A number multiplied by two one-digit numbers can be rewritten as the product of this number multiplied by these two numbers according to the situation, which makes the calculation simple.

Example:

Calculation: 19×4×5

19×4×5

= 19×(4×5)

= 19×20

=380

When calculating, adding a bracket can make the calculation simple. Because there is a multiplication symbol in front of the brackets, there is no symbol in the brackets.

Second, the decomposition method

A number multiplied by a two-digit number can be decomposed into two one-digit multiplication forms according to the situation, and then this number is multiplied by two one-digit numbers continuously, so the calculation is simple.

Example:

Calculation: 45× 18

48× 18

=45×(2×9)

=45×2×9

=90×9

=8 10

Decompose 18 into 2×9 form, and then remove the brackets to make the calculation simple.

Third, the split number method

Some problems, if calculated step by step, will be more troublesome. According to the characteristics of factors and other numbers, we can flexibly use factorization to make simple calculations.

Example:

Calculation: 99× 99+ 199

(1) In the calculation, 199 can be written as 99+ 100, from which the first simple algorithm can be obtained:

99×99+ 199

=99×99+99+ 100

=99×(99+ 1)+ 100

=99× 100+ 100

= 10000

(2) Write 99 as 100- 1 and 199 as100+(100-1), and you can get the second simple algorithm:

99×99+ 199

=( 100- 1)×99+( 100- 1)+ 100

=( 100- 1)×(99+ 1)+ 100

=( 100- 1)× 100+ 100

= 10000

Fourth, the number change method

Some topics can be converted into some numbers according to the situation, creating conditions to simplify the complex.

Example:

Calculation: 25×5×48

25×5×48

=25×5×4× 12

=(25×4)×(5× 12)

= 100×60

=6000

Convert 48 into 4× 12, which makes the calculation simple.

Law of mathematical multiplication operation

The multiplication of integers meets the following requirements: commutative law, associative law,? Law of distribution, law of elimination.

With the development of mathematics, the object of operation has developed from integer to more general group.

Intra-group multiplication is no longer needed to satisfy the commutative law. The most famous noncommutative example is the quaternion group discovered by Hamilton. But the law of association is still satisfied.

1. Multiplicative commutative law: ab=ba. Note: letters are multiplied by letters, and the multiplication sign can be written without writing. "

2. Multiplicative associative law: (ab)c=a(bc)

3. Multiplication distribution law: (a+b)c=ac+bc