The first unit is abbreviated.

Unit 2 Cuboid and Cube

1. The line where two faces intersect is called an edge, and the point where three edges intersect is called a vertex.

2. The lengths of three sides of a cuboid intersecting at the same vertex are called its length, width and height respectively.

3. Features of a cuboid: faces-there are six faces, all rectangular (in special cases, two opposite faces are square), and the opposite faces are exactly the same; Side-There are 12 sides, and the opposite sides are equal in length; Vertex-There are eight vertices.

4, the characteristics of the cube: face-there are six faces, all square, all the faces are exactly the same; Edge-There are 12 edges, all of which are equal in length; Vertex-There are eight vertices.

5. Cube is also a special cuboid.

6. Unfold a cuboid or cube carton and cut at least 7 sides.

7. The total area of six faces of a cuboid (or cube) is called its surface area.

8. The surface area of a cuboid = (length× width+width× height+height× length) ×2.

Surface area of cube = side length × side length ×6.

9. The size of the space occupied by an object is called its volume.

10, the volume of the object that a container can hold is called the volume of this container.

1 1, commonly used unit of volume has cubic centimeters, cubic decimeters and cubic meters. 1 m3 = 1000 cubic decimeter, 1 cubic decimeter = 1000 cubic centimeter.

12, measuring the volume of liquid, usually in liters and milliliters. 1 cubic decimeter = 1 liter, 1 cubic centimeter = 1 ml, 1 liter = 1000 ml.

13, cuboid volume = length× width× height V =abh.

14, volume of cube = side length × side length× side length v = a× a× a.

15, cuboid (or cube) volume = bottom area × height = cross section × length V=Sh

16、 1 = 1 2 =8 3 =27 4 =64 5 = 125 6 =2 16

7 =343 8 =5 12 9 =729 10 = 1000

17, the propulsion rate of every two adjacent length units (except kilometers) is 10, the propulsion rate between every two adjacent area units is 100, and the propulsion rate between every two adjacent unit of volume is 1000.

18. When the side length of a cube is expanded by n times, the surface area will be expanded by n times and the volume will be expanded by n times.

Unit 3 Fractional Multiplication

1, 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.

2. Multiplying a number with a fraction is to find a fraction of this number, and finding a fraction of a number is calculated by multiplication.

3. Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.

4. Two numbers whose product is 1 are reciprocal.

5. The reciprocal of 1 is1,and 0 has no reciprocal.

6. The product of a number multiplied by a true fraction (a number less than 1) is less than the original number; The product of a number multiplied by a false fraction greater than 1 (a number greater than 1) is greater than the original number.

7. The reciprocal of true score is false score, which is greater than1; The reciprocal of a false score is the true score or 1, less than or equal to 1.

Unit 4 Fractional Division

Comparison quantity = quantity of unit "1" × score;

Quantity of unit "1" = comparative quantity ÷ corresponding score;

Score = Comparison Quantity ÷ Quantity in "1"

3. The number A divided by the number B (except 0) is equal to the number A multiplied by the reciprocal of the number B (the sign becomes reciprocal).

4. A number divided by more than 1 will be less than the original number, and a number divided by less than 1 will be greater than the original number.

Unit 5 Cognitive Ratio

1 and the division of two numbers is also called the ratio of these two numbers.

2. The number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison.

3. The front part of the ratio is equivalent to the numerator of the dividend and fraction of the division formula; The comparison symbol is equivalent to divisor and fractional line: the latter term of ratio is equivalent to the denominator of divisor and fraction of division; The ratio is equivalent to the quotient of division and the value of fraction.

4. The ratio of two numbers can be connected by comparison symbols or written as a fraction.

5. The first term and the last term of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged, which is the basic property of the ratio.

Unit 8 Possibility

Probability = the number of winning situations divided by all possible situations.

Nine percent of cognition

1, indicating that a number is a percentage of another number is called a percentage, and a percentage is also called a percentage or a percentage.

2. Fractions can represent fractions and quantities, but percentages can only represent fractions but not quantities, so percentages cannot be related to units.

3. We can't say that the fraction whose denominator is 100 is called percentage, because it may be a fraction representing quantity.

4. Convert decimals into percentages: first move the decimal point of decimals two places to the right, and then add "%". Decimal percentage: remove "%"first, and then move the decimal point to the left by two places.

5. Convert the score into a percentage. When it is not used up, divide it to the fourth place after the decimal point, keep three places after the decimal point and then change it into a percentage. Percent component number is divided into fractions of 100, and then simplified to the simplest fraction.