When a calculation problem only has the same level operation (only multiplication and division or only addition and subtraction) without brackets, we can "move with signs"
(a+b+c=a+c+b，a+b-c=a-c+b，a-b+c=a+c-b，a-b-c = a-c-b； a×b×c=a×c×b，
a \b \c = a \c \b，a×b \c = a \c×b，a \b×c = a×c \b)
Second, the law of combination.
(A) bracket method
1. When a calculation problem only includes addition and subtraction without brackets, we can directly add brackets after the plus sign, including whether the operation in brackets is addition or addition, subtraction or subtraction. But when parentheses are added after the MINUS sign, the operation in parentheses, which used to be addition, will now become subtraction; It used to be negative, but now it is positive. (that is, when adding parentheses for addition and subtraction, there is a plus sign in front of the parentheses, a constant sign in the parentheses, a minus sign in front of the parentheses, and a sign in the parentheses. )
a+b+c=a+(b+c)，a+b-c=a +(b-c)，a-b+c=a-(b-c)，a-b-c = a-(b+c)； 2. When there is only multiplication and division in a calculation problem without brackets, we can put brackets directly after the multiplication sign, and the operation results in brackets are multiplication or multiplication, division or division. But when parentheses are added after the division symbol, the operation in parentheses was originally multiplication, and now it will become division; It used to be division, but now it's multiplication. (that is, when multiplication and division are bracketed, the multiplication symbol is in front of the bracket, the constant symbol is in the bracket, the division symbol is in front of the bracket, and the symbol is changed in the bracket. )
a×b×c=a×(b×c)，a×b÷c=a×(b÷c)，a÷b÷c=a÷(b×c)，a÷b×c=a÷(b÷c
(2) Method of removing brackets
1. When there are only addition and subtraction and brackets in a calculation problem, we can directly remove the brackets after the plus sign, whether it is adding or adding now, or subtracting or subtracting. But when the brackets after the minus sign are removed, the addition in the original brackets will now be reduced; It used to be negative, but now it is positive. (Note: Deleting brackets is the reverse of adding brackets.)
A+(B+C)= A+B+CA+(B-C)= A+B-CA-(B-C)= A-B+CA-(B+C)= A-B-C2。 When a calculation problem only has multiplication, division and brackets, we can directly remove the brackets after the multiplication sign. But when the brackets after the division sign are removed, the multiplication in the original brackets now becomes division; It used to be division, but now it's multiplication. There are no brackets now, so you can move with symbols. Note: removing brackets is the reverse of adding brackets. )
a×(b×c) = a×b×c，a×(b÷c) = a×b÷c，a÷(b×c) = a÷b÷c，a÷(b÷c) = a÷b×c
Third, the laws of multiplication and distribution.
1. allocation method
2. Extract the common factor, and pay attention to extract the same factor.
3. Pay attention to the structure to make the formula conform to the conditions of multiplication and division.
Fourth, split method.
As the name implies, the splitting method is to split a number into several numbers for the convenience of calculation.
Such as: 2 and 5, 4 and 5, 2 and 2.5, 4 and 2.5, 8 and 1.25, etc. Be careful not to change the size of the number when splitting. 3.2× 12.5×25 1.25×88 3.6×0.25
Fifth, skillfully change division into multiplication.
In other words, turn division into multiplication.
Sixth, the cracking method
Fraction splitting refers to splitting the items in the fraction formula so that the split items can be offset before and after. This splitting calculation is called splitting method. The common splitting method is to split a number into the sum or difference of two or more digital units. When you encounter the calculation problem of split items, you should carefully observe the numerator and denominator of each item, find out the same relationship between the numerator and denominator of each item, and find out the part with * * * *. The problem of splitting term does not need complicated calculation, and it is generally the process of eliminating the middle part. In this case, it is most fundamental to find the similar parts of two adjacent items and let them be eliminated.
Three key features of fractional splitting terms:
(1) molecules are all the same, the simplest form is all 1, and the complex form can be all x(x is any natural number), but as long as x is extracted, it can be transformed into an operation that all molecules are 1.
(2) The denominator is the product of several natural numbers, and the factors on two adjacent denominators are "end to end". (3) The difference between several factors on the denominator is a constant value.
In short, simple calculation is nothing more than the associative law, commutative law, distributive law, split and pieced together.