What are the key points of addition and subtraction of rational numbers? 5

1. If there are parentheses, the brackets are counted first, and then the brackets are counted first, and then the brackets are then braces.

2. Remove the parentheses, if the parentheses are preceded by +, the symbol of the brackets does not change, if it is -, the bracket miles become its opposite.

The results can be calculated either by associative or sequential law.

First replace the subtraction with the addition, and then add it all and forget it.

Replace subtraction with addition first, and then add.

Integer. The numeric value of an integer distance of 0 is called the absolute value. The absolute value of 0 is stated to be 0, the absolute value of a negative number is its opposite, and the absolute value of a positive integer is itself. Integers also include positive, negative, and 0.

Positive and negative numbers are added.

Add the same sign, take the same symbol, add the two numbers and add the symbol. The different signs are added to take the sign with the larger absolute value, and subtract the smaller absolute value from the larger absolute value.

An integer can be thought of as a fraction with a denominator of 1. Positive integers, 0s, negative integers, positive fractions, and negative fractions can all be written as fractions, and such numbers are called "rational numbers". （rational number）

Mixed operation of addition and subtraction of rational numbers, clever calculation of rational numbers.

1.The significance of the addition and subtraction of rational numbers unified into addition:

For the subtraction in the addition and subtraction mixed operation, we can convert the subtraction into addition according to the subtraction rule of rational numbers, so that the mixed operation can be unified into an addition operation, and the unified equation is in the form of the sum of several positive or negative numbers, and we call such an equation algebraic sum.

2.Methods and steps for the mixed operation of addition and subtraction of rational numbers:

1) Use the subtraction rule to convert the subtraction in the mixed operation of rational numbers into addition.

2) Use the law of addition, the commutative law of addition, and the law of combination of addition to perform simple operations.

The law of multiplication of rational numbers.

1) Multiply two numbers, the same sign is positive, the different sign is negative, and multiply the absolute value. Example; (-5) (3)=15 (-6) 4=-24 (2) Multiply any number by 0 to get 0Example; 0×1=0

3) Multiply several numbers that are not equal to 0, and the sign of the product is determined by the number of negative factors. When there is an odd number of negative factors, the product is negative; When the negative factor has an even number, the product is positive. and multiply their absolute values.

Example; (-10) 5 (product is positive, while (-4) (7) (25) = product is negative.

4) Multiply several numbers, and when there is a factor of 0, the product is 0Example; 3×（-2）*0=0

The division is pretty much the same, just a little bit of multiplication and division followed by addition and subtraction.

P.S. In general, rational numbers are classified as follows: integers, fractions; positive, negative, and zero; Negative rational numbers, positive rational numbers.

Integers and fractions are collectively referred to as rational numbers, and rational numbers can be expressed in the form of a b, where a and b are integers and are mutually primary. We often use rational numbers in our daily lives. For example, how much, how many catties, etc.

Any real number that cannot be expressed in the form a b is an irrational number, also known as an infinite non-cyclic decimals. In rational numbers, the decimal is either an infinite non-cyclic decimal or a fraction.

Here are some questions, take a look.

Do it yourself and see if you get it.

The rules of the mixed operation algorithm of addition and subtraction of rational numbers are as follows:

1. Add two numbers with the same sign, take the same symbol as the additive, and add the absolute value.

2. If the absolute value is equal, the sum of the two numbers of the opposite number is 0; If the absolute values are not equal, take the sign of the addition with the greater absolute value, and subtract the smaller absolute value from the larger absolute value.

3. Add two numbers that are opposite to each other to get 0.

4. Add a number to 0 and still get this number.

5. Two numbers that are opposite to each other can be added first.

6. Numbers with the same symbol can be added first.

7. Numbers with the same denominator can be added first.

8. If several numbers can be added to get an integer, they can be added first.

9. Subtracting a number is equivalent to adding the opposite number of the number, that is, the subtraction of rational numbers uses the opposite number of numbers to become addition for operation.

1. The law of addition operation:

1. The commutative law of addition: the addition of two numbers, the position of the exchange addition, and the unchanged, i.e. . .

2. Addition associative law: add three numbers, add the first two numbers or add the last two numbers first, and the sum is unchanged, that is.

2. Multiplication Laws:

1. Multiplicative commutative law: two numbers are multiplied, and the position of the exchange factor is unchanged, i.e. .

2. Multiplication combination law: multiply three numbers, multiply the first two numbers first, or multiply the last two first, and the product remains unchanged, that is.

The method of adding and subtracting rational numbers is to add two numbers with the same sign, take the same symbol, and add the absolute values.

Here it is:

Rational numbers are a collective term for integers (positive integers, 0s, negative integers) and fractions, and are a collection of integers and fractions. An integer can also be thought of as a fraction with a denominator of one. Real numbers that are not rational numbers are called irrational numbers, i.e., the fractional part of an irrational number is an infinite number that is not cyclical.

It is one of the important contents in the field of "number and algebra", which has a wide range of applications in real life, and is the basis for continuing to learn real numbers, algebraic formulas, equations, inequalities, Cartesian coordinate systems, functions, statistics and other mathematical content and related subject knowledge.

The name "rational number" is incomprehensible, and rational numbers are no more "reasonable" than other numbers. In fact, it seems to be a translation error. The term rational number came from the West and is rational number in English, and rational usually means "rational".

The above information refers to the encyclopedia - rational numbers.

Conceptual analysis of "Addition and Subtraction of Rational Numbers".

1) Rational number addition rule:

That is, add two numbers with the same sign, take the same symbol, and add the absolute value. , add two numbers with unequal absolute values, take the additive sign with the larger absolute value, and subtract the smaller absolute value with the larger absolute value; Two numbers that are opposite to each other are added to give 0.

Add a number to 0 and still get this number.

2) The law of subtraction of rational numbers:

That is, subtracting a number is equal to adding the opposite of that number. The subtraction of rational numbers can be converted to addition.

Idea analysis] as long as you keep the various algorithms in mind.

And you can use it skillfully.

Do more exercises.

Problem Solving Process] 1.When the addition and subtraction of rational numbers is carried out, the subtraction can be converted into addition according to the subtraction law of rational numbers, which unifies the addition and subtraction of rational numbers into a single addition operation. At this point, it becomes the sum of several positive and negative numbers.

2.When converting mixed operations into addition operations, write algebraic sum, pay attention to the two different readings of algebra and form.

3.The form of the sum omitted from parentheses can be seen as an addition operation of rational numbers. Therefore, the addition law can be used to simplify the calculation, and attention should be paid to the rationality of the operation.

The general steps of the mixed operation of addition and subtraction of rational numbers are: (1) subtraction is converted into addition, written in the form of omitting plus signs and parentheses; (2) the application of the commutative law of addition and the associative law to simplify the operation; (3) Finding the Result Here are some examples of some techniques in the mixed operation of addition and subtraction

1. Be proficient in the "two rules" and "two laws" of rational numbers

1. The addition rule of rational numbers: add two numbers with 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 value is equal, and 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. Two numbers that are opposites of each other are added to give zero.

2 The law of subtraction of rational numbers: subtracting a number is equal to adding the opposite of the number.

3 The commutative law of addition:; Associative Law of Addition:

2. The basic steps and methods of mixed operation of addition and subtraction of rational numbers:

1) The basic steps of the mixed operation of addition and subtraction are: to convert the subtraction in the mixed operation into addition, and write it in the form of a plus sign in front; Omit plus marks and parentheses; Appropriate use of additive commutative and associative properties to simplify calculations; In each step of the operation, the symbol must be determined first, and then the value must be calculated.

2) In the specific calculation process, there are the following two commonly used methods: according to the order of operation, calculate one by one from left to right (as shown in solution 1); The mixed operation of addition and subtraction is unified into addition, and after it is written in the form of a sum formula, it is calculated using the arithmetic law.

1) After the operation is proficient, the step of subtraction to addition can be omitted, and it can be directly written in the form of omitting the plus sign; (2) When exchanging the position before and after the number, it should be exchanged together with the symbol in front of it;

3) When performing mixed operations, the method of determining the order of operations learned in elementary school is still applicable, and if there are parentheses, the brackets should be counted first.

Technique Penetration 1: Opposite Number Combination Method

The sum of two numbers that are opposite to each other is 0, and when we calculate, we can combine the two numbers that are opposite to each other to calculate first.

Technique 2: Combination of the same number

In the addition and subtraction of rational numbers, the addition and subtraction of negative numbers are introduced more than in primary school, and some students will confuse the minus sign with the negative sign when calculating, and do not know how to calculate, so we can combine the same sign when calculating, and finally calculate according to the addition and subtraction rules of rational numbers.

Technique 3: Combination method with the same denominator

When calculating, we can calculate the same denominator first, and the different denominator needs to be modularized to be universal, and sometimes the calculation will be more cumbersome.

Technique 4: Rounding method

In addition to mastering the relationship between the three, we can also use the rounding method to simplify the problem.

The general steps of the mixed operation of addition and subtraction of rational numbers are: (1) subtraction is converted into addition, written in the form of omitting plus signs and parentheses; (2) the application of the commutative law of addition and the associative law to simplify the operation; (3) Finding the Result Here are some examples of some techniques in the mixed operation of addition and subtraction

1.Unify subtraction into (addition).

2.Written in the form of ( and ) with the plus sign omitted.

3.Combined with ( arithmetic ) to calculate.

Attention to the problem.

4.When performing subtraction operations, first clarify the ( meaning of subtraction ).

5.When converting the subtraction of a rational number into addition, two symbols are changed at the same time: one is the operation sign minus sign becomes the plus sign, and the other is the property sign that the subtraction becomes its (opposite number).

6. Mixed operations of addition and subtraction should be combined with the sum of the laws of operation (order of operation).

1.Addition.

2.Omit. 3.The law of addition of rational numbers.

4.Symbol. 5.Addend.

6.Commutative law.

Step 1: Use the subtraction rule to convert the subtraction in the mixed operation of rational numbers into (addition) Step 2: Write it in the form of omitted (plus) or (parentheses);

Step 3: Simple operation using the law of addition, the law of addition (commutative), and the law of addition (combination).

1.Unify subtraction into (

Addition. 2.Written with the plus sign omitted (

and) in the form.

3.Combined with ( arithmetic ) to calculate.

Attention to the problem.

4.When performing subtraction operations, first find out the subtraction (

significance). 5.When converting the subtraction of a rational number into addition, two symbols are changed at the same time: one is the operation sign minus sign becomes the plus sign, and the other is the property sign that the subtraction becomes its (opposite number).

6. Mixed operations of addition and subtraction should be combined with the sum of the laws of operation (order of operation).

The general steps of the mixed operation of addition and subtraction of rational numbers are: (1) subtraction is converted into addition, written in the form of omitting plus signs and parentheses; (2) the application of the commutative law of addition and the associative law to simplify the operation; (3) Finding the Result Here are some examples of some techniques in the mixed operation of addition and subtraction

It should be multiplied and divided first, then added and subtracted. There are parentheses to scratch the number first.

Calculate the power of the square first; then multiply and divide; Finally, add and subtract; If there are parentheses, the ones in the brackets should be counted first (the small brackets are counted first, and then the ones in the middle brackets are counted).

1.Addition: Symbolic Rule:

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

Add the two numbers of different signs, take the sign with the largest absolute value, and subtract the absolute value of the two numbers of the different sign and add the two numbers, and when the absolute value is equal, the sum is 0

Regardless of the positive or negative signs, when the 0 is added, this number is still obtained.

2.Subtraction: The inverse of addition.

Subtracting a number is equal to adding its opposite.

3.In the mixed operation of rational numbers, it is generally written in an abbreviated form for adoption

by: Xue Xiaoxi.

1.Unify subtraction into (

Addition. 2.Written with the plus sign omitted (

and) in the form.

3.Combined with ( arithmetic ) to calculate.

Attention to the problem.

4.When performing subtraction operations, first find out the subtraction (

significance). 5.When converting the subtraction of a rational number into addition, two symbols are changed at the same time: one is the operation sign minus sign becomes the plus sign, and the other is the property sign that the subtraction becomes its (opposite number).

6. Mixed operations of addition and subtraction should be combined with the sum of the laws of operation (order of operation).

1.0 - [2 and two-thirds - (-4 quarters) + (2 and three old minds two-thirds)] - 5 and 7/12

2.(four-thirds) - (8) + (2 and a third) - (3 and a quarter) - (1 and two-thirds).

11 and 1/6

3.(and collapse - 3 and one-seventh) - (6 and two-fifths called with round) - (2 fifths) - (5 sevenths sixth) - (four-fifths).

5 and 3/5