The essence of "1" and "simple operation of finding the sum of several identical addends" is the same in the past and today's textbooks. Formally, the new textbook allows "4+4+4+4+4" to be rewritten as "4×5" or written as "5×4". In other words, "5×4" can mean "the sum of four five" or "the sum of five four".

The significance of (1) integer multiplication: a simple operation to find the sum of several identical addenda. For example, 3×4 can be said: What is the sum of four 3s? It can also be expressed as: what is four times 3?

(2) The meaning of multiplying a decimal by an integer is the same as that of multiplying an integer by an integer, which is a simple operation to find the sum of several identical addends. For example: 2.5×6, which indicates the sum of six 2.5 sums; It can also be expressed as 6 times 2.5.

2. Fractional multiplication also eliminates the need to distinguish the multiplicand from the multiplier.

3. Multiplication is not a simple symbol of addition

(1) multiplication principle: if the dependent variable f is in direct proportion to the independent variable X 1, X2, X3...Xn, and each independent variable is qualitatively different, if any independent variable f is missing, it will lose its meaning, then it is multiplication.

(2) addition principle: If the dependent variable F and the independent variable (z 1, z2, z3…,? Zn) is directly proportional to each other, and each independent variable has the same mass. If the dependent variable f still makes sense without any independent variables, it is addition.

Extended data

Fast calculation method of mathematical multiplication

The ten digits of 1. are the product of two digits of 1.

The digits of the multiplier are added to the multiplicand to get the first product, and the digits of the multiplier are multiplied by the digits of the multiplicand to get the last product, which is full of ten and the first one.

15× 17= 255

15 + 7 = 22

5 × 7 = 35

Namely: 220+35=255

Second, the unit bit is the product of two digits of 1

Methods: Multiply ten digits to get the number as the front product, add ten digits and ten digits, then write the number, and finally add 1. Example 1:

5 1 × 3 1 = 158 1

50 × 30 = 1500

50 + 30 = 80

1500 + 80 = 1580

Because 1 × 1 = 1, the last digit must be 1, and the result is followed by 1.

That is 1580+ 1 =? 158 1。

The number "0" is used as a mnemonic when it is not proficient, but it can be used after it is proficient.

Multiply two numbers with the same bit but different bits.

Multiplier plus multiplier digits, sum multiplied by ten-digit integer, the product is the front product, and single digits multiplied by single digits is the back product. ?

43 × 46 = 1978

(43 + 6)× 40 = 1960

3 × 6 = 18

1960+ 18 = 1978

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