 is neither positive nor negative, and anything greater than 0 is positive.

If a positive number is greater than zero, then a positive number is greater than a negative number. Zero is neither positive nor negative. then a<0<(+a.)

There is no largest number in a positive number, and there is no smallest number.

The positive sign before removing the positive number is equal to the absolute value of the positive number, and it is also equal to the positive number itself.

Add two positive numbers and take the sum of the absolute values of the two integers. Two negative numbers are added together, and the result is like the sum of absolute values, preceded by a negative sign. Positive and negative numbers are added together, and the sign takes the sign with the greater absolute value than the number, and subtracts the small absolute value from the larger absolute value.

1. A positive number plus a positive number equals a positive number;

2. A negative number plus a negative number equals a negative number:

3. Positive numbers plus negative numbers, whose absolute value is the largest to take whose symbol;

4. Positive numbers such as positive numbers minus negative numbers, and one number minus another number is equal to the opposite number of one number plus another number;

5. A negative number minus a positive number equals a negative number.

A positive number is a number greater than zero, a negative number is a number less than zero, zero is neither an integer nor an integer, and negative numbers should be represented with a negative sign "-", for example, "-1" and "-2". The addition and subtraction of positive and negative numbers follows certain rules: the first rule is that subtracting two numbers of the same sign is equal to the subtraction of their absolute value, subtracting two numbers of different signs, and subtracting negative numbers is equal to adding an integer.

For example, the "4" and "2" symbols are the same, and the subtraction is "4-2=2", and the "4" and "-2" symbols are different, and the subtraction is "4-(-2)=4+2=6".

The two numbers of different signs are added, and the symbol is taken as the symbol of the number with the largest absolute value, and the two numbers of the same sign are added, the symbol does not change, and the absolute value is added. For example, "3" and "-6" are added together, and the absolute value of "-6" is large, so the result is a negative sign, that is, "3+(-6)=-3", "3" and "6" are added, and the two symbols are the same, and the result is "3+6=9", "3" and "-6" are added, because both are negative, the result is negative, that is, "(-3)+(6)=-3+6)=-9".

1.Add two numbers of the same sign, take the same symbol, and add their absolute values. 2.

Add the two numbers with different signs, take the sign of the number with the greater absolute value, and subtract the smaller absolute value from the larger absolute value. 3. Subtract two negative numbers, remove the negative brackets first, and then add or subtract them. 4. The two numbers of different signs are subtracted, and the sign is the same as the number to be subtracted, and the value is the sum of the absolute values of the two numbers.

Negative 1 + Negative 2 = (Negative 1 + Negative 2) = Negative.

Negative number + positive number = sign takes the sign of the addition with the greater absolute value, and the value takes the value obtained by "subtracting the smaller absolute value from the larger absolute value".

Negative number 1 Negative number 2 = negative number 1 + negative number 2 opposite number = then calculate according to the method of negative number plus positive number.

Negative Positive = (Positive + Negative Absolute Value) = Negative.

Positive Negative = Positive + Negative Opposite = Positive.

The two numbers of different signs are subtracted, and the value is equal to the addition of their absolute values.

Positive numbers are added to positive numbers, and the sum is positive; For example, 3+5=8. Negative numbers are added to negative numbers, and the sum is negative; For example, 3+5=8. Add positive and negative numbers, and take the sign with the larger absolute value, and subtract the absolute value; For example, (+3)+(5)=-2;（-3）+（5）=+2。

One number minus another is equal to the opposite of one number plus another.

Negative

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 negative 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.

The rule of addition and subtraction of positive and negative numbers is: the subtraction of two numbers with the same sign is equal to the subtraction of their absolute value, and the subtraction of two numbers with different signs is equal to the addition of their absolute values. Zero minus positive numbers gives negative numbers, and zero minus negative numbers get positive numbers.

The addition of two numbers with different signs is equal to the subtraction of their absolute values, and the addition of two numbers with the same sign is equal to the addition of their absolute values. Zero plus a positive number equals a positive number, and a zero plus negative number equals a negative number. ”

This narrative of the arithmetic of positive and negative numbers is completely correct, and the introduction of negative numbers is one of the outstanding contributions of Chinese mathematicians.

It is customary to use numbers of different colors to indicate positive and negative numbers, and to use red to indicate negative numbers, and newspapers publish that a country has a deficit in its economy, indicating that its expenditures are less than its revenues, and that it has made money financially.

A negative number is the opposite of a positive number. In real life, we often use positive and negative numbers to represent two quantities with opposite meanings. In summer, the temperature in Wuhan is as high as 42°C, you will think that Wuhan is indeed like a furnace, and in winter, the temperature in Harbin is -32°C, a minus sign makes you feel the cold of the northern winter.

Introduction to multiplication and division of positive and negative numbers:

Positive number. 1. Number 1 Positive number 2 = positive number.

2. Positive number 1 negative number 2 = negative number.

3. Positive number 1 positive number 2 = positive number.

4. Positive number 1 negative number 2 = negative number.

In general, the division of the same sign equals a positive number, and the division of a different sign equals a negative number.

Negative1. Negative number 1 Negative number 2 = (negative number 1 negative number 2) = positive number.

2. Negative positive = (positive negative number) = negative number.

3. Negative number 1 Negative number 2 = (negative number 1 negative number 2) = positive number.

4. Negative positive = (negative positive) = negative.

In general, the division of the same sign equals a positive number, and the division of a different sign equals a negative number.

Negative negative to get positive formula: positive to positive, negative negative to positive, positive negative to negative.

The mantra refers to the law of rational number multiplication, which means that the two numbers are multiplied, the same sign is positive, the different number is negative, and any number multiplied by 0 is 0. In fact, this mantra is adapted from the rules of multiplication operations, which is easy to memorize and use.

Rules of addition and subtraction of positive and negative numbers:

The addition of two numbers of the same sign is equal to the addition of their absolute values.

The addition of the two numbers is equal to the subtraction of their absolute values.

The subtraction of two numbers of the same sign is equal to the subtraction of their absolute values.

The subtraction of the two numbers is equal to the addition of their absolute values.

Zero minus positive numbers gives negative numbers, and zero minus negative numbers get positive numbers.

The rule of addition and subtraction of positive and negative numbers.

1.Add two numbers of the same sign, take the same symbol Xiaodong, and add their absolute values.

Example: (1) (2) = 1 + 2 = 3 ( 1) (2 ) = 1-2 = -3.

2.The two numbers of different numbers are added to take the sign of the number with the greater absolute value, and the larger absolute value is subtracted from the smaller absolute value.

Example: 1+( 2) -2-1) = 1 +2+( 1) 2-1=+1.

3.The two numbers of different numbers are subtracted, and the negative and negative are positive.

Example: 2 -(1) 2+1=+3.

4.Zero plus or minus any number is equal to the original number.

Example: 0+( 1) 1;0-1 = 1。