Quick calculation skills of calculating math problems in the sixth grade of primary school
Magic speed algorithm of addition
First, add subtraction.
1. formula
The integer of the previous addend and the last addend, minus the difference between the last addend and the integer is equal to the sum.
Step 2: Example
1376+98= 1474 calculation method: 1376+ 100-2.
3586+898=4484 Calculation method: 3586+ 1000- 102.
5768+9897= 15665 Calculation method: 5768+ 10000- 103.
Second, find the sum of two digits with reversed positions.
1. formula
The ten digits of a number plus its single digits multiplied by 1 1 equals the sum.
Step 2: Example
47+74= 12 1 calculation method: (4+7) x11=121.
68+86= 154 calculation method: (6+8) x11=154.
58+85= 143 calculation method: (5+8) x11=143.
Magic speed algorithm of subtraction
A, minus big plus difference method
1. Example
32 1-98=223
Calculation method: subtract 100 and add 2.
8 135-878=7257
Calculation method: subtract 1000 and add 122.
9 132 1-8987= 82334
Calculation method: subtract 10000 and add 10 13.
summary
Minus the minuend from the integer of the minuend, plus the difference between the minuend and the integer, equals the difference.
Second, find the difference between two numbers whose positions are reversed.
1. Example
74-47=27
Calculation method: (7-4)x9=27
83-38=45
Calculation method: (8-3)x9=45
92-29=63
Calculation method: (9-2)x9=63
summary
Minus the ten digits of the minuend and multiply it by nine, which equals the difference.
Third, find the difference between the three digits whose middle numbers are the same, but whose head and tail are transposed.
1. Example
936-639=297
Calculation method: (9-6)x9=27
Attention! 9 must be added to the middle of 27, which is the difference of 297.
723-327=396
Calculation method: (7-3)x9=36
Attention! 9 must be added in the middle of 36, which is the difference of 396.
873-378=495
Calculation method: (8-3)x9=45
Attention! 9 must be added in the middle of 45, which is the difference of 495.
summary
Subtract its single digit from the hundred digits of the minuend and multiply it by 9. (9 must be written in the middle of the difference) is equal to the difference.
Fourth, find the difference between two complements.
1. Example
73-27=46
Calculation method: (73-50)x2=46
6 13-387=226
Calculation method: (6 13-500)x2=226.
8 1 12- 1888=6224
Calculation method: (8112-5000) x2 = 6224.
summary
Two complements are subtracted, and the minuend is subtracted by 50 times 2; Subtract three complements and be subtracted by 500 times 2; Subtract four complements and be subtracted by 5000 times 2; etc ......
Magic speed algorithm of multiplication
A multiplication of two digits with the same ten digits and complementary single digits.
1. formula
Ten digits plus one times ten digits, multiplied by one digit and written at the back (10 plus zero below).
Step 2: Example
67x 63= 422 1
Calculation method: (6+ 1)x6=42.
7x3=2 1 written after 42 is the product of 422 1.
38x32= 12 16
Calculation method: (3+ 1)x3= 12.
8x2= 16 is written after 12 and is the product of 12 16.
76x74=5624
Calculation method: (7+ 1)x7=56.
6x4=24 written after 56 is the product 5624.
8 1 x89=7209
Calculation method: (8+ 1)x8=72.
1x9=09 is written after 72, and (less than 10 is filled with zero) is the product 7209.
Second, the ten digits are complementary, and the single digits are the same.
1. formula
Multiply ten bits and add one bit. Multiply by one bit and write it at the back (under 10, fill in zero).
Step 2: Example
76x 36=2736
Calculation method: 7x3+6=27
6x6= 36 is written after 27, which is the product of 2736.
68x 48=3264
Calculation method: 6x4+8=32
8x8=64 is written after 32 and is the product of 3264.
Similarly, the square of 56 is 5x5+6+6x6=3 136.
The square of 57 is 5x5+7+7x7=3249.
Three, a number 10 and 10 bits are complementary, and the other number is also the same multiplication operation.
1. Example
37x66=2442
Calculation method: (3+ 1)x6=24.
7x6=42 is written after 24, which is the product of 2442.
44x28= 1232
Calculation method: (2+ 1)x4= 12.
4x8=32 is written after 12, that is, the product 1232.
summary
Add a 1 to the complementary ten bits, multiply it by another ten bits, and then write the product of two bits, which is the final product.
Quadratic, Tenth and Tenth Multiplication Operations
1. Example
13x 12= 156
Calculation method: (13+2) x10 =150.
3x2=6 150+6= 156
15x 17=255
Calculation method: (15+7)x 10=220.
5x7=35 220+35=255
2. Formula
One number plus another mantissa, multiplied by 10, and mantissa product.
5. Single-digit multiplication of1
1. Example
3 1x2 1=65 1
Calculation method: 3x2 = 62+3 = 51x1=1.
5 1 x7 1=362 1
Calculation method: 5x7=35+1 =36.
5+7= 12 (write 2 as1)1x1=1.
6 1 x8 1=494 1
Calculation method: 6x8=48+ 1=49.
6+8= 14 (write 4 as1)1x1=1.
2. Formula
The same is true for the last digit. The product of the first digit is followed by the sum of the first digits (all decimal), followed by the product of the mantissa.
Six, one hundred times one hundred.
1. Example
10 1x 102 = 10302
Calculation method: 10 1+2= 103.
1X2=02 The product of two numbers is 10302.
103 x 104 = 107 12
Calculation method: 103+4= 107.
3X4= 12
The product of two numbers is 107 12.
Similarly, to find the square of 10 1, 102, 103... 109, you can also use the above method. For example, the square of 107 = 107+7 =14, 7x7 = 49. When the two numbers are connected, 1 1449 is the square of107.
2. Formula
When a number is added to other mantissas, the product of mantissas follows (below 10, with zeros in front).
Magic speed algorithm of division
The purpose of division is to find the quotient, but when you suddenly can't see how many quotients are contained in the dividend, you can try to estimate the quotient, see how many divisors are contained in the highest digit of the multiplicand (that is, how many times the quotient is contained), and then add several times the complement from the standard number to get the quotient.
First, small arrays
Where the dividend includes the divisor 1, multiples of 2 and 3, and the method is as follows:
Dividend includes quotient 1 multiple: the complement is added once from the standard.
Dividends include two quotients: from standard to supplementary.
Dividends include three quotients: from standard to supplementary three times.
1. Example
7995? 65= 123, (the complement of 65 is 35)
2. Calculation sequence
(1) The first two digits of the dividend 79 contain the divisor 65 times, and the complement is added once (35) to get 1- 1495 (quotient before dash and dividend after dash, the same below);
(2) The multiplicand 149 contains twice the divisor and twice the complement (35? 2=70) 12- 195;
③ Divider 195 contains triple divisor and triple complement (35? 3= 105) gives 123 (quotient).
Second, the array
When the dividend contains 4, 5 and 6 times of the divisor, the method is as follows:
Dividend contains quotient 4: the previous digit is added with half complement, and the previous digit is subtracted with one complement.
Dividend includes quotient 5 times: half of complement is added before, and the standard is fixed.
Dividend includes quotient 6: the previous digit is added with half complement, and the previous digit is added with one complement.
1. Example
35568? 78=456(78' s complement is 22)
2. Calculation sequence
355 contains a divisor of 4 times, so add 1 1 to the front position and subtract 22 from the cardinal position to get 4-4368;
If the divisor in 436 is 5 times, then add 1 1 to the previous position, and the standard is fixed, and you get 45-468;
The divisor in 468 is 6 times, the leading bit is added with 1 1, and the standard is added with 22 to get 456 (quotient).
Third, large arrays.
When the dividend contains 7, 8 and 9 times of the divisor, the method is as follows:
Dividend includes quotient 9 times: the previous digit complements 1 time, and the previous digit subtracts 1 time.
Dividend contains quotient 8 times: the former adds complement once and the former subtracts complement twice.
Dividend includes quotient 7: the former adds one complement and the standard subtracts three complements.
1. Example
884352? 896 = 987 (the complement of 896 is 104)
2. Calculation sequence
(1) 8843 contains divisor 9 times. Add 104 to the previous position and subtract 104 from the standard position to get 9-77952.
②7795 contains divisor 8 times 104, and the base minus 208 gets 98-6272;
③6272 contains 7 times divisor, with the first complement 104 once and the standard complement three times (104? 3=3 12 (986 (quotient)).
Fast computing skills
First of all, we must ensure that children have a good learning attitude, concentrate on class, grasp the important and difficult points, and remember the calculation formulas, theorems, problem-solving ideas and skills of each type of questions. Do the questions in time after class to consolidate the knowledge learned that day.
Secondly, we should cultivate children's good study habits. We must form a good study habit of taking exams carefully, calculating accurately and writing neatly. In re-education, I often find that such children have a high IQ. Once they learn, they will make mistakes. What is the reason? It's not a mistake, it's inaccurate, and sometimes it's even irrelevant. As a result, math test scores are often unsatisfactory.
If you want to improve your math scores, it is necessary to do more problems, but don't engage in sea tactics, which will have a bad effect and easily make children lose interest in math. Do the questions selectively and buy two or three authoritative workbooks for your children. Don't repeat the questions that children already know. Choose children to solve difficult problems and do more problems that they have not done, so that children can achieve practice.
It is also necessary to prepare an error book for children, copy the typical problems that children often make on it, and constantly correct mistakes, with good results.