Summarize and sort out the main points of knowledge
Unit 1 Fractional Multiplication
Importance of (1) fractional multiplication:
1, the meaning of fractional multiplication by integer: (multiplication with integer) is a simple operation to find the sum of several identical addends.
"Fraction times 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) Calculation rules of fractional multiplication:
1, the arithmetic of decimal times integer is: numerator times integer, denominator remains unchanged.
2. The arithmetic of fractional multiplication is: use the product of molecular multiplication as numerator and the product of denominator multiplication as denominator.
◆ In order to simplify the calculation, what can be reduced should be reduced first and then calculated.
3. The basic nature of the fraction: the numerator and denominator are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged.
(3) the relationship between products and elements:
1, a number (except 0) times a number greater than 1, and the product is greater than this number. A×b=c, when b >; At 1, c>a.
2. 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
3. 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) fractional mixing operation
1, the order of decimal operation: (same integer), multiply first, divide later, add and subtract, the first number in brackets.
2. The law of integer multiplication is also applicable to fractional multiplication; Algorithms can make some calculations simple.
Multiplicative commutative law: a×b=b×a
Law of multiplicative association: (a×b)×c=a×(b×c)
Multiplicative distribution law: a× (b c) = a× b a× c