Mathematics: Basic concept: Travel problem is to study the movement of objects, and it studies the relationship between the speed, time and travel of objects. Basic formula: distance = speed × time; Distance ÷ time = speed; Distance ÷ Speed = Time Key Problem: Determine the position during the trip. Meeting problem: speed sum × meeting time = meeting distance (please write other formulas) Chasing problem: Chasing time = distance difference ÷ speed difference (write other formulas) Running problem: Smooth sailing = (ship speed+water speed) × smooth sailing time = (ship speed-water speed) degrees+water speed) ÷2 Water speed = (water speed-water speed) Bridge crossing problem: the key is to determine the moving distance of the object, refer to the above formula. For reference only: sum difference problem formula (sum+difference) ÷2= larger number; (sum and difference) ÷2= smaller number. Sum and the formula of multiple problem sum ÷ (multiple+1)= a multiple; A multiple x multiple = another number, or sum-a multiple = another number. The formula of differential multiple problem is differential ÷ (multiple-1)= smaller number; Smaller number × multiple = larger number, or smaller number+difference = larger number. Average problem formula total quantity ÷ total number of copies = average. General travel problem formula average speed × time = distance; Distance/time = average speed; Distance-average speed = time. The formula of reverse travel problem can be divided into "encounter problem" (two people start from two places and walk in opposite directions) and "separation problem" (two people walk with their backs to each other). These two problems can be solved by the following formula: (speed sum) × meeting (departure) time = meeting (departure) distance; Meet (leave) distance ÷ (speed sum) = meet (leave) time; Meet (leave) distance-meet (leave) time = speed and. The formula of the same direction travel problem is chase (pull) distance ÷ (speed difference) = chase (pull) time; Catch up (pull away) the distance; Catch-up (pull-away) time = speed difference; (speed difference) × catching (pulling) time = catching (pulling) distance. Train crossing formula (bridge length+conductor) ÷ speed = crossing time; (Bridge length+conductor) ÷ Crossing time = speed; Speed × crossing time = sum of bridge and vehicle length. The general formula of navigation problem (1): still water speed (ship speed)+current speed (water speed) = downstream speed; Ship speed-water speed = water flow speed; (downstream speed+upstream speed) ÷2= ship speed; (downstream speed-upstream speed) ÷2= water flow speed. (2) Formula for two ships sailing in opposite directions: downstream speed of ship A+countercurrent speed of ship B = still water speed of ship A+still water speed of ship B (3) Formula for two ships sailing in the same direction: still water speed of rear (front) ship-still water speed of front (rear) ship = speed for narrowing (expanding) the distance between two ships. (Find out the speed of narrowing or widening the distance between the two ships, and then solve it according to the relevant formula above). For reference only: engineering problem formula (1) General formula: efficiency × working hours = total workload; Total workload ÷ working time = working efficiency; Total amount of work ÷ efficiency = working hours. (2) Assuming that the total workload is "1", the formula for solving engineering problems is: 1÷ working time = the fraction of the total workload completed in unit time; 1What is the score that can be completed per unit time = working time. (Note: If the hypothetical method is used to solve the engineering problem, you can arbitrarily assume that the total workload is 2, 3, 4, 5 ... Especially if the total workload is the least common multiple of several working hours, the fractional engineering problem can be transformed into a relatively simple integer engineering problem, and the calculation will become simpler. ) profit and loss problem's formula (1) has a surplus once and a deficit once. The formula can be used: (surplus+deficit) ÷ (the difference between two distributions per person) = number of people. For example, "children divide peaches, each person 10, 9 less, and 8 more 7s per person." Q: How many children and peaches are there? "Solution (7+9) ÷ (10-8) =16 ÷ 2 = 8 (a) .............................................................................................................., for example," Soldiers carry bullets for marching training, and each person carries 45 rounds, up to 680 rounds; "If everyone carries 50 bullets, there will be 200 more. Q: How many soldiers are there? How many bullets are there? " Solution (680-200)÷(50-45)=480÷5 =96 (person) 45×96+680=5000 (hair) or 50×96+200=5000 (hair) (the answer is abbreviated) (3) If each person sends 8 copies, there are still 8 copies left. How many students and books are there? "Solution (90-8) ÷ (10-8) = 82 ÷ 2 = 41(human) 10×4 1-90=320 (this) (omitted). (Example omitted) (5) One has more than one (remaining) and one has just finished. The formula can be used: surplus ÷ (the difference between two distributions per person) = number of people. (For example, the formula of chicken-rabbit problem (1) Given the total number of heads and feet, find the number of chickens and rabbits: (total number of feet-number of feet per chicken × total number of heads) ÷ (number of feet per rabbit-number of feet per chicken) = number of rabbits; Total number of rabbits = number of chickens. Or (number of feet per rabbit × total head-total feet) ÷ (number of feet per rabbit-number of feet per chicken) = number of chickens; Total number of chickens = rabbits. For example, "Thirty-six chickens and rabbits, enough 100. How many chickens and rabbits are there? "Solution1(100-2× 36) ÷ (4-2) =14 (only applicable to) 36- 14=22 (only applicable to chickens). Solution 2 (4×36- 100)÷(4-2)=22 (only) ............................................................................................................................ 36-22= 14 (only) ......................... rabbit. (omitted) (2) Given the difference between the total number of chickens and the number of feet of chickens and rabbits, when the total number of feet of chickens is greater than that of rabbits, the formula (the difference between the number of feet of each chicken × the total number of head feet) ÷ (the number of feet of each chicken+the number of feet of each rabbit) = the number of feet of rabbits; Total number of rabbits = number of chickens or (the difference between the number of feet of each rabbit × the number of feet of chickens and rabbits) ÷ (the number of feet of each chicken+the number of feet of each chicken) = number of chickens; Total number of chickens = rabbits. (Example) (3) Given the difference between the total number of feet of chickens and rabbits, when the total number of feet of rabbits is more than that of chickens, the formula can be used. (the number of feet per chicken × the total number of heads+the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet per rabbit) = the number of rabbits; Total number of rabbits = number of chickens. Or (the number of feet per rabbit × the total number of heads-the difference between the number of feet of chickens and rabbits) ÷ (the number of feet per chicken+the number of feet per rabbit) = the number of chickens; Total number of chickens = rabbits. (Examples omitted) (4) The solution of the gain and loss problem (a generalization of the chicken-rabbit problem) can be expressed by the following formula: (65438+ 0 points for qualified products × total products-total realization points) ÷ (points for qualified products+points for unqualified products) = number of unqualified products. Or total number of products-(points deducted for each unqualified product × total number of products+total score obtained) ÷ (points deducted for each qualified product+points deducted for each unqualified product) = number of unqualified products. For example, "the workers who produce light bulbs in the light bulb factory are paid by scores." "Every qualified product is 4 points, and every unqualified product is not, but deducted 15 points. A worker produced 1000 light bulbs, and * * * got 3525 points. How many of them are unqualified? " Solution 1 (4×1000-3525) ÷ (4+15) = 475 ÷19 = 25 (pieces) Solution 21000-(/kloc-0) Cs1 \ v \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 \ kerning0 ) (5) The problem of chicken-rabbit exchange (how many chickens and rabbits are given the total number of feet and how many chickens and rabbits are given after chicken-rabbit exchange) can be solved by the following formula: [(sum of two total feet) ÷ (sum of feet of each chicken and rabbit)+(difference of two total feet) ÷ (difference of feet of each chicken and rabbit)] ÷ 2 = ÷. If the number of chickens and rabbits is reversed, * * * has 52 feet. How many chickens and rabbits are there? " Solution [(52+44) ÷ (4+2)+(52-44) ÷ (4-2)] 2 = 20 ÷ 2 =10 (only) ................ (planting trees at both ends) road length ÷ interval length+/kloc. Or interval number-1= number of trees; (No planting at both ends) Road length ÷ Interval length-1= number of trees; Road length ÷ number of sections = length of each section; Length of each section × number of sections = road length. (2) Tree planting on closed lines: road length ÷ number of sections = number of trees; Road length/number of sections = road length/number of trees = length of each section; Length of each section × number of sections = length of each section × number of trees = road length. (3) Planar tree planting problem: total floor area ÷ floor area per tree = formula comparison number of the problem of number of trees and percentage ÷ standard number = percentage (percentage) corresponding to the comparison number; Number of growth ÷ standard number = growth rate; Reduction number ÷ standard number = reduction rate. Or the difference between two numbers ÷ the smaller number = a few more (one percent) (increase); The difference between two numbers ÷ the larger number = a few (hundredths) (minus). Increase or decrease percentage (percentage) rate mutual formula growth rate ÷( 1+ growth rate) = reduction rate; Reduction rate ÷( 1- reduction rate) = growth rate. How much smaller than the area of Jiaqiu? "This is an application problem to find the reduction rate according to the growth rate. According to the formula, what percentage can you answer? According to the formula, the standard number × percentage rate = comparison number corresponding to the percentage rate can be solved; Standard number × growth rate = growth number; Standard number × reduction rate = reduction number; Standard number × (sum of dichotomy) = sum of two numbers; Standard number × (difference of dichotomy) = difference of two numbers. Find the comparison number of the formula of the standard number application problem ÷ the percentage corresponding to the comparison number (percentage) = the standard number; Growth number ÷ growth rate = standard number; Reduction number ÷ reduction rate = standard number; Sum of two numbers and sum of two rates = standard number; The difference between two numbers ÷ the difference between two rates = standard number; Square matrix problem formula (1) Real square matrix: (number of people on each side of the outer layer) 2= total number of people. (2) Hollow Square: (number of people on each side of the outermost layer) 2- (number of people on each side of the outermost layer -2× number of layers) 2= number of people in the hollow square. Or (number of people on each side of outermost layer-number of layers) × number of layers× 4 = number of hollow squares. Total number of people ÷4÷ layers+layers = number of people on each side of the outer layer. For example, there is a three-story hollow square with 10 people on the outermost layer. How many people are there in the whole square? If the solution 1 is regarded as a solid square, the total number of people is 10× 10= 100 (people), and then the square number of people in the hollow part is calculated. From the outside to the inside, if the number of people on each side is less than 2, they will enter the fourth floor, and the number of people on each side is 10-2×3=4 (people). So the number of people in the hollow square is 4×4= 16 (people), so the number of people in this hollow square is 100-65438+. According to the formula of (10-3)×3×4=84 (people) interest rate problem, there are many types of interest rate problems. The common problems of simple interest and compound interest are introduced as follows. (1) Simple interest problem: principal × interest rate× term = interest; Principal ×( 1+ interest rate× term) = principal and interest; Principal and interest and cash (1+ interest rate × term) = principal. Annual interest rate ÷ 12= monthly interest rate; Monthly interest rate × 12= annual interest rate. (2) Compound interest: principal ×( 1+ interest rate) deposit periods = sum of principal and interest. For example, "someone deposits 2400 yuan with a term of 3 years, and the monthly interest rate is 10.2 ‰ (that is, monthly interest 1.02). After three years, what is the principal and interest and * * *? "Solution (1) is calculated at the monthly interest rate. 3 years = 65438+February× 3 = 36 months 2400× (1+10.2 %× 36) = 2400×1.3672 = 3281.28 (yuan). First, convert the monthly interest rate into the annual interest rate:10.2 ‰×12 =12.24%, and then calculate the sum of principal and interest: 2400× (1+12.24 %× 3) = 2400. From the title of the first volume of the sixth-grade people's education edition: "Handbook of Chinese for Primary Schools", the first volume of the sixth-grade people's education edition ISBNNo. : 978-7-5634-0926-6 Author: Guangxi Publishing House: Yanbian University Press Publication Date: June 2008 format: 32 words: 960,000 words discount: full market price:.

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