(B) the significance of fractional multiplication
1, the fractional multiplication of integers has the same meaning as integer multiplication, and it is a simple operation to find the sum of several identical addends. "Fraction multiplied by integer" means that the second factor must be an integer, not a fraction.
2. Multiplying a number by a fraction means finding the fraction of a number. "A number multiplied by a fraction" means that the second factor must be a fraction, not an integer. The first factor is anything. )
(2) Decimal multiplication calculation rules
1, the arithmetic of decimal times integer is: numerator times integer, denominator remains unchanged.
(1) In order to make the calculation simple, it can be reduced first and then calculated. (integer and denominator divisor) (2) divisor is to subtract the greatest common factor from the following integer and denominator. (Integer cannot be multiplied by denominator, and the calculation result must be the simplest fraction).
2. The arithmetic of fractional multiplication is: use the product of numerator multiplication as numerator, and the product of denominator multiplication as denominator (numerator multiplied by numerator, denominator multiplied by denominator).
(1) If the fractional multiplication formula contains a band fraction, the band fraction should be converted into a false fraction before calculation.
(2) The method of fractional simplification is to divide the numerator and denominator by their greatest common factor at the same time.
(3) In the process of multiplication, the divisor is to cross out two divisible numbers in the numerator and denominator, and then write the divisor above and below respectively. (After reduction, the numerator and denominator can no longer contain common factors, so the calculated result is the simplest score).
(4) The basic nature of the fraction: the numerator and denominator are multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged.
(3) the relationship between products and elements:
A number (except 0) is multiplied by a number greater than 1, and the product is greater than this number. A×b=c, when b >; In 1, c> answer.
A number (except 0) is multiplied by a number less than 1, and the product is less than this number. A×b=c, when b < 1, c
A number (except 0) is multiplied by a number equal to 1, and the product is equal to this number. A×b=c, and when b= 1, c = a.
When comparing the sizes of factors and products, we should pay attention to the special situation when the factor is 0.
(d) mixed operation of fractional multiplication
1, the mixed operation order of fractional multiplication is the same as that of integers. Multiply first, then divide, and then add and subtract. If there are parentheses, count them first and then count them outside.
2. The law of integer multiplication is also applicable to fractional multiplication; Algorithms can make some calculations simple.
Multiplicative commutative law: a×b=bXa multiplicative associative law: (a×b)Xc=a×(b×c)
Multiplication distribution law: a× (b c) = a× b soil a×c
(V) Meaning of reciprocal: Two numbers whose product is 1 are reciprocal.
1 and reciprocal are two numbers, which are interdependent and cannot exist alone. A number cannot be called reciprocal. (It must be clear who is the reciprocal of who)
2. The only criterion to judge whether two numbers are reciprocal is whether the product of the multiplication of two numbers is "1". For example: a×b= 1, then a and b are reciprocal.
3. Reciprocal method:
① Find the reciprocal of the fraction: exchange the positions of numerator and denominator.
② Find the reciprocal of an integer: 1 of an integer.
③ Find the reciprocal of the score: first turn it into a false score, and then find the reciprocal.
(4) Find the reciprocal of the decimal: first find the number of components, and then find the reciprocal.
There is a lot of content. For the complete printed version, please refer to the first volume of the sixth grade of People's Education Press, Baidu Library: Essentials of Mathematics Final Knowledge.