This chapter consists of six parts, namely fractional division of integer divisor, fractional divisor of quotient, cyclic decimal, exploring laws and solving problems with calculator.
The main requirement of this unit is to make students master the calculation method of fractional division. Let the students use the rounding method and combine the actual situation to find the approximate number of quotient by the methods of "one in" and "one out".
Preliminary understanding of cyclic decimal, finite decimal and infinite decimal. Students can explore the calculation law with the help of calculator, and can apply the explored law to the calculation of decimal multiplication and division. Make students understand how to solve the practical problems of simple fractional division and realize the application value of fractional division.
Teaching suggestion of this unit: grasp the connection point between old and new knowledge and build a cognitive bridge for the study of fractional division. The content of this unit is closely related to old knowledge.
The calculation rule of fractional division is based on the quotient invariance law of integer division and the decimal point position movement law. The trial quotient method and division steps of fractional division are basically the same as those of integer division, the only difference is the treatment of decimal point.
The meaning of connection number gives mathematical guidance to help students master the calculation method of fractional division. The focus of fractional division is the treatment of decimal point. Why the decimal point of quotient should be aligned with the decimal point of dividend involves the meaning of number.
When calculating 22.4 divided by 4, divide 22 by 4. The remainder after quotient 5 is one tenth of 2 into 20, and when combined with the tenth 4, it is one tenth of 24. Divided by twenty-four tenths, the quotient is six tenths, so the tenth place of the quotient should be written as 6. When explaining the calculation method of fractional division, we should contact the meaning of numbers to help students understand arithmetic.
Extended data:
The relationship between dividend and quotient: the dividend is enlarged (reduced) by n times, and the quotient is correspondingly enlarged (reduced) by n times. The divisor is expanded (reduced) by n times, and the quotient is correspondingly reduced (expanded) by n times.
Arithmetic of integer division: from the most noisy digits of the dividend, take out the number with the same digit as the divisor (if the number taken out is less than the divisor, take out the number with one digit more than the divisor), and divide by guessing the divisor to get the highest digit of the quotient and the remainder (the remainder may be zero).
Change the remainder to the next unit, add the number on the dividend, and then divide by the divisor (when the divisor is less than this number, the quotient is 0) to get the quotient and the remainder. This continues until all the digits on the dividend are used up to get the final quotient and remainder.