I. Fractional multiplication and fractional division

1.

The significance of fractional multiplication: a simple operation to find the sum of several identical fractions

2.

Significance of fractional division: Know the product of two multipliers and one of them, and find the operation of the other multiplier.

3.

Algorithm of fractional multiplication:

( 1)

Fraction and integer multiplication: numerator and integer multiplication, denominator unchanged.

(2)

Fraction multiplied by fraction: numerator multiplied by numerator, denominator multiplied by denominator, and what can be reduced is reduced first.

4.

Algorithm of fractional division:

(1) A number divided by an integer (except 0) is equal to this number multiplied by the reciprocal of this integer.

(2) A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.

(3)

Dividing by a number (except 0) is equal to multiplying the reciprocal of this number.

5.

If the product of two numbers is 1, then we call one of them the reciprocal of the other. For example, the reciprocal of 1/2 is 2, and the reciprocal of 2 is 1/2. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal.

6.

Practical problems of fractional multiplication and division

(1) Find the fraction of a number and multiply it.

(2) Know the fraction of a number, find this number, divide it, or solve the equation.

Second, the mixed operation of fractions

1.

The order of fractional mixing operation is the same as that of integer mixing operation: multiply first, then divide, and then add and subtract. If there are brackets, the ones inside the brackets are counted first, and then the ones outside the brackets are counted.

2.

Operating rules:

(1) Multiplicative Distribution Law:

(2) Multiplicative associative law:

(3) Multiplicative commutative law:

Using the algorithm, you can simply perform the mixed operation of fractions.

Third, the understanding, surface area, volume and volume of cuboids.

1.

A cuboid has six faces, generally rectangular (in special cases, two opposite faces are square), and the areas of the opposite faces are equal; There are 8 vertices, 12 edges, and 12 edges can be divided into 3 groups: 4 long, 4 wide and 4 high.

2.

A cube has six faces, all of which are squares with equal areas; There are 8 vertices, 12 sides, and each side has the same length.

3.

Cubes are special cuboids. (Length, width and height are equal)

4.

Sum of sides of a cuboid = (length+width+height) ×4

5.

Sum of cube sides = side length × 12

6.

The total area of six faces of a cuboid is called its surface area. The areas of two opposite sides of a cuboid are equal, and the areas of the front and back sides are equal to length × height; Left and right area = width × height; Up and down area = length × width

7.

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

8.

The total area of six faces of a cube is called its surface area, and the areas of all six faces are equal.

9.

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

10.

The size of the space occupied by an object is called its volume. Commonly used unit of volume are: cubic centimeter, cubic decimeter and cubic meter.

1 m3 = 1000 cubic decimeter

1 cubic decimeter = 1000 cubic centimeter

1 m3 = 1000000 cubic centimeters

1 1.

The volume of the object that a container can hold is called the volume of the container. The commonly used unit of volume are liters and milliliters.

1 l = 1 cubic decimeter

1 ml = 1 cm3