① addition
Additive commutative law: A+B = B+A;
Additive associative law: a+b+c = a+(b+c) = (a+b)+c;
② subtraction
A-B =-(B-A)
a-b-c=a-(b+c)
There is a formula for subtraction: parentheses and sign change.
③ multiplication
Multiplicative commutative law: a x b = b x a；;
Law of multiplicative association: a x b x c = a x (b x c); );
Multiplication and distribution law: a x (b c) = a x b a x c;
Calculating the formula of complex number —— A common problem in elementary school mathematics examination questions.
Multiplication and distribution laws are usually used to extract common factors and simplify calculations.
Example 1 calculation: 7.19x1.36+3.13x2.81+19.
Analysis: This problem is a comprehensive application of additive associative law, multiplicative commutative law and multiplicative distributive law.
7. 19x 1.36+3. 13x 2.8 1+ 1.77 x 7. 19
= 7. 19x( 1.36+ 1.77)+3. 13x 2.8 1
= 7. 19x 3. 13+3. 13x 2.8 1
=(7. 19+2.8 1)x 3. 13
= 10x3. 13
=3 1.3
④ Split
A÷b÷c=a÷(b x c)(b, c is not equal to 0);
a x b \c = a \c？ x？ B(c is not equal to 0);
The above formula is the basic relationship to solve four operation problems.
Learn and use it flexibly.
Besides being used, they sometimes have to be used backwards.
Example 2 calculation: 47.9 x 6.6+529 x 0.34；;
Analysis: 6.6+3.4= 10, can you find a way to make a 3.4, plus 3.4 and 6.6?
47.9x6.6+529x0.34
= 47.9 x 6.6+529÷ 10x 10x 0.34
=47.9x6.6+52.9x3.4 (3.4 has been calculated)
=47.9x6.6+(47.9+5)x3.4
= 47.9x6.6+47.9x3.4+5x3.4 (6.6+3.4 is also compiled).
=47.9x(6.6+3.4)+ 17
=496?
Note: In Example 2, we use the law of multiplication and distribution in reverse.
52.9 x 3.4 =(47.9+5)x 3.4 = 47.9 x 3.4+5x 3.4
In addition, a special formula is used.
529 x 0.34 = 529÷ 10x 10x 0.34
To sum up, this formula is:
A x b=a÷c x c x b(c is not equal to 0).