1. The same number is added or subtracted on both sides of the equation at the same time, and the result is still an equation, which is the nature of the equation. When both sides of an equation are multiplied or divided by the same number that is not equal to 0, the result is still an equation. This is also the nature of the equation.

2. The relationship between the parts of the four operations: one addend = and-another addend = minus+minus = minus-minus one factor = product ÷ dividend of another factor = divisor × quotient divisor = dividend ÷ quotient.

3. The quantity relationship commonly used in solving equations: unit price × quantity = total price × speed × time = distance × working efficiency × working time = total work.

Unit 2:

Characteristic length and surface area volume (volume) unit of volume (unit of volume)

Similarities and differences, define formulas, define formulas.

A cuboid has 6 faces and 8 vertices. The opposite sides of 12 sides are exactly the same, and the length of the opposite sides is equal. Each face is rectangular, or two opposite faces may be square, and the other four faces are exactly the same length.

Square. The total length of 12 sides of a cuboid or cube is called the side length of a cuboid or cube.

And ... (Length+Width+Height) ×4 The total area of six faces of a cuboid or cube is called the face of a cuboid or cube.

Products. (length× width+length× height+width× height) ×2

S=2(ab+ah+bh) The size of the space occupied by an object is called the volume of the object.

The volume of an object that a container can hold is called the volume of this container. Length× width× height

V=abh

or

Bottom area × height

V=sh

Commonly used unit of volume has cubic centimeters, cubic decimeters and cubic meters. The propulsion rate between two adjacent unit of volume is 1000.

In order to measure the volume of liquid, liters and milliliters are often used as units of measurement.

A little.

Six sides of a cube are exactly the same square, and the lengths of 12 sides are all equal. Side length × 12 side length× side length× 6

S=6a2 side length × side length ×

edge

V=a3

The bottom area of a cuboid = the bottom area of a long × wide cube = the side length × the lateral area of a cuboid with a side length = the perimeter of the bottom surface × the height.

Length unit conversion:1km =1000m1m =10mm1mm =10cm1cm = 60.

Area unit conversion: 1 km2 = 100 hectares 1 hectare = 10000 square meters 1 square meter = 1 square decimeter =/kloc-0.

Unit of volume conversion: 1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter 1 cubic decimeter = 1 liter 1 cubic centimeter =/kloc-0.

Unit 3:

1, find out what the score is, and calculate by multiplication; Finding the fraction of a number also requires multiplication.

2. Multiply a fraction with an integer, and use the product of the multiplication of the numerator of the fraction and the integer as the numerator, with the denominator unchanged; Integer and fraction are multiplied, and the numerator is the molecular product of integer and fraction, and the denominator remains unchanged; Score times score,

Use the product of molecular multiplication as the numerator and the product of denominator multiplication as the denominator. Multiplication of three numbers can divide the numerator and denominator of all fractions first, then multiply the numerator and numerator after division, and multiply the denominator and denominator.

3. Multiply a number with a number less than 1, and the product is less than the original number; Multiply a number by a number greater than 1, and the product is greater than the original number.

4. Two numbers whose product is 1 are reciprocal. To ask for the reciprocal of a number, just exchange its numerator and denominator. The reciprocal of the true score is a false score greater than 1; The reciprocal of a false score greater than 1 is a true score; The reciprocal of an integer is a fraction; The reciprocal of a fraction is an integer. The reciprocal of 1 is 1. Because 0 is multiplied by any number to get 0, there is no reciprocal of 0.

5. The denominator is two adjacent non-zero natural numbers and the numerator is two fractions of 1. Their difference is equal to their product, for example:-=× =

Unit 4:

1, divide a number into several parts on average, and calculate how much each part is by division. Knowing what the fraction of a number is, we can find the number by equation or division.

2. The significance of fractional division is the same as integer division, that is, knowing the product of two factors and one of them, and finding the operation of the other factor.

3. Dividing a fraction by an integer (except 0) is equal to multiplying this fraction by the reciprocal of this integer. The number A divided by the number B (except 0) is equal to the reciprocal of the number A divided by the number B. When a number is divided by a number greater than 1, the quotient is less than the dividend; When a number is divided by a number less than 1, the quotient is greater than the dividend; The mixed operation of fractional continuous division or fractional multiplication and division can be converted into fractional continuous multiplication first, and then calculated according to the calculation method of fractional continuous multiplication.

4. To solve the practical problem about the score, we should first look at who compares the score in the problem with whom, and what is the unit "1" when comparing, find the score of the unit "1" and calculate it by multiplication. Know what fraction the unit "1" is, and find the series equation of the unit "1" or solve it by division.

Unit 5:

1, ":"is the comparison symbol, the number before the comparison symbol is called the preceding item of the comparison symbol, and the number after the comparison symbol is called the subsequent item of the comparison symbol. The ratio of two numbers represents the division of two numbers, and the quotient obtained by dividing the former part of the ratio by the latter part is called the ratio.

2. The front part of the ratio is equivalent to the dividend in division and the numerator in the fraction; The latter term of the ratio is equivalent to the divisor in division and the denominator in fraction; The comparison number is equivalent to the division number in division and the fractional line in fraction; The ratio is equivalent to the quotient in division and the decimal value in fraction. The divisor in division cannot be 0, the denominator in fraction cannot be 0, and the later term of ratio cannot be 0.

3. Before and after the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged. This is the basic nature of the ratio. By applying the basic properties of ratios, some ratios can be converted into the simplest integer ratios.

4. Simplify the integer ratio and divide the front and rear terms of the ratio by its greatest common factor; Simplify the fraction ratio and multiply the front and rear terms by the least common multiple of the denominator of the front and rear terms at the same time; Simplify decimal ratio, first convert it into integer ratio multiplication, and then simplify it by simplifying integer ratio. The ratio of gold to gold is about 0.618; The ratio of the circumference to the diameter of a circle is π.

5. In the same place, measure bamboo poles with the same length at the same time, and the shadow length of each bamboo pole is equal; In the same place, measuring different bamboo poles at the same time, the ratio of height to shadow length is equal;

Unit 6:

1 and fractional elementary arithmetic operate in the same order as integer elementary arithmetic. Integer arithmetic also applies to arithmetic.

2. Using multiplication and division: a×b+a×c=a×(b+c) and subtraction: can make the calculation simple.

Unit 7: The problem-solving strategies in this semester include substitution method and hypothesis method. The relationship between the two unknowns is multiple: after replacement, the quantity changes and the total amount remains unchanged; When two unknown quantities are different, the quantity remains unchanged after replacement, but the total quantity will change. If you replace the expensive ones with the cheap ones, the total price will drop, and if you replace the cheap ones with Cheng Gui, the total price will rise.

Unit 8: How likely is it to touch an object? It depends on how much part of the whole the object touches.

Unit 9:

1, which means that one number is a percentage of another number, is called percentage. Percentage is also called percentage or percentage. Percent only represents the multiple relationship between two quantities, not the specific quantity.

2. Decimals become percentages, as long as the decimal point is moved two places to the right, and hundreds of semicolons are added (if the digits are not enough, fill in 0); To convert percentages into decimals, just remove the percent sign and move the decimal point two places to the left. To turn a fraction into a percentage, you usually turn a fraction into a decimal (if there are infinite decimal places or many decimal places, you usually keep three), and then turn the decimal into a percentage; Percentages are divided into numbers. First, rewrite the fraction with the letter 100, and then divide the divisor into the simplest fractions.

3. Germination rate = number of germinated seeds ÷ total attendance rate of experimental seeds = attendance rate ÷ actual population survival rate = number of surviving plants ÷ total plant qualification rate = qualified number ÷ total production.