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Introduction to Mathematics Thinking in Grade Five
Unit 1 Decimal Multiplication

1, decimal times integer: meaning-a simple operation to find the sum of several identical addends.

2. Decimal multiplied by decimal: meaning-that is, what is the fraction of this number.

3. Rule: a number (except 0) is multiplied by a number greater than 1, and the product is greater than the original number; A number (except 0) is multiplied by a number less than 1, and the product is less than the original number.

4. There are generally three methods to find the divisor: (1) rounding method; (2), into law; (3) Tailing method

5. Calculate the amount of money and keep two decimal places, indicating that the calculation is completed. Keep one decimal place, indicating that the angle has been calculated.

6. The order of four decimal operations is the same as that of integers.

7, operation law and nature:

Second unit position

8. To determine the position of an object, you need to use several pairs (the first column is vertical and the second column is horizontal). Two problems can be solved by using number pairs: one is to give a number pair and mark the point where the object is in the coordinate diagram. The second is to give a point in the coordinates, which can be expressed by several pairs.

Unit 3 Decimal Division

10, the meaning of fractional division: by knowing the product of two factors of one and one factor, find the operation of another factor. For example, 0.6÷0.3 means that the product of two known factors is 0.6, one factor is 0.3, and what is the other factor?

1 1. Calculation method of decimal divided by integer: decimal divided by integer, divided by integer to divide. The decimal point of quotient should be aligned with the decimal point of dividend. The integer part is not divided enough, quotient 0, decimal point. If there is a remainder, add 0 and divide it.

12. Calculation method of division with divisor as decimal: first expand the divisor and dividend by the same multiple to make the divisor become an integer, and then calculate according to the rule of fractional division with divisor as integer.

Note: If there are not enough digits in the dividend, make up the dividend with 0 at the end.

13. In practical application, the quotient obtained by fractional division can also be reserved with a certain number of decimal places by "four breaks and five days" as needed to find the approximate number of quotients.

14, the change law of division: ① the essence of quotient invariance: the dividend and divisor expand or shrink the same multiple at the same time (except 0), and the quotient remains unchanged. (2) The divisor is constant, the dividend is enlarged (reduced), and the quotient is enlarged (reduced). (3) The divisor is constant, the divisor decreases, but the quotient expands; The dividend is constant, the divisor is enlarged, but the quotient is reduced.

15, cyclic decimal: the decimal part of a number. Starting from a certain number, one number or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals. Circular part: the decimal part of a circular decimal, which is a number that appears repeatedly in turn. For example, the periodic part of 6.3232. ..................................................................................................................................................................

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