Mental Arithmetic Tips - One Minute Quick Calculation and Top Ten Quick Calculation Techniques (Full Version)
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Ten fingers, palm facing you, counting from left to right.
units digit is larger than tens digit 1×9 formula
units digit is the number, the left side of the bent finger is the hundreds place, 34×9=306 89×9=801
bent finger reads 0 as the tens digit, and the bent finger to the right is the ones digit. . 78×9=702 45×9=405
the ones digit is greater than the tens digit×9 formula
the ones digit is the number of bends, the original tens digit is the hundreds digit, 38×9=3.42 25×9=225
subtract the hundred from the left Digits, the remaining fingers are tens, 13×9=117 18×9=162
Bend your fingers as the dividing line. The right side of the curved finger is the one position.
The ones digit is the same as the tens digit 44×9=396
The ones digit is smaller than the tens place ) = 846
html The difference between 0 and hundred is written in the ones digit (add the complement), if the difference is tens, add the tens digit.83×9=(8-1)×100+ 30+17=747
62×9=(6-1)×100+2×10+(100-62)=558
addition
increase subtraction method
front addend Add the integer of the subsequent addend, and subtract the difference between the subsequent addend and the integer to equal the sum (minus the complement).
+1 -2
1378+98=1378—100+2=1476
5768+9897=5768+10000—103 =15665
. Find the sum of two digits by changing the position of two numbers.
The tens digit of the addend in front plus its individual Number of digits, multiplied by 11 is equal to
47+74=(4+7)×11=121 68+86=(6+8)×11=154
58+85=(5+8)×11=143
One-eye and three-line addition
65427158 Tips
+644785963 1 If the number is less than 9, add it directly using the segmentation method, and must be added in advance 1
+742334452 2 If the middle number is 19, discard 19, add 1 more in front (discard 9 in the middle)
1752547573 3 The sum of the last digit Discard 20 for 19, add 1 more to the front (discard 10 for the last position)
Notes:
①If the middle number and less than 9 use direct addition or segmentation method
segmentation method direct addition 1+ -19 1+ -20
① 36 0427158 ② 36 042 9158 ③ 36042715 9
64 1785963 64 178 9963 64178596 9
+74 2334452 +74 233 9452 +74233445 9
174 4547573 1 74 455 8573 174454758 7
② Three 9s appear in the middle number: discard 19 in the middle, add 1
in the front ③ Three 9s in the last number, 20 , discard 20 at the end, add 1
in the front. Subtraction method
minus the addition method
Formula: subtract the integer of the minuend from the minuend, plus the complement of the minuend equals the difference.
321-98=223 8135-878=7257 91321-8987=82334
-1+2 -1+122 -1+1013
(—100+2) (—1000+122) (—10000+1013)
is just a numerical position. Reverse the difference between two two-digit numbers
Tip: subtract the tens digit of the minuend from its units digit, multiplied by 9, equals the difference.
74-47=(7-4)×9=27 83-38=(8-3)×9=45 92-29=(9-2)×9=63
is just a transposition of the first and last, the two numbers in the middle are the same The difference between a three-digit number
formula: subtract the hundreds digit of the minuend from its units digit, multiplied by 9 (9 must be written in the middle of the difference), equal to the difference.
936—639=297 723—327=396 873—378=495
(9—6)×9=3×9=27 (7—3)×9=36 (8—3)×9=45
Find two complementary ones Difference of numbers
formula: Subtract 50 from the minuend, and its difference is doubled to be the final difference.
73-27= (73-50) (8112-5000) After the obtained product, write the two unit products, which is the final product sought.
67×63=(6+1)×6×100+7×3=4221
38 76 81
×32 ×74 ×89
1216 5624 7209 (Do not add a zero to the tens digit)
Rule: The tens are complementary, The ones digits are the same.
formula: multiply the tens digit by the tens digit plus one of the ones digits, multiply the ones digit by the ones digit
76×36=（7×3+6）×100+6×6=2736
562=（5×5+ 6)×100+6×6=3136
68×48=(6×4+8)×100+8×8=3264
One tens digit is complementary to the ones digit, and the other tens digit is the same as the ones digit.
Add a 1 to the complementary tens digit, multiply it with another tens digit to get the product, and then write the product of the two units digits, which is the final product you want.
37×66=(3+1)×6×100+6×7=2442
46×77=(4+1) ×7×100+6×7=3542
44×28=(2+1) ×4+4× 8=1232 (3+1)×8=32
88888888888
× 37
3288888888856
11’s multiplication
. If the high bit is the number, enter the number. Add the two and write them next to each other. Add 1 before the sum exceeds 10, and write down the ones digit.
231415
× 11
2545565
The multiplication of the tens digit is 1. The multiplication of 1 is the multiplication of
units digit to write the ones digit, multiplication of 13 units digits to write the units digit, 31 51 61
units digit is added to write the tens digit, ×12 tens digit The addition is written in the tens place, ×21 ×71 ×81
is written in the hundreds place when the tens place is multiplied, 156 is written in the hundreds place when the tens place is multiplied, 651 3621 4941
adds carry if there is a carry. If there is a carry, add the carry.
supplements
. The multiplicand is the same as the tens digit when multiplied. The sum of the single digits is not equal to 10
html. Multiply the 0 units digits and write the units digit. Add the units digit and multiply by a tens digit and write the product in the tens digit. The tens digit is the same. When multiplying to the hundreds place, add the carry if there is a carry.23 23×25=(2×2)×100+(3+5)×2×10+3×5=575
×25
57 5
. The single digits of the multiplicand and the multiplier are the same, but the sum of the tens digits is different. It is equal to 10
23 23×43=(2×4)×100+(2+4)×3×10+3×3=989
×43
989
. The difference between the multiplicand and the tens digit of the multiplier is 1, and the sum of the single digits is equal to 10
Method: Square difference formula: (A+B) (A—B)=A²—B²
52×48= (50+2) (50—2)=50²—2²=2496
Note: ① The difference between the two numbers is 2, 4 , this method can also be used to multiply two numbers 6, 8 and 10
24×28= (26+2) (26-2)=26²-2²=676-4=672
② This method can also be extended to multi-digit multiplication
592×608=（600—8）（600+8）=600²—8²=360000—64=359936
Multiplication operation of special numbers
72×15=（72÷2）×(15×2)=36×30=1080 15×2→30
366×25=(366÷4) ×(25×4)=91.5×100=9150 25×4→100
612×35=(612÷2)×(35×2)=306×70=21420 35×2→70
214×45=(214÷2) ×(45×2)=107×90=9630 45×2→90
568×125=(568÷8) ×(125×8)=71×1000=71000 125×8→1000
38×15=(38÷2) ×(15×2)=19×30=570
48×25=(48÷4) ×(25×4)=12×100=1200
42×35=(42 ÷2) ×(35×2)=21×70=1470
78×45=(78÷2) ×(45×2)=39×90=3510
856×125=(856÷8) ×(125×8)= 10 seven If there is a carry, add carry)
35 34 41
×52 ×52 ×35
1820 1768 1435
Multiply any three-digit two-digit universal method
Four-step method:
1. Multiply the single digits up and down and write the ones digit;
2. Cross-multiply the single digits and tens digits, add the products (add carry if there is a carry) and write the tens digit;
3. Cross-multiply the single digits and hundreds digits, multiply the tens digits up and down, and then add ( If there is a carry, add the carry)
4. Cross-multiply the tens and hundreds digits and write them to the highest digit.
312 438
x 56 , write the tens place;
3. The ones place and the hundreds place are crossed, multiplied and added, plus the tens place is multiplied by the tens place, and the hundreds place is written;
4. The tens place and the hundreds place are cross-multiplied, the product is added, and the thousands place is written;
5 .Multiply the hundreds place by the hundreds place and write the tens of thousands place.
The bigger the number, the better.
999²=998001 99999999²=9999999800000001
. Multiply several 9 numbers; ; After 9, write 8 to make up one digit; for
8, add the first few 9s, and after 8, add a few 0s; for several 9s, count a few 0s; for
, write a 1 at the end; only write a 1 at the end; that is the final product of the multiplication.
1. Find the complement number;
999-413 (complement number) = 586
999×587 = 586413
2. Cross subtraction and subtraction (one time)
999-544 = 455
999 × 456 = 455544
3. Write the complement after the multiplication ( Seek first If two numbers are complemented, subtract the other number and write the first part. Multiply the complements and write the second part. If the number is wrong, the number is wrong).
998-103=895 2 (the complement of 998)
hundreds digit Multiply the single digit by double and write it in the middle;
multiply the single digit by the single digit and write it in the back.
Multiplication of single numbers
Division of single numbers
2 Multiplication of
1234 direct writing times,
1356987×2=2713974
plus 1 before the big 5;
5 is 0, 6 is 2;
375696587×2=751393174
7 is 4, 8 6s; 47598 × 2 = 95196
9 digits are 8. Remember it; read it before and after calculation and don’t forget it.
The operation when the divisor is 2
formula: Divide by 2 and read the number in half.
48÷2=24 76÷2=38
3 multiplication operation
123 number is written directly as a multiple,
is followed by 34 plus 1,
1346986×3=4040958
is entered by 2 if it is greater than 67,
(recurring decimals must be remembered correctly)
473968×3= 1421904
4 numbers are 2, 5 numbers are 5,
6 numbers are 8, 7 numbers are 1,
8 numbers are 4, 9 numbers are 7.
(don’t forget it after reading it before calculating)
divisor is the operation of 3
formula:
must be divided by 3 To calculate more carefully, 4÷3=1.333
remainder 1 has a cycle of 5÷3=1.666
remainder 1 cycle 333, remainder 2 cycle 666
25÷3=8.333
requires how many decimal places to leave, and remainder 1 needs to be rounded off remainder 2. 29÷3=9.666
4 multiplication operation
1 number 2 is written directly;
is followed by 25, plus 1;
365478×4=1461912
is greater than 50, enter 2;
is greater than 75, enter 3;
28798649×4=115194596
even numbers are each They are all complementary;
's odd numbers each make up 5 odd numbers;
must remember its carry rate.
operation formula for divisor by 4
formula: division by 4 can be integer or remainder,
remainder can be read according to the rate, 5÷4=1.25
remainder 1, which is point 25; 6÷4=1.5
remainder 2, it must be Point 50; 7÷4=1.75
more than 3, which is point 75;
126÷4=31.5
You can know the number without calculation. Multiplication operation of
438÷4=109.5
5
Any number multiplied by 5 is equal to half of it plus 0.
486×5=2430
18×5=(18÷2)×(5×2)=9×10=90
264×5 =1320 368×5=1840
7356×5=36780
The operation when the divisor is 5
Formula: any number divided by 5 is equal to twice the number and then divided by 10 (the dividend is doubled and the decimal point is moved one place to the left).
18÷5=（18×2）÷（5×2）
=36÷10=3.6
368÷5=（368×2）÷（5×2）
=736÷10=73.6
6 multiplication operation
167 number To enter 1; after
, the big 34 will be entered into ;
3768×6=22608
should be entered into 3 if it is greater than 50; after
, the big 67 should be entered into 4;
671589×6=4029534
834 The number should be entered into 5;
should remember the recurring decimal accurately; even numbers Each is its own;
odd numbers are compared with 5; numbers less than 5 are subtracted by 5;
recurring decimals must be remembered correctly.
operation when the divisor is 6
formula:
divides by 6 and there is a remainder, 7÷6=1.166
and the remainder is read as a decimal according to the rate, 8÷6=1.333
and the remainder is 1, decimal 166 cycles;
9÷6=1.5
remainder 2, 33 cycle number;
10÷6=1.666
remainder 3, the decimal point is 5;
11÷6=1.833
remainder 4 decimal 666 cycles;
remainder 5, cycle 833;
requires a certain number of rounding. The multiplication operation of
7
three-digit three-digit ratio
142857---into 1
16758×7=117306
285714—into 2
428571—into 3
365475×7=2558325
571428—into 4
714285— Enter 5
857142—Enter 6
, the divisor is 7. The operation
formula:
integer needs Divide carefully, and the remainder will cycle through six digits.
Remember the multiplication rate accurately, and what is the rate of the remainder cycle;
The remainder 1 is the 142857 cycle
8÷7=1.142857
76÷7=10.857142
The remainder 2 is the last digit of 14; __285714 cycle
9÷7=1.285714
137÷7=19.571428
The remaining 3 is to press the head to the tail; __428571
10÷7=1.428571
225÷7=32.142857
The remaining 4 is to move 57 forward; __571428
11 ÷7=1.571428
more than 5 is the last Press at the beginning; __714285
12÷7=1.714285
and the remaining 6 are moved forward and backward in half. __857142
13÷7=1.857142
First look at the number of decimal places to decide whether to round or round. The multiplication operation of
8
125—into 1
25—into 2 3658×8=29264
375—into 3
5—into 4 47586×8=380688
625—into 5
75—into 6
875—into 7
The operation formula of
is as follows:
8 In addition to the whole number, there is a remainder,
remainder 1, decimal point 125; remainder 1 is .125
9÷8=1.125
remainder 2 decimal is point 25, remainder 2 is .25 10÷8=1.25
remainder 3, decimal point 375; remainder 3 is .375 11÷8=1.375
remainder 4 which is the number of point 5, remainder 4 is .5
12÷8=1.5
remainder 5, decimal point 625; remainder 5 is .625
13÷8=1.625
remainder 6 decimal It is point 75, remainder 6 is .75
14÷8=1.75
remainder 7, decimal point 878; remainder 7 is .875
15÷8=1.875
8. Although the remainder is large, 132÷8=16.5
, it can be divided. The multiplication operation of
9
The front and back ratio between two digits is 5477
. The front is smaller than the back and the number is forward;
365478×9=3289302
. If the front is greater than the back, 1 must be subtracted;
745632×9=6710688
. The digits of each number are complementary;
27159867×9=244438803
counts It will be reduced by 1 at the end.
83951243×9=75556287
The operation when the divisor is 9
formula: divide any number by 9, the remaining number will be repeated.
can't be removed by 9; remainder 1__111 loop
82÷9=9.111
remainder 2__222 is the remainder;
83÷9=9.222
remainder 3__333 remainder 4__444 depends on how many decimals are left; 58÷9=6.444
remainder 5__555 Yu 6__666 Yu 7__777 Yu 8__888 Decide whether to discard or advance.
64÷9=7.111
