Tisch
* * Knowledge point ** 1, an object, a unit of measurement or a whole composed of many objects can be expressed by natural number 1, which we usually call the unit "1". Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction. The number representing one of them is called a fractional unit. What is the denominator of a fraction? Its decimal unit is a fraction.
2. The larger the denominator, the smaller the decimal unit, and the decimal unit is 1/2.
3. Give an example to illustrate the meaning of a score: 3/7 means that the unit "1" is divided into 7 parts on average, that is, 3 parts. That is to say, three parts are divided into seven parts on average, which is 1 part. 3/7 ton means 1 ton is divided into 7 parts, which means 3 parts. It also means that 3 tons is divided into 7 parts, which is 1 part.
4, 4 meters of 1/5 is 4/5 of the length of 1 meter.
5. Fractions with numerator smaller than denominator are called true fractions; Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions.
6. The true score is less than 1. False score is greater than or equal to 1. True scores are always less than false scores.
7. If the number of boys is 3/4 of the number of girls, the number of girls is 4/3 of the number of boys.
8. Relationship between fraction and division: dividend is equivalent to numerator of fraction, and divisor is equivalent to denominator of fraction. Divider ÷ Divider = Divider If A stands for dividend and B stands for divisor, it can be written as a÷b=b(a)(b≠0).
9. A false fraction that can be converted into an integer whose numerator is a multiple of the denominator. On the contrary, the numerator is a false fraction of the denominator multiple and can be turned into an integer. (numerator divided by denominator)
10, where the numerator is not a false fraction of the denominator multiple, can be written as a number consisting of an integer and a true fraction, usually called a fraction. Getting points is another form of false points. For example, 4/3 can be regarded as the composite number of 3/3 (i.e. 1) and 1/3, which is read as one and a third. Band scores are all greater than real scores, and they are all greater than 1.
1 1, how to convert a fraction into a decimal: divide the numerator of the fraction by the denominator.
12. Method of dividing decimals into numbers: if it is a decimal place, write it as a few tenths, if it is a decimal place, write it as a few percent, if it is a decimal place, write it as a few thousandths.
13, the method of converting a false fraction into an integer or a fraction: the numerator is divided by the denominator, and if the numerator is a multiple of the denominator, it can be converted into an integer; If the numerator is not a multiple of the denominator, fractional division can be carried out, and the quotient obtained by division and the fraction are used as the integer part, and the remainder is used as the numerator of the decimal part, and the denominator remains unchanged. 14, the method of changing a fraction into a false fraction: the integer is multiplied by the denominator, and the numerator is used as the numerator of the false fraction, and the denominator remains unchanged.
15, the method of turning an integer that is not 0 into a false fraction: use the product of the integer multiplied by the denominator as the numerator.
16, more than 7(3), less than 7(5) scores are countless; The decimal unit is 7( 1), only 7(4).
17, application problems of score comparison: fast working efficiency and less working time.
18. Find the fraction of one number occupied by another number and calculate it by the division formula.
* * Exercise questions * *
fill (up) a vacancy
1. Fold a rectangular piece of paper in half, and then fold it again. This paper is divided into () parts, and each part is its (). Writing: ().
2. Divide a cake into 5 pieces on average, of which 3 pieces are () points (). Writing: (), whose numerator is () and denominator is ().
Second, judge right or wrong.
(1) A circle is divided into four parts, and each part is its 1/4. ( )
(2)3/7+3/7=6/ 14。 ( )
* * Reference answer * *
fill (up) a vacancy
1. Fold a rectangular piece of paper in half, and then fold it again. This paper is divided into (4) parts, and each part is its (quarter). Writing: (1/4).
Divide a cake into five pieces, three of which are (5) and (3) respectively. Write: (3/5), whose numerator is (3) and denominator is (5).
Second, judge right or wrong.
(1) A circle is divided into four parts, and each part is its 1/4. ( ×)
(2)3/7+3/7=6/ 14。 ( ×)
extreme
* * Knowledge points ** 1. Definition of area The size of an object's surface or plane figure is called its area.
2. Area unit:
① A square with a side length of 1 cm and an area of1cm 2 can also be written as1cm 2 (or cm 2). Such as erasers, stamps, coins, etc.
② A square with a side length of 1 decimeter and an area of 1 square decimeter can also be written as 1 decimeter 2 (or dm 2). Such as textbook surface, book desktop, etc.
③ A square with a side length of 1m and an area of 1m2 can also be written as 1m2 (or m2). Such as blackboard surface, classroom floor, flower bed, playground, etc.
3, commonly used area unit:
Square meter m 2, square decimeter dm 2, square centimeter cm 2
1 m2 = 100 dm2 = 10000 cm2、 1dm 2= 100 cm2
The forward speed between two adjacent area units is 100.
4. Common length units: meter, decimeter and centimeter.
The propulsion rate between two adjacent length units is 10.
5 Length units and area units cannot compare sizes.
6 units reciprocity: great multiplication and small multiplication are good, and small multiplication and big division are good.
3 square meters =(2 7 square decimeters = () square centimeters.
5 square meters = () square centimeters 900 square meters = () square meters
8000 square centimeters = () Deutsche Mark 2 30000 square centimeters = () square meters.
2m 230 dm2=( ) dm2 4dm 260 cm2=( ) cm2
7 Calculation formula:
Square perimeter = side length × 4; Side length = perimeter ÷4 square area = side length × side length 8
Square, the side length is expanded n times, the perimeter is expanded n times, and the area is expanded n times.
Square, the side length increases by n, the perimeter increases by n ×4, and the area increases by n× n.
* * Exercise questions * *
(1) square area = () × ()
The side length of a square is 8 decimeters, and its area is ().
* * Reference answer * *
Area of (1) square = (side length) × (side length)
The side length of a square is 8 decimeters and the area is (64 square decimeters).
Tisso
* * Knowledge points ** (1) Combined with life situations, we can initially perceive the characteristics of parallelograms and distinguish which graphics are parallelograms.
(2) You can draw a parallelogram on a bitmap or grid paper, or circle a parallelogram on the nail board.
(3) The connection and difference between the penetrating parallelogram and the rectangle.
* * Exercise questions * *
1. The base of the parallelogram is12cm, the area is156cm2, and the height is () cm.
2. A parallelogram steel plate with a base of 1.5 m and a height of 1.2 m. If the steel plate weighs 23.5 kg per square meter, the steel plate weighs () kg.
3. The area of an equilateral parallelogram is (). The perimeter of the parallelogram is 46 cm, the length of one side is 14 cm, and the lengths of the other three sides are (), () and () respectively.
* * Reference answer * *
1. The base of the parallelogram is 12cm, the area is 156cm and the height is (13cm).
2. parallelogram steel plate, bottom 1.5m and height1.2m. If the steel plate weighs 23.5kg per square meter, the steel plate weighs (42.3) kg.
3. The areas of parallelogram with equal base and equal height are all (equal). The perimeter of the parallelogram is 46 cm, the length of one side is 14 cm, and the lengths of the other three sides are (14), (9) and (9).