Use letters to represent numbers.
1. Formulas with letters can represent not only quantitative relations, but also quantities.
2. Formulas containing letters can also express the operation rules and calculation formulas concisely and generally, which is convenient for studying and solving practical problems.
If you know the number represented by each letter in a given formula, you can work out the number represented by this formula.
note:
1. When a number is multiplied by letters, letters and letters, the multiplication sign can also be recorded as "?" , can also be omitted. When omitting the multiplication sign, you should write the number before the letter. For example: a×4 can be written as "A? 4 inches or 4 inches.
2. When "1" is multiplied by any letter, "1" can be omitted. For example, a× 1 is written as "a" instead of "1a".
3. Because letters can represent any number, it is necessary to explain that letters represent numbers in some formulas. For example: 7/a (a ≠ 0).
4. Because letters represent numbers, each letter in the formula does not represent the company name, and the calculation result does not represent the company name, only the company name is written in the answer.
Two. Simple equation
The expression of 1. equation is called equality.
2. An equation with unknowns is called an equation.
3. An equation consists of three parts: the left side of the equation, the right side of the equation and the equal sign. For example: 23+30=53, x+6= 12 are all equations. 7+8, 4x-2, x-7x-7 ~ 9, etc. Not an equation. In the equation x+6= 12, it is an equation because it contains unknowns. An equation is not necessarily an equation, but it must be an equation. Their relationship is shown in the following figure:
4. The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation. For example, if x= 10 makes the left and right sides of equation 4x- 10=30 equal, then x= 10 is the solution of equation 4x- 10=30.
5. The process of solving the equation is called solving the equation.
6. The solution of the equation is a value, and solving the equation is the calculus process of finding the solution of the equation.
7. The main operation of solving simple equations in primary school is the reciprocal relationship of addition, subtraction, multiplication and division.
This relationship is as follows:
(1) One addend = and-another addend
(2) the minuend = difference+reduction
(3) Negative = negative difference
(4) One factor = product ÷ another factor
(5) Dividend = quotient × divisor
Divider = dividend quotient
8. Find the value of the unknown quantity and substitute it into both sides of the original equation (that is, find the value of the formula containing letters). If the left and right sides of the equal sign of the original equation are equal, the value of the unknown is the solution of the original equation.
Test site ratio and ratio
Key points of knowledge
I. Significance and nature of ratio and proportion
1. The meaning of ratio and proportion:
The division of (1) two numbers is also called the comparison of these two numbers.
(2) The two numbers here can be the same quantity or different quantities.
(3) Two expressions with equal ratios are called proportions.
2. Basic nature:
The two items before and after the ratio of (1) are multiplied or divided by the same number at the same time (except zero), and the ratio remains unchanged. In proportion, the product of two internal terms is equal to the product of two external terms.
3. Relationship and difference between ratio and proportion:
(1) Contact:
Ratio and proportion are closely related, and proportion consists of two equal ratios.
(2) the difference:
Ratio means that two numbers get along, which is a form of the relationship between two numbers (quantities). There are two items (item 1 and item 2).
Proportion is an equation, which means that two proportions are equal. There are four projects (two internal projects and two external projects).
Second, the relationship between ratio, fraction and division
Name meaning (relationship) of each part of a name
Than a: b or
a
B represents the term ratio value after dividing the previous term ratio sign by two numbers.
a
B represents the fractional value of a fractional-decimal dividing line.
separate
A÷b stands for the divisor quotient of the operation divisor sign.
The last term, denominator and divisor of the 1. ratio cannot be 0.
2. The meaning of competition is different from "several competitions" in ordinary competitions.
3. Difference and connection between seeking ratio and simplifying ratio
Result in a meaningful and just way
The quotient obtained by dividing the former term by the latter term is a number, which can be an integer, a fraction or a decimal.
Simplify the ratio of two numbers to the simplest integer ratio. 1. The former item and the latter item are multiplied or divided by the same number at the same time (except zero).
2. You can also find the ratio first, and then write it as the simplest ratio.
A ratio
Three. Group proportion and settlement proportion
According to the basic properties of proportion, we can judge whether two proportions can form a proportion or not, and we can also find out the unknown in the proportion, that is, the solution ratio.
1. group proportion: one way to judge whether two proportions can form a proportion is to find the ratio of the two proportions, and if the ratio is equal, a proportion can be formed; Another method is to assume that two ratios have formed a proportion and find the product of the outer term and the product of the inner term. If they are equal, they can form a proportion.
2. Solution ratio: The unknown number in the solution ratio is called the solution ratio.
4. The difference and connection between positive proportion and inverse proportion.
Nominal positive comparison example and negative comparison example
Two related quantities with the same meaning and meaning, one quantity changes, and the other quantity changes accordingly.
The ratio (i.e. quotient) of two corresponding numbers in two quantities with different points must be the product of two corresponding numbers in two quantities.
Relationship x/y = k (definite) x? Y=k (ok)
1. Method for judging whether two quantities are directly proportional, inversely proportional or not;
(1) Find two related quantities.
(2) According to the relationship between two related quantities, the quantitative relationship is listed.
(3) If the ratio (i.e. quotient) of the corresponding two numbers in two quantities is fixed, it is a proportional quantity; If the product is certain, it is an inverse proportional quantity.
Verb (abbreviation for verb) scale
1. The ratio of the distance on the map to the actual distance is called the scale of this map.
Namely: distance on the map: actual distance = scale.
Map distance/actual distance = scale