1, additive commutative law: expressed in letters: a+b=b+a?

When two numbers are added, the positions of the addend are exchanged and the sum is unchanged.

2. The laws of addition and association are expressed by letters: (a+b)+c=a+(b+c)?

When three numbers are added, the first two numbers are added first and then the third number, or the last two numbers are added with the first number, and the sum remains unchanged.

3. Multiplicative associative law: expressed in letters: (a×b)×c=a×(b×c).

Three numbers are multiplied, the first two numbers are multiplied and then the third number is multiplied, or the last two numbers are multiplied and then the first number is multiplied, and their products are unchanged.

Timing of use: When several numbers are multiplied, if two of them are multiplied into integer ten, integer hundred and integer thousand, the multiplicative commutative law and multiplicative associative law can be applied. Multiplication association law can change the order of multiplication operations. For example, 25 and 4, 50 and 2, 125 and 8, 50 and 4,500 and 2, and so on.

4. Multiplication and distribution law: Numbers are represented by letters: (a+b)×c=a×c+b×c or (a-b) × c = a× c-b× c.

When the sum (or difference) of two numbers is multiplied by a number, you can multiply the two addends (or the minuend and the minuend) by this number respectively, and then add (or subtract) the two products, and the result remains unchanged.

5. Multiplicative commutative law is expressed in letters: axb=bxa.

Multiply two numbers, exchange the position of the multiplier, and the product remains the same.

Extended data

1. In addition calculation, when some addends can be added to form integer ten, integer hundred and integer thousand, the addition algorithm can make the calculation simple.

Formula: Look at the calculation carefully and consider the addend is the key. Whole ten, whole hundred and whole thousand are easier to combine. Law of Exchange Remember that the sum of exchange positions is constant. The law of combination is widely used, and it is easier to round the addend.

2. In the multiplication calculation, when the product of two multipliers is exactly integer ten, integer hundred and integer thousand, the multiplication algorithm can make the calculation simple.

By using the method of decomposition, a multiplier is decomposed into the form of multiplication of several numbers, so that the product of this multiplier and other multipliers is rounded up.

The law of multiplication and distribution should pay special attention to the two words in "the sum of two numbers is multiplied by a number, which can be multiplied first and then added"

note:

1, be sure to multiply the number outside the bracket by the two numbers inside the bracket, and then add the products. The distribution law of multiplication to subtraction is that the numbers outside brackets are multiplied by the two numbers in brackets respectively, and then the product is subtracted.

2. The same factor in two products can only be written once.