This method actually uses multiplication, division and distribution to extract the same factor, and the remaining items in the exam are often added and subtracted, and an integer will appear.
Pay attention to the extraction of the same factor.
For example:
0.92× 1.4 1+0.92×8.59
=0.92×( 1.4 1+8.59)
2. Borrowing method
See the name, and you will know the meaning of this method. When using this method, we need to pay attention to observation and find the law. Also pay attention to paying back the money. If you borrow it, it is not difficult to borrow it again.
In the exam, when you see that 998,999 or 1.98 is close to a very easy-to-calculate integer, you often use the borrowing method.
For example:
9999+999+99+9
=9999+ 1+999+ 1+99+ 1+9+ 1-4
3. Split method
As the name implies, the splitting method is to split a number into several numbers for the convenience of calculation. This requires mastering some "good friends", such as 2 and 5, 4 and 5, 2 and 2.5, 4 and 2.5, 8 and 1.25. Be careful not to change the size of the number when splitting.
For example:
3.2× 12.5×25
=8×0.4× 12.5×25
=8× 12.5×0.4×25
4. Additive associative law
Pay attention to the law of additive association
(a+b)+c=a+(b+c)
By changing the position of the addend, we can get a simpler operation.
For example:
5.76+ 13.67+4.24+6.33
=(5.76+4.24)+( 13.67+6.33)
5. The combination of splitting method and multiplicative distribution law
This method needs to master the distribution rules of division and multiplication flexibly. When you see that 99, 10 1 9.8 is close to an integer, you should first consider division.
For example:
34×9.9 = 34×( 10-0. 1)
Case reappearance: 57× 10 1=?
Use benchmark figures
In several kinds of series, find a more eclectic number to represent this series. Of course, remember that the selection of this number should not deviate too far from this series.
For example:
2072+2052+2062+2042+2083
=(2062 X5)+ 10- 10-20+2 1
7. Use the formula method
(1) addition:
Commutative law, a+b=b+a
Law of association, (a+b)+c=a+(b+c)
(2) The nature of subtraction:
a-(b+c)=a-b-c，
a-(b-c)=a-b+c
a-b-c=a-c-b
(a+b)-c=a-c+b=b-c+a
(3): multiplication (similar to addition):
Commutative law, a*b=b*a
Law of association, (a*b)*c=a*(b*c)
Distribution rate, (a+b)xc=ac+bc
(a-b)*c=ac-bc
(4) The nature of division operation (similar to subtraction):
a \(b * c)= a \b \c
a \(b \c)= a \b xc
a \b \c = a \c \b
(a+b)c = a \c+b \c
(a-b)÷c=a÷c-b÷c
Many previous algorithms and property formulas are changed by removing or adding brackets. Its rule is that in the same level of operation, parentheses are added or removed after the plus sign or multiplication sign, and the operation sign of the following value remains unchanged.
8. Split terminology method
Fractional splitting refers to splitting the items in the fractional formula so that the split items can be offset before and after. This split item calculation is called split item 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 1, and the complex form can all be 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.
Formula: