How to multiply decimal numbers easily and quickly

Quick computation writes.

12137 Simple operation of decimal multiplication.

1. The application of the commutative law of multiplication and the law of union. Tip 1: In the following calculations, some need to split a decimal number into two numbers and multiply, pay attention to the size of the multiplication of the two numbers after splitting should be equal to the original number, especially the number of decimal places.

e.g. == Tip 2: Apply the associative law of multiplication.

The mantra for solving the problem is Conjunction, multiplication, and combinationTip 3: Apply the associative law of multiplicationThe format of the solution is a b c=a (b c) The last step is " "Don't think of it as "+" as such as Group Group 25 Second, the distributive law of multiplication.

of the application. Tip 1: Each factor in group a has a characteristic, which is close to an integer, etc., so that the number can be split into two numbers to add or subtract.

As , but there are such numbers Tip 2: The mantra for applying the multiplicative distributive property solution is: Multiplication, addition, multiplication, subtraction, and distributive Tip 3: Apply the multiplicative distributive property The format for solving the problem is (a+b) c=a c+b cThe last step is "+" Don't take it as "If + is not =1 + 2Prompt 4:

The last step of applying the multiplicative distributive law to solve the problem is sometimes the addition and subtraction of two numbers with relatively large numbers, and the oral arithmetic is prone to errors. Group A Group 3: Compare the difference between the associative and distributive properties of multiplication and distributive in simple operations. The following questions are summarized in two ways.

Fourth, change a change, can be calculated. 48 Let me try: 5. Expand and improve.

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Decimal multiplication calculation method:First, move the decimal point of the factor to the right to expand the decimal to an integer (or directly treat the decimal as an integer without looking at the decimal point); Then the product is calculated according to the calculation method of integer multiplication; If you look at how many decimal places there are in the factor, count the number from the right side of the product and add the decimal point to the point.

Rounding.

If the next digit is greater than or equal to 5 (i.e., ), then advance the previous digit by 1, and then round off all the decimal places that follow this digit; If the last digit is less than or equal to 4 (i.e., ), you can simply round off all the following decimals.

Commutative law of addition: a+b=b+a.

Associative law of addition.

a+b+c=a+(b+c)。

Commutative law of multiplication: a*b=b*a.

The associative law of multiplication.

a*b*c=a*(b*c)。

Multiplicative distributive property.

ab+ac=a(b+c)。

A number can be subtracted by two numbers in a row, and the sum of these two numbers can be subtracted: a-b-c=a-(b+c).

For example, equation:

The vertical type is as follows: <>

First, the decimal is integer first, and then calculated according to the integer multiplication method.

2. 3*2=6, write 6, 0 multiplied by any number is 0, leaving an empty space.

3. The answer is what you want.

What are the simple calculation methods of decimal multiplication, which have the same distribution rate, binding rate, and commutative property as integers.

First, the combination method.

Multiplying a number by two single digits in a row, it can be rewritten in the form of multiplying this number by the product of these two numbers according to the situation, making the calculation easy.

Example 1 Calculation: 19 4 5

When calculating, adding a small parenthesis can make the calculation easy. Because the parentheses are preceded by a multiplier sign, there is no change in the parentheses.

Second, the decomposition method.

Multiply a number by a two-digit number, and decompose the two-digit number into two single-digit multiplication forms according to the situation, and then use this number to multiply two single-digit numbers in a row to make the calculation easy.

Example 2 Calculation: 45 18

Break down 18 into 2 9 and remove the brackets to make the calculation easier.

Third, the method of splitting numbers.

For some problems, if you do the calculation step by step, it is more troublesome, but we can flexibly use the splitting method to make simple calculations according to the characteristics of factors and other numbers.

Example 3 Calculation: 99 99+199

1) When calculating, 199 can be written as 99+100, so as to obtain the first simple algorithm:

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

The laws and properties of integer multiplication are also applicable to decimal multiplication. Applying these laws of operation can make some decimal multiplication calculations easier. Do you know what are the laws and properties of multiplication? Multiplication exchange rate: a b = b a

Multiplicative Binding Rate:

a×b）×c=a×(b×c)

Multiplicative Assignment Rate:

a+b）×c=a×c+b×c

Example: Calculate the following questions in a simple way.

Solution: = Solution: =10+

Solution: = Solution: =20

Summary: Neither (1) nor (2) can directly apply the laws and properties of multiplication to make simple calculations. However, it is easier to decompose a certain factor according to the characteristics of the original question and the characteristics of the data, and then after appropriate transformation.

The two questions (3) and (4) can be simplified by using the exchange rate and the combination rate.

We have learned and mastered multiplying a number by a whole number earlier.

10. A whole hundred ......The number of losses is very easy to calculate. For this reason, the application of the law that "one factor expands several times (except zero) and the other factor shrinks to a fraction of its original size, and their product remains unchanged" can also make some decimal multiplication calculations easier.

Example: (1) Solution: Analysis: The above two problems can be solved by using the law of invariant product. It is also possible to decompose one of the multipliers into a factor, which is the product of the other multiplier as a whole number.

10. Whole hundreds. Namely:

Summary: The key to solving questions (3) and (4) is to put and14 and so on these numbers are unified into one identical number, and the other factor changes according to the law of product invariance, and then it can be simplified according to the law of operation.

1. Multiply decimal numbers by whole numbers.

First, by moving the decimal point, the decimal is expanded into an integer, and then the whole number is calculated by the rules of integer multiplication, and when the result is finally taken, then look at the moved digits, and count a few digits from the last digit of the product from right to left, and point to the decimal point.

2. Multiply decimal by decimal place.

First by moving the decimal point position, the two decimal places are expanded to integers, and then calculated by the integer multiplication rules, and finally when the result is taken, see how many digits have moved in total when the two decimal places are expanded to integers, and count a few places from the right to the left from the last place of the product, and point to the decimal point.

Note: When calculating the result, the 0 at the end of the decimal part should be removed to simplify the decimal; If the number of decimal places is insufficient, use 0 to occupy the place.

The decimal multiplication and division is simply calculated as follows:

Multiplication of decimal numbers by integers meaning:

A simple operation to find the sum of several identical additions; The meaning of multiplying a number by a pure decimal is to find out how many tenths, hundredths, and thousandths of the number are. The decimal multiplication rule, first calculate the product according to the calculation rule of integer multiplication, and then see how many decimal places there are in the factor, count the number of talking sail shirts from the right side of the product, and point the decimal point.

If there aren't enough digits, use 0"Complement. Decimal division, the meaning of decimal division is the same as the meaning of integer division, that is, the product of two factors and one of the factors is known, and the operation of finding the other factor. The divisor is the decimal division calculation rule of an integer, which is first removed according to the law of integer division, and the decimal point of the quotient should be aligned with the decimal point of the dividend.

If there is still a remainder at the end of the dividend, add 0 to the remainder and continue dividing. The divisor is a decimal division calculation The cavity rule first moves the decimal point of the divisor so that it becomes an integer, and the decimal point of the divisor is also moved a few places to the right, and then calculates according to the division rule that the divisor is an integer.

The calculation of decimal division: first move the decimal point of the divisor to make it an integer, the decimal point of the divisor is moved a few places to the right, and the decimal point of the dividend is also moved to the right by the same number of digits. Calculation rules for decimal multiplication:

First calculate the product according to the law of integer multiplication, and then see how many decimal places there are in the factor, count the number of decimal places from the right side of the product, and use 0 to make up if the number is not enough.