Additive commutative law;

When two numbers are added, the positions of addends are exchanged, and their sum remains the same. That is, a+b = b+a.

Generally speaking, when multiple numbers are added, the order of addition is arbitrary and the sum is constant.

a+b+c+d=d+b+a+c

Additive associative law:

Add a few numbers, first add the first two numbers, then add the third number; Or, add the last two numbers first, and then add them to the first number, and their sum remains the same. Namely: a+b+c=(a+b)+c=a+(b+c),

Second, three basic ideas commonly used in quick calculation and clever calculation

1, rounded (target: whole ten thousand ...)

2. Split (after splitting, you can make a whole hundred thousand ...)

3. Combination (reasonable grouping and reorganization)

Third, common methods

Rounding method

When two numbers are added, if they can just be added to whole ten, whole hundred, whole thousand and whole ten thousand, one of them is called the "complement" of the other number. Using the "complement" to calculate the addition skillfully is usually called "rounding method".

For example,1+9 =10,3+7 =10,2+8 =10,4+6 =10,5+5 =10.

Another example: 1 1+89= 100, 33+67 = 100, 22+78= 100, 44+56= 100.

In the above formula, 1 is called the "complement" of 9; 89 is called the "complement" of 1 1, and1is also called the "complement" of 89. In other words, two numbers are complementary to each other.

For a large number, how to quickly calculate its "complement"? Generally speaking, you can "round up" numbers by adding all the numbers from the most significant bit to get 9, and then adding the last digit to get 10.

Such as: 87655→ 12345, 46802→53 198, 87362→ 12638.

Using "complement" skillfully to calculate addition is usually called "rounding method".

Skillfully calculate the following questions:

①36+87+64

②99+ 136+ 10 1

③ 136 1+972+639+28

Solution:

① Formula = (36+64)+87 =100+87 =187.

② formula = (99+101)+136 = 200+136 = 336.

③ Formula = (1361+639)+(972+28) = 2000+1000 = 3000.

Wei Dewu's fast calculation

Wei's quick calculation allows learners to master the quick calculation method of addition, subtraction, multiplication and division of any number quickly and accurately in a short time with an idea and a method without any calculation tools. So as to quickly improve learners' quick calculation ability in oral and mental arithmetic.

1. Fast addition: The method of calculating the fast addition of arbitrary numbers is very simple. As long as learners remember a general formula for fast addition-"standard addition (decimal number) minus complement, and the previous digit plus 1", they can completely solve the fast addition method of any digit from high to low, for example:

( 1),67+48=(6+5)× 10+(7-2)= 1 15;

(2) 758+496 = (7+5) × 100+(5-0) × 10+8-4 = 1254.

2. Fast subtraction: The fast subtraction for calculating any number of digits is also a general formula for fast subtraction-"Standard subtraction (borrowed digits) plus or minus the previous digit" can completely solve the fast subtraction for calculating any number of digits from high to low, such as:

( 1),67-48=(6-5)× 10+(7+2)= 19;

(2), 758-496 = (7-5) × 100+(5+ 1) × 10+8-6 = 262.

Refer to the above? Baidu Encyclopedia-Fast Algorithm of Mathematics