What are multiplicative distribution law, associative law and commutative law?

1, Multiplication method of substitution: It is a simple law, which is involved in the second volume of the fourth grade mathematics textbook of People's Education Press: in the multiplication operation of two numbers, according to the calculation order from left to right, the two factors are multiplied, and the position of the exchange factor remains unchanged. Specifically, when two numbers are multiplied, the positions of exchange factors and their products remain unchanged. It's called multiplicative commutative law.

2. Distribution law: Multiplying the sum of two numbers by a number is equivalent to multiplying two addends by this number respectively, and then adding the two products, so that the calculation is easier and the result remains unchanged. When the sum of two numbers is multiplied by a number, they can be multiplied by this number separately and then added. This is the so-called law of multiplicative distribution.

3. Associative law: The multiplicative associative law is a kind of multiplication operation and one of many simple methods. Multiply three numbers, the first two numbers are multiplied and then multiplied, or the last two numbers are multiplied and then multiplied, and the product remains the same. This is called the law of multiplication and association.

Calculation method

The common methods of using pencil and paper multiplier need a small number (usually any two numbers between 0 and 9) to store or query the product multiplication table, but a farmer multiplication algorithm does not need it.

Multiplying a number with multiple decimal places is troublesome and error-prone. The universal logarithm was invented to simplify this calculation. The slide rule allows numbers to be quickly multiplied by about three digits of precision. Since the early 20th century, mechanical calculators, such as Marchant, have automatically multiplied as many as 10 digits. Modern electronic computers and calculators greatly reduce the need for manual multiplication.