Ten quick calculation skills in mathematics
First, make full use of the five laws.
Teachers should teach the five major algorithms in the current textbooks (additive commutative law, law of addition and association, law of multiplication and exchange, law of multiplication and association, and law of multiplication and distribution), so as to guide students to find out the ins and outs, so as not to let a student fall behind, and to cultivate each student to consciously use simple methods and flexibly choose simple methods to calculate correctly and quickly according to different types of questions.
Second, clever use? The first one is the same as the last one?
Use? The first one is the same as the last one? The way of training. ? The first one is the same as the last one? The method is two two-digit numbers with the same ten digits, and the sum of the single digits is 10. Use? The first one is the same as the last one? Multiply the two digits of, the two digits on the right side of the product are exactly the product of single digits, and the number on the left side of the product is exactly the product of the number on the tenth digit multiplied by 1 larger than it, and the combination is their product. Like 54? 56=3024,8 1? 89=7209。
Third, pay attention? Combination of left and right numbers?
The fast algorithm of multiplying any two digits by 99 or multiplying any three digits by 999 is called? Combination of left and right numbers? .
1. The ingenious calculation method of multiplying any two digits by 99 is to subtract 1 from these two digits as the two digits on the left side of the product, and then subtract 100 from these two digits as the two digits on the right side of the product, and the combination is their product. Like 62? 99=6 138,48? 99=4752。
2. The ingenious calculation method of multiplying any three digits by 999 is to subtract 1 from any three digits as the three digits on the left side of the product, and then subtract 1000 from the difference of any three digits as the three digits on the right side of the product, and the combination is their product. Such as 78 1? 999=7802 19,396? 999=395604。
Fourth, skillfully use the relationship between fraction and division to calculate.
In a problem with only two levels of operation, sequential calculation needs multi-step calculation, and it will be very simple to calculate by using multiplication and division relationship. For example,
24? 18? 36? 12=(24? 18)? (36? 12)=24/ 18? 36/ 12=4。
5. Make a simple calculation by using the law of expansion and contraction.
Direct calculation of some division problems is cumbersome and easy to make mistakes. Law of expansion and contraction? A simple solution can be found through reasonable deformation. For example,
7? 25=(7? 4)? (25? 4)=28? 100=0.28,
24? 125=(24? 8)? ( 125? 8)= 192? 1000=0. 192。
6. Subtraction of two or three digits and the inverse
What are the numbers 73 and 37, 185, 58 1? The numbers are upside down? Two or three digits, clever calculation method is:
1. Subtract two digits with the inverse number. You can subtract the decimal from the large number in the two digits and multiply it by 9. The product is their difference. Such as 73-37=(7-3)? 9=36,82-28=(8-2)? 9=54。
2. For the three-digit subtraction with reciprocal, you can subtract the minimum number from the maximum number of three digits, multiply it by 9, multiply the two sides of the integral, and fill in 9 in the middle, which is their difference. For example, 581-158 = (8-1)? 9=63, so 85 1- 158=693.
Seven, use? Add zero and half? Clever calculation method
A fast calculation method of multiplying a number by 15 is called? Add zero and half? . Like 26? 15 26 plus 0 is 260, and 260 plus half of 130, that is, 260+ 130=390, so 26? 15=360。
Eight, the use of split and clever calculation
Some calculation problems, at first glance, have nothing to do with the algorithm, but they are directly calculated by the algorithm after deformation.
Nine, use? Pull on both sides and add in the middle? Fast calculation method
Multiply any number by 1 1, as long as the original number is shifted to the single digit position of the product and the highest digit position of the product, the sum of the middle numbers is the number of single digits plus the number of ten digits, and the sum of the number of ten digits plus the number of hundred digits is the hundred digits. For example 124? 1 1= 1364,568? 1 1=6248。
X. use? Ten plus one MINUS? Fast calculation
? Ten plus one MINUS? It is the sum of any two digits plus 9, which can be changed into ten digits plus 1 digits minus 1, that is, 36+9 = 45, 17+9 = 26. This calculation skill is suitable for lower grade pupils.
Many students' incorrect calculation results are caused by bad habits such as carelessness. When cultivating students' good computing habits, teachers should pay attention to the training forms, stimulate students' interest in computing, entertain and educate, and adopt diversified training forms. For example, games, competitions, cards and small blackboards are used for training, such as watching calculations, listening to calculations in a limited time, editing calculation questions and short stories. Teachers should be patient, persistent, unify methods and requirements and stick to it. Teachers should guide students to develop good habits of examining questions, writing and testing.
Wei Dewu's fast calculation
Fast addition: the calculation method of fast addition of arbitrary digits is very simple. Learners can add quickly by memorizing a general formula. Standard addition (for decimal places) Subtraction and addition, adding one to the previous addition? It can completely solve the problem of adding arbitrary digits from high to low.
For example: (1), 67+48=(6+5)? 10+(7-2)= 1 15,(2)758+496=(7+5)? 100+(5-0)? 10+8-4= 1254.
Fast subtraction: the fast subtraction of calculating any number of digits is also a fast subtraction with a general formula? Standard subtraction (for borrowing) adds and subtracts, and subtracts more than one before? It can completely solve the problems of subtraction and fast calculation of any number of digits from high to low.
For example: (1), 67-48=(6-5)? 10+(7+2)= 19,(2),758-496=(7-5)? 100+(5+ 1)? 10+8-6=262.
Fast multiplication: the general formula of fast multiplication: ab? cd=(a+ 1)？ c？ 100+b？ D+ Wei quickly calculates the evolution number? 10。
Fast calculation of evolution number |=(a-c)? d+(b+d- 10)？ c，，
Fast calculation of evolution number ‖=(a+b- 10)? c+(d-c)？ One,
Fast calculation of evolution number ⅲ = a? d-？ b？ (supplementary)? C. It's unique and unparalleled.
(1), calculate the evolution number with the first speed =(a-c)? d+(b+d- 10)？ C, suitable for any two-digit multiplication with any head and tail.
For example: 26? 28, 47? 48,87? 84- and so on, its evolution number is clear at a glance, which is equal to? 8? ,? 20 ? And then what? 8? Do it.
(2) Calculate the evolution number with the speed of seconds =(a+b- 10)? c+(d-c)？ The sum of two digits of a factor is close to equal to? 10? The difference between the two digits of another factor is close to equal to? 0? Fast calculation of arbitrary two-digit multiplication,
For example: 28? 67, 47? 98, 73? 88- Wait, its evolutionary number can also be clearly equal to? 2? ,? 5 ? And then what? 0? Do it. (3) Calculate the evolution number with the third speed =a? d-？ b？ (supplementary)? C is suitable for fast multiplication of arbitrary two-digit numbers.
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