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),

2 three basic ideas commonly used in fast calculation and clever calculation

1. Round (target: one hundred thousand yuan only ...)

2. Divide it (after dividing it, you can make ten thousand ...)

3. Combination (reasonable grouping and reorganization)

Three 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, …

Let's talk about the clever use of "complement" to calculate addition, which is commonly 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.

Combined rounding method

(1) When removing brackets, if there is a "+"before the brackets, the operation sign of the numbers in the brackets will remain unchanged after removing the brackets; If there is a "-"in front of the parentheses, after removing the parentheses, the operation symbol "+"of the number in parentheses becomes "-"and "-"becomes "+".

(2) In addition and subtraction mixed operation, when adding brackets: if there is a "+"sign in front of the brackets, the original operation sign of the numbers in brackets remains unchanged; If you add parentheses before a symbol "-",the original operator "+"of the number in parentheses will become "-"and "-"will become "+".

(3) Before the operation, use "complement" to round up the numbers close to integer ten, integer hundred, integer thousand, etc. (pay attention to subtracting redundant numbers and adding redundant numbers).

Benchmark method

In the process of subtraction, using the principle of complement, several subtractions are rounded up first and then subtracted. When using the benchmark number method, we should choose the number with small difference from each number as the benchmark number, which is convenient for calculating the cumulative difference. At the same time, considering that the multiplication of the base number and the addend can be easily calculated, the base number should be selected as much as possible.

Calculate 78+76+83+82+77+80+79+85 = 640.