1. Make a simple calculation by using the additive combination law.
(A+B)+C = A+(B+C) or a+b+c+d=(a+c)+(b+d)
For example 1, 5.76+ 13.67+4.24+6.33.
=(5.76+4.24)+( 13.67+6.33)
= 10+ 10
=20
Example 2, 37.24+23.79- 17.24
=37.24- 17.24+23.79
=20+23.79
=43.79
Second, use the law of multiplicative association to make simple calculations: this kind of problems often include multiplication between special numbers.
(a×b)×c=a×(b×c)
Multiplication between special numbers:
25×4= 100 125×8= 1000 25×8=200 125×4=500
Example 3,4× 3.78× 0.25
=4×0.25×3.78
= 1×3.78
=3.78
Example 4: 125×246×0.8
= 125×0.8×246
= 100×246
=24600
2.5×0. 125×8×4, etc. If division is also applicable, or division is converted into multiplication to calculate, such as 8.3×67÷8.3÷6.7, etc.
Thirdly, the multiplication and distribution law is used for simple calculation:
(a+b)×c=a×c+ b×c
(a-b)×c=a×c- b×c
Do this kind of problem, don't rush to calculate. First of all, you must analyze the special relationship between numbers. Just be sure to observe carefully and find the trick to do the problem.
Example 5, (2.5+ 12.5) × 40
=2.5×40+ 12.5×40
= 100+500
=600
Example 6, 3.68× 4.79+6.32× 4.79
=(3.68+6.32)×4.79
= 10×4.79
=47.9
Example 7.26.86× 25.66-16.86× 25.66
=(26.86- 16.86) ×25.66
= 10×25.66
=256.6
Example 8, 5.7× 99+5.7
= 5.7×(99+ 1)
=5.7× 100
=570
Multiplicative distribution law is used for simple calculation. When you divide by a number, it is first multiplied by the reciprocal of a number and then distributed.
For example, 2.5×( 100+0.4). It should also be noted that some problems are simplified by using the inverse operation of the distribution law, that is, extracting the common factor, such as 0.93×67+33×0.93.
Fourth, the number is simplified by addition, subtraction, multiplication and division, and then by multiplication and division:
Example 9, 34×9.9
=34×( 10-0. 1)
=34× 10-34×0. 1
=340-3.4
=336.6
For example, 10,57×101.
=57×( 100+ 1)
=57× 100+57× 1
=5757
For example, 1 1, 7.8× 1. 1.
=7.8×( 1+0. 1)
=7.8× 1+7.8×0. 1
=7.8+0.78
=8.58
Example12,25× 32
=25×4×8
= 100×8
=800
For example, 13, 125×0.72.
= 125×8×0.09
= 1000×0.09
=90
Example14,87× 2/85
=(85+2) ×2/85
=85×2/85+2×2/85
=2+4/85
=2 4/85
Five, even the reduction and division
a-b-c=a-(b+c)
a÷b÷c=a÷(b×c)
Example15,56.5-3.7-6.3
=56.5-(3.7+6.3)
=56.5- 10
=46.5
Example16,32.6 ÷ 0.4 ÷ 2.5
=32.6÷(0.4×2.5)
=32.6÷ 1
=32.6
6. Simple calculation that requires deformation: To do this kind of problem, you should observe first, find out the law, and then do simple calculation after deformation.
For example,16,86.7× 0.356+1.33× 3.56.
=8.67×3.56+ 1.33×3.56
=(8.67+ 1.33)×3.56
= 10×3.56
=35.6
For example, 17, 15.6 ÷ 4-5.6× 1/4.
= 15.6× 1/4-5.6× 1/4
=( 15.6-5.6)× 1/4
= 10× 1/4
=2 and 1/2
For example: 18,16/23× 27+16×19/23.
=27/23× 16+ 16× 19/23
= 16×(27/23+ 19/23)
= 16×2
=32
Seven, the number is close to the whole hundred operation. This kind of problem needs the cooperation of disassembly and transformation.
Such as; 302+76 = 300+76+2,298-188 = 300-188-2 and so on.
Eight, carefully observe an operation that is 0 or 1.
Such as: 7.93+2.07×(4.5-4.5), etc.
Generally speaking, the idea of simple operation is: (1) Use the properties and laws of operation; (2) It may disturb the routine calculation order; (3) When disassembling or converting, the size of the number cannot be changed; (4) The connection of each step is handled correctly; (5) Quick calculation is also calculation, that is, turning hard calculation into clever calculation; (6) It can be used.