The commutative law and associative law of multiplication are used for simple calculation.
Use the nature of subtraction to do simple calculations, and pay attention to the other way around.
Use the nature of division to make simple calculations (divide by a number, multiply by the reciprocal of a number first, and then distribute).
Multiplicative distribution law is used for simple calculation.
Mixed operation (according to the law of mixed operation)
Specific explanation:
First, "rounding"-using the commutative law and associative law of addition to calculate.
Roundness, especially "rounding ten", "rounding hundred" and "rounding thousand", is an important method to quickly calculate addition and subtraction.
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.
associative law of addition
Definition: add the first two numbers, 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)
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
Secondly, simple calculation is made by using the commutative law and associative law of multiplication.
Commutative law of multiplication
Definition: Two factors exchange positions, and the product remains unchanged.
Formula: a× b = b× a.
For example:125×12× 8 =125× 8×12.
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)
Third, simplify the calculation by using the nature of subtraction, and pay attention to the reverse.
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)
Fourth, use the nature of division to make simple calculations (divide by a number, multiply by the reciprocal of a number first, and then distribute).
separate
Definition: One number divides 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.
Fifthly, the multiplication distribution law is used for simple calculation.
Powder companion
Definition: the sum of two numbers multiplied by one number. You can multiply this number separately and then add it up.
Formula: (a+b) × c = a× c+b× c.
For example; 2.5×( 100+0.4)= 2.5× 100+2.5×0.4= 250+ 1= 25 1
6. Mixed operation (according to the law of mixed operation).
Learn to match numbers (0.5 and 2, 0.25 and 4,0.125 and 8)