Now, more and more parents want their children to enter private schools. Mathematics is the core of junior high school evaluation in private schools every year, and simple operation is an important test item. I have sorted out the methods and skills of simple operation in primary schools, which I believe will be helpful to parents.
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 99, 10 1 9.8 approaches an integer on the test paper, division should be considered first.
For example:
34×9.9 = 34×( 10-0. 1)
Case reappearance: 57× 10 1=?
Using formula method
0 1
Add:
Commutative law, a+b=b+a,
Law of association, (a+b)+c=a+(b+c).
02
Subtraction operation attribute:
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。
03
Multiplication:
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。
04
The nature of the division operation:
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 1:
283+52+ 1 17+ 148
=(283+ 1 17)+(52+48)
(Using additive commutative law and the Law of Association)
Example 2:
657-263-257
=657-257-263
=400-263
(Using the nature of subtraction, it is equivalent to additive commutative law)
Example 3:
195-(95+24)
= 195-95-24
= 100-24
(Using the nature of subtraction)
Example 4:
150-( 100-42)
= 150- 100+42
(Using the nature of subtraction)
Example 5:
(0.75+ 125)*8
=0.75*8+ 125*8=6+ 1000
(using the law of multiplicative distribution)
Example 6:
( 125-0.25)*8
= 125*8-0.25*8
= 1000-2
(using the law of multiplicative distribution)
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*0.5=3*0.5= 1.5.
(Using the nature of division)
Example 10:
4.2÷(0。 6*0.35)
=4.2÷0.6÷0.35
=7÷0.35=20.
(Using the nature of division)
Example 1 1:
12* 125*0.25*8
=( 125*8)*( 12*0.25)
= 1000*3=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:
(48*25*3)÷8
=48÷8*25*3
=6*25*3=450.
(Using the nature of division, it is equivalent to addition)
Split terminology
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 The molecules are all the same, the simplest form is that they are all 1, and the complex form can be that they are all x(x is any natural number), but as long as X is extracted, it can be converted into the operation that the molecules are all 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:
;