(1) Sum, Difference, Multiplication and Division.
In this issue, words such as "more, less, larger, smaller, score" or "increase, decrease, shrink" are often used to reflect the reciprocal relationship. When examining questions, we should grasp the key words, determine the standard quantity and comparison quantity, and pay attention to the nuances of each word.
(2) Equal product deformation problem.
The key to this kind of problem lies in "equal product", which is where the equal relationship lies. You must master the area and volume formulas of common geometric figures.
(3) Distribution problem.
Find the equivalence relationship from the adjusted quantity relationship, which is usually the relationship of "sum, difference, times and points". Pay attention to the direction and number of deployment objects.
(4) Travel problems.
To master the basic relationship in the trip: distance = speed × time.
When encountering a problem (walking in the opposite direction), the equality relationship of this kind of problem is: the sum of the distances each person walks is equal to the total distance, or the time two people walk at the same time is equal to the equality relationship.
The equivalence relation of chasing problem (walking in the same direction) is: the distance difference between two people is equal to the distance of catching up or the equivalence relation is the time of catching up.
Meeting and chasing on the circular runway: the equivalent relationship of walking in the same place in the opposite direction is that the sum of the distances traveled by two people is equal to the distance of a circle; The equivalent relationship of walking in the same place and the same direction is that the distance difference between two people is equal to the distance of a circle.
Navigation problem: the relationship between the combined speeds of relative motion is: speed along the river = speed in still water+speed of water flow; Velocity = still water velocity-water velocity.
The travel problem can help to understand the meaning of the problem by drawing a schematic diagram, and pay attention to the time and place when two people travel.
(5) Engineering problems.
Its basic quantitative relationship: total work = working efficiency × working time; Joint operation efficiency = sum of individual operation efficiency. When the total workload is not given, the permanent total workload is "1", and a list or drawing can be used to help understand the meaning of the problem.
(6) solution preparation.
Its basic quantitative relationship is: solution mass = solute mass+solvent mass; Solute mass = mass fraction of solute contained in solution. This kind of problem often finds the equivalent relationship according to the solute quality or solvent quality before and after preparation, and the tabular method can be used to help understand the meaning of the problem.
(7) profit rate.
Its quantitative relationship is: commodity profit = commodity price-commodity purchase price; Commodity profit rate = commodity profit/commodity purchase price × 100%. Pay attention to several discounts, which are a few percent of the original price.
(8) bank savings.
Its quantitative relationship is: interest = principal × interest rate × deposit term; Principal and interest = principal+interest, interest tax = interest × interest tax rate. Note that interest rates include daily interest rate, monthly interest rate and annual interest rate, with annual interest rate = monthly interest rate × 12 = daily interest rate ×365.
(9) Numbers.
To correctly distinguish the two concepts of "number" and "number", this kind of problems usually adopt indirect methods, and the common problem-solving thinking analysis is to grasp the relationship between numbers or between new numbers and original numbers and find the equivalent relationship. The premise of the column equation must also correctly express the algebraic expression of multi-digits. A multi-digit is the sum of the products of each digit and its counting unit.
(10) The basic quantitative relationship of the age problem: the age difference will not change.
This kind of problem mainly requires equivalence: seize the growth of age, one year old, everyone is equal.