(1) "Coincidence calculation"-calculation by using the commutative law and associative law of addition. Students are required to be good at observing topics and have a sense of integration.
Rounding notes, especially "rounding ten", "rounding one hundred" and "rounding one thousand", are important methods for fast calculation of addition and subtraction.
1, additive commutative law
Definition: the sum of the positions of two numbers is constant,
Formula: A+B =B+A,
For example: 6+ 18+4=6+4+ 18.
2. Additive associative law
Definition: Add the first two numbers first, or add the last two numbers first, and the sum is unchanged.
Formula: (A+B)+C=A+(B+C),
For example: (6+ 18)+2=6+( 18+2)
3. Expansion-rounding
For example:1.999+19.99+199.9+1999.
=2+20+200+2000-0.00 1-0.0 1-0. 1- 1
=2222- 1. 1 1 1
=2220.889
The so-called rounding in the commentary is to combine two or three numbers and add them up, which just adds up to a whole hundred. For example, "1.999" in this question is exactly 0.00 1 of "2", so we can read it as "2" to calculate it first. However, we must remember that what has just been "added" should be "subtracted". "Less" means "more"!
(2) Simple calculation is made by using the commutative law and associative law of multiplication.
1, multiplication commutation law
Definition: Two factors exchange positions, and the product remains unchanged.
Formula: a× b = b× a.
For example:125×12× 8 =125× 8×12.
2. Multiplicative associative law
Definition: multiply the first two factors, or multiply the last two factors first, and the product remains unchanged.
Formula: A×B×C=A×(B×C),
For example: 30×25×4=30×(25×4)
(3) Use the nature of subtraction for simple calculation, and pay attention to reverse calculation.
1, subtraction
Definition: One number subtracts two numbers continuously, and the last two numbers can be added first and then subtracted.
Formula: A-B-C = A-(B+C). Pay attention to the application of A-(B+C) = A-B-C.
For example: 20-8-2 = 20-(8+2)
(4) Use the nature of division for simple calculation (divide by a number, multiply by the reciprocal of a number first, and then distribute).
1, division
Definition: A number is divided by two numbers continuously. You can multiply the last two numbers first and then divide by them.
Formula: a \b \c = a \u( b×C),
For example: 20 ÷ 8 ÷1.25 = 20 ÷ (8×1.25)
Definition: Divider is divided by dividend, and dividend is divided into two numbers (the product of these two numbers must be dividend).
For example: 64 ÷ 16=64÷8÷2=8÷2=4.
(5) Simple calculation is made by using the law of multiplication and distribution.
Powder companion
Definition: the sum of two numbers multiplied by one number. You can multiply this number separately and then add it up.