What are the laws of simple operation, and the 8 laws of simple operation?

1.Commutative law of addition: a+b=b+a

Two additions swap positions, and the sum is invariant, which is called the commutative law of addition.

2.additive associative law; （a+b）+c=a+（b+c）

Adding the first two numbers first or adding the last two numbers first, and the sum is unchanged, which is called the law of addition and associativity.

3.Commutative law of multiplication: a b = b a

Swap the positions of two factors, and the product is invariant, which is called the multiplicative commutative law.

4.Multiplicative associativity: (a b) c = a (b c) or a b c = a (b c).

Multiplying the first two numbers or the last two numbers first, and the product remains the same, which is called the associative law of multiplication.

5.Multiplicative distributive property: (a+b) c=a c+b c or (a-b) c=a c-b c

Inverse application of the multiplicative distributive property: a c + a b = (a + b) c or a c - b c = (a-b) c

When the sum of two numbers is multiplied by a number, they can be multiplied separately by the number and then added, which is called the multiplicative distributive law.

6.The difference between one number and two numbers is equal to subtracting the first number first, plus the second number, i.e.: a-(b-c)=a-b+c

7.A number is subtracted from the first number, and then the second number is added to the difference between the numbers minus the two numbers: a-b+c=a-(b-c).

8.The sum of the subtracted numbers from a certain number is equal to the continuous subtraction of these numbers, i.e., a-(b+c)=a-b-c

9.Conversely, a number subtracted from a number in a row is equal to the sum of a number minus those numbers. i.e.: a-b-c=a-(b+c).

10.In a mixture of addition and subtraction, it is possible to swap the positions of subtraction and addition. However, it is necessary to "move" together with the previous operator symbol when swapping places, and the result of the operation will not change.

11.A number divided by two numbers in a row is equal to the product of a number divided by those two numbers, and it is also equal to the quotient of a number divided by the third number, which is divided by the second number, i.e.: a b c = a (b c) = a c b

12.The product of a number divided by two other numbers is equal to a number divided by this number consecutively, i.e.: a (b c) = a b c

13.The quotient of a certain number divided by another number multiplied by the third number is equal to the quotient of a certain number divided by the second number and the third number, i.e.: a b c = a (b c).

14.The product of two numbers divided by the third number is equivalent to dividing one number by the third number and multiplying it by another multiplier, i.e., a b c=

a×（b÷c

a÷c）×b

15.In a hybrid operation of multiplication and division, the order of multiplication and division operations can be exchanged, and the result of the operation does not change. However, it is necessary to "move" together with the preceding operator symbol when swapping places

16.The sum or difference of two numbers divided by one number is equal to the two numbers divided by this number and then added (or subtracted), i.e.:

a+b）÷c=a÷c+b÷c

a-b）÷c=a÷c-b÷c

There are five in total. The commutative law of addition The associative law of addition.

The commutative law of multiplication, the law of combination of multiplication, the distributive law of multiplication. Satisfied.

1. Addition operation:

The commutative law of addition The associative law of addition.

The simple operation of two additive exchange positions, and the invariant, is called the commutative law of addition.

Letter formula: a+b=b+a.

additive associative law;

Adding the first two numbers, or adding the last two numbers first, and the invariant is called the additive associative law.

2. Subtractive nature:

If two numbers are subtracted from a number in a row, the sum of the two numbers can be subtracted from this number.

Letter formula: a-b-c=a-(b+c).

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3. Multiplication:

The commutative law of multiplication, the associative law of multiplication.

The inverse of the multiplicative distributive property, the multiplicative distributive property.

The two factors exchange positions and the product does not change, which is called the commutative law of multiplication.

Letter formula: a+b=b+a.

Multiplicative Associative Law:

The concept of the associative law of multiplication is: multiply the first two numbers, or multiply the last two numbers, and the product does not change.

Letter formula: a-b-c=a-(b+c).

Multiplicative distributive property:

The concept of the multiplicative distributive law is: the sum of two numbers, multiplied by a number, can be split to calculate, and the product remains unchanged.

Letter formula: (a+b)*c=a*c+b*c.

Inverse operation of the multiplicative distributive property:

The concept of the inverse operation of the multiplicative distributive law is that the product of one number multiplied by another number multiplied by itself by the product of another number can be added up and multiplied by this number.

Letter formula: ac+ab=a(c+b).

4. Division nature:

The concept of quotient invariance, the nature of division. If a number is divided by two numbers consecutively, you can multiply the last two numbers and then divide them.

Letter formula: a-b-c=a-(b+c).

The law of quotient immutability:

Dividend. Multiply or divide by the same number (except 0) at the same time as the divisor, and their quotient does not change. The basic nature of fractions: the numerator and denominator of fractions.

Multiply or divide by the same number at the same time (except 0) and the size of the fraction remains the same. The ratio is the same: two compared numbers expand or decrease by the same mill multiple, and the ratio remains the same.

Formula: a b = (an) (bn) = (a n) (b n)(n≠0 b≠0).

Addition commutative law: a + b = b + a additive associative law: (a + b) +c = a + b + c) multiplicative exchange talk tenant law:

Disadvantages a b = b a multiplicative associative property: (a b) c = a b c) multiplicative distributive property: a b + c) = a b + a c

Commutative law of addition, commutative law of addition, commutative law of multiplication, commutative law of multiplication, distributive law of multiplication.

1. The commutative law of addition:

The three numbers are added together, and the position of the two added numbers is exchanged, and the sum is unchanged.

Formula: a b+c= a+c+bExample question:

In the process of simple operation, the key is that the two numbers after exchange can be rounded. Scrambled to do.

2. Addition combined with law imitation:

Add three numbers, add the first two numbers first, or add the last two numbers first, and the sum is unchanged.

a b) c = a (b c) Example question:

738 + (68 + 132).

This method is suitable for combining two numbers and adding them to form an integer.

3. Multiplicative commutative law: two numbers are multiplied, the position of the two factors is exchanged, and the product remains unchanged.

Formula: a b = b a example question:

4. Multiplication associative law: multiply three numbers, multiply the first two numbers, or multiply the last two numbers first, and the product remains unchanged.

Formula: (a b) c = a (b c) Example Question:

5. Multiplicative distributive law:

Multiply the sum of two numbers by one number, multiply them by each number, and then add them together.

Formula: (a b) c = a c b c

Deformation formula: (a b) c = a c b c example:

6. The nature of subtraction.

Note: These are derived from the commutative and associative laws of addition.

Subtraction properties: If two numbers are subtracted from one number in a row, then the positions of the next two minus numbers are interchangeable.

The letter indicates: abc=acb Example:

7. The nature of division.

The sum or difference of two numbers divided by the same number is equivalent to the two numbers being subtracted by this number and then added.

Formula: (a+b) c=a c+b c example:

8. Benchmark number method.

Find a compromise number in a series of numbers to represent all numbers, and remember that the number should not be selected to deviate from this series of numbers. Example:

2062x5）+10-10-20+21

1.Lift and dismantle the cavity to take the common factor.

2.Borrow and borrow and borrow.

3.Splitting method.

4.The addition is grinding combined with the law to lift the royal fight.

5.Splitting method.

7.Make use of the formula method.

8.Fractional splitting method. Thanks

Easy calculation one.

1. Common multiplication calculations: 25 4 100 125 8 1000 2. Brief calculation of the commutative law of addition: 3. Brief calculation of the associative law of addition:

4. Brief calculation of the commutative law of multiplication: 5. Brief calculation of the combined law of multiplication:

6. Brief calculation of commutative law and associative law with addition: 7. Brief calculation of commutative law and associative law with multiplication:

Easy Calculation II.

Multiplicative distributive law simple calculation example:

1. Decomposition 2. Merger.

3. Special 1 Special 2 Special 3

Easy Calculation Three.

1. Example of continuous subtraction and simple calculation:

2. Example of continuous division of simple calculation:

3. Other examples of simple operations:

Simple calculation is the use of special calculation methods, using the laws of operation and the basic properties of numbers, so as to make the calculation easy, and make a very complex formula easy to calculate the result.

There are three main methods: addition, subtraction, grouping, and common factor method.

They use the idea of splitting and rounding in mathematical calculations.

Main steps: When encountering complex calculations, first observe whether it is possible to round up;

Use the four arithmetic to make up a whole ten hundred and then perform a simple calculation.

2 4 Addition, subtraction, rounding.

1. Split a certain number in the calculation formula so that it can be combined with other numbers into whole tens, whole hundreds;

2. Make up a number, which can be rounded up with other numbers, and finally subtract this number to group the rounding method In the calculation problem with only addition and subtraction, the items in the formula are re-divided into groups and rounded, mainly using two formulas: Mr. G talks about Olympiad numbers (micro). [Example 3].

Additive associative property: a+b+c=a+(b+c)=(a+b)+c;

The nature of subtraction: a-b-c=a-(b+c)The common factor method uses the multiplicative distributive property to extract the common factor, a x (b c)=a x b a x c;

If there is no common factor, the common factor can be varied according to the associative law of multiplication, see see .

a×b=(a×10)×(b÷10)，a×b÷c=a÷c×b，a×b×c=a×(b×c)。

The laws of simple operation are: the law of addition commutation, the law of addition combination, the law of multiplication commutation, the law of multiplication and the law of chain of things, and the law of multiplicative distribution. Simple arithmetic is one of the most common math problems in primary school math calculations.

From the very beginning of students' exposure to computing, the idea of simple arithmetic is infiltrated from different perspectives.

A law is an assertion that is proved by practice and facts and reflects the objective laws of the development and change of things under certain conditions. A law is a theoretical model that describes the real world at a specific scale in a particular situation, but may be invalid or inaccurate at other scales.