a+b=b+a
2, the law of addition and association: three numbers are added, first add the first two numbers, and then add another addend; Or add the last two numbers first, then add another addend, and the sum remains the same. Letters indicate:
(a+b)+c=a+(b+c)
3. Law of Multiplication and Interchange: In the multiplication operation of multiplying two numbers, the positions of the two multipliers are interchanged and the product remains unchanged. Letters indicate:
a×b=b×a
4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied first, or the last two numbers are multiplied first, and the product remains unchanged. Letters indicate:
(a×b)×c=a×(b×c)
5. Multiplication and distribution law: when two numbers are added (or subtracted) and then multiplied by another number, it is equivalent to multiplying this number by two addends (subtractions) respectively, and then adding (subtracting) the two products to keep this number unchanged. Letters indicate:
①(a+b)×c = a×c+b×c； a×c+b×c =(a+b)×c；
②a×(b—c)= a×b—a×c； a×b—a×c=a×(b—c)
6, the law of continuous decline:
(1) A number minus two numbers in a row equals the sum of the two numbers after subtracting this number, and this number remains unchanged; Letters indicate:
a—b—c = a—(b+ c)； a—(b+c)= a—b—c；
(2) In the addition and subtraction of three numbers, the positions of the two numbers remain unchanged after the exchange. Letters indicate:
a—b—c = a—c—b； a-b+c = a+c-b
7, division law:
(1) When a number is divided by two numbers in a row, it is equal to the product of the two numbers after the number is divided, and this number remains unchanged. Letters indicate:
a \b \c = a \u( b×c)； a \(b×c)= a \b \c；
(2) In the multiplication and division of three numbers, the positions of the two numbers remain unchanged after the exchange. Letters indicate:
a÷b÷c = a÷c÷b； a \b×c = a×c \b
Extended data
Calculation method of fractional and decimal elementary arithmetic
1, fraction, decimal addition and subtraction mixed operation, when the fraction can be converted into a finite decimal (denominator only contains prime factors 2 and 5), it is generally easier to calculate the fraction after it is converted into a decimal, and when some fractions cannot be converted into a finite decimal, the number of components of the fraction is calculated.
2. Fraction and decimal multiplication are mixed operations. If the decimal is about the denominator of the fraction, it can be calculated directly or by dividing the decimal into numbers. If the fraction is converted into decimal, it can be simplified or converted into decimal.
3. For some types of questions, it is not necessary to unify the whole type of questions or calculate them into decimals. It can be divided into several parts according to the operation order, and the appropriate algorithm can be selected.
Note: The result of elementary arithmetic is that fractions should be converted into the simplest fractions, and false fractions should be converted into fractions or integers. When you encounter an inexhaustible part without specifying an approximate value, you can use a fraction to express the quotient, or you can keep two decimal places as usual.
Baidu encyclopedia-elementary arithmetic