Extract common factor
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)
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
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
associative law of addition
Pay attention to the application of additive associative law (A+B)+C = A+(B+C), and get simpler operation by changing the position of addend.
For example:
5.76+ 13.67+4.24+6.33
=(5.76+4.24)+( 13.67+6.33)
Law of division and multiplication distribution
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: 57×101= 57× (100+1)
Use reference number
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
Using 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, axb=bxa,
The law of association, (axb)xc=ax(bxc),
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 \bxc，
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.
example
Example 1:
283+52+ 1 17+ 148
=(283+ 1 17)+(52+48)
(Using additive commutative law and the Law of Association).
Add or remove parentheses after the minus sign or the division sign, and the operation sign of the following value will be changed.
Example 2:
657-263-257
=657-257-263
=400-263
(Using the nature of subtraction, it is equivalent to additive commutative law. "move with symbol")
Example 3:
195-(95+24)
= 195-95-24
= 100-24
(Using the nature of subtraction)
Example 4:
150-( 100-42)
= 150- 100+42
(Remove the brackets, the minus sign comes before the brackets, and the operation symbol in the brackets will become the inverse operation. )
Example 5:
(0.75+ 125)x8
= 0.75 x8+ 125 x8 = 6+ 1000
(Using the Law of Multiplication and Distribution))
Example 6:
( 125-0.25)x8
= 125x8-0.25x8
= 1000-2
(same as above)
Example 7:
( 1. 125-0.75)÷0.25
= 1. 125÷0.25-0.75÷0.25
=4.5-3= 1.5。
(Using the nature of division)
Example 8:
(450+8 1)÷9
=450÷9+8 1÷9
=50+9=59.
(Same as above, law of equal multiplication and distribution)
Example 9:
375÷( 125÷0.5)
= 375÷ 125 x 0.5 = 3x 0.5 = 1.5。
(Using the nature of division)
Example 10:
4.2 inches (0.6x0.35 inches)
=4.2÷0.6÷0.35
=7÷0.35=20
(Using the nature of division)
Example 1 1:
12x 125x0.25x8
=( 125x8)x( 12x0.25)
= 1000x3=3000。
(Using Multiplicative method of substitution and Combination Method)
Example 12:
( 175+45+55+27)-75
= 175-75+(45+55)+27
= 100+ 100+27=227.
(Using additive attributes and association rules)
Example 13:
(48x25x3)÷8
=48÷8x25x3
=6x25x3=450。