1. In the average problem, leveling is leveling, and they are all equal, that is, several unequal numbers. Under the condition of "harmony" unchanged, through "moving more to make up less", giving more to less will eventually become the same. This figure is the average.
Since the sum is unchanged, the last few numbers will become the same again, so it is natural to get the solution of the average: average = total quantity ÷ total number of copies.
This formula profoundly explains: first of all, "sum" means that the total number is unchanged, so add up each number; Finally, we have to take an average, so we have to divide it by the total number of copies to make it the same.
In the teaching process, many students can quickly master and use this formula, but often ignore the concept that the original source of the average is to make them the same by "shifting more to make up less". If we can master this point, many problems that are not directly averaged can be solved. Let's look at a basic topic:
1. Xiao Qiang jumped rope, jumping 67 times for the first time and 76 times for the second time. How many times does he have to jump for the third time to get an average score of 80 times?
Solution: Because the average score is the same after more activities and less supplements, that is, the total * * * is the same as that of less than 80.
According to the concept of average, more and less are the same. The first two times were * * * less 17, so the third time was more 17 and the average score was 80.
So: the third time: 80+ 17=97.
2. The average score of the players who participated in a school's mathematics competition was 75, including male players 10 and female players 15, while the average score of female players was 80. What is the average score of male players? Solution: The average score of female players is higher than that of all players (80-75)× 15=75. According to the meaning of average score, the average score of male players should be 75 points lower than the average score.
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So each male player should be 75÷ 10=7.5 points less than the average score, so the average score of male players is 75-7.5=67.5 points.
Second, the average problem: the average is the development of equal division. The key to solve the problem is to determine the total quantity and the corresponding total number of copies. Arithmetic average: Given several unequal quantities of the same kind and the corresponding number of copies, find the average of each number of copies. Quantity relationship: sum of quantity ÷ quantity = arithmetic average.
Weighted average: Given the average of two or more copies, what is the total average? Sum of quantitative relations (partial average × weight) ÷ (total weight) = weighted average. Average difference: divide the sum of parts greater than or less than the standard number by the total number of shares to get the average difference between the standard number and each number. Quantitative relationship (large number-decimal number) ÷2= sum of differences between the largest number of decimals and the number of decimals ÷ Total number of copies = sum of differences between the largest number of decimals and the number of decimals ÷ Total number of copies = number of decimals. Example: A car travels from A to B at a speed of 100 km/h and from B to A at a speed of 60 km/h.. Find the average speed of this car. Analysis: The formula can also be used to find the average speed of the car. In this problem, the distance from A to B can be set as "1", and the total distance traveled by the car is "2". Total number of copies/total number of copies = average number of copies × total number of copies = total number of copies/total number of copies = total number of copies.
1, the sixth grade students of Dongfang Primary School are divided into two groups to make up books. The first group consisted of 28 people, each of whom wrote 15 books on average; The second group consists of 22 people and has 280 repair books. How many books are repaired in each class on average?
2, there are 5 kilograms of fruit candy, 2.4 yuan per kilogram; 4 kg of toffee, 3.2 yuan per kg; Soft candy 1 1 kg, 4.2 yuan per kg. Mix these sugars into various sugars. How much is this sugar per kilogram?
3. Dig a canal with a length of 1455 meters, which has been dug for 3 days, with an average of 285 meters per day, and the rest are dug for 300 meters per day. How many meters is the canal dug on average every day?
Before Xiaohua's mid-term exam results were announced, his average score in four subjects was 90. After the announcement of foreign language scores, his average score dropped by 2 points. What is Xiaohua's foreign language score?
5. Party A, Party B and Party C deposit in the bank. The deposit of Party C is 1.5 times the average deposit of Party A and Party B, and the sum of the deposits of Party A and Party B is 2400 yuan. What is the average deposit for three people?
6, a kind of wine per kilogram of 30 yuan, b kind of wine per kilogram of 24 yuan. Now the first-class wine 13kg and the second-class wine 8kg are mixed for sale. When the remaining 1kg is available, the cost is just obtained, and the price per kilogram of mixed wine is even higher.
7. Party A, Party B and Party C each spend the same amount of money on the same book. When distributing, Party A needs 22 copies, Party B needs 23 copies and Party C needs 30 copies. Therefore, C is returned to A 13.5 yuan. How much should C be returned to B?
8. Xiaorong lives in Shannan and Xiao Fang lives in Shanbei. Shannan Mountain Road is 269 meters long and Shanbei Road is 370 meters long. Xiaorong set out from home to Xiao Fang's home, walking 16 meters per minute when going uphill, and walking 24 meters per minute when going downhill. Find the average speed of Xiao Rong's round trip.
9. The straw hat factory has two straw hat production workshops. Last month, the two workshops produced an average of 185 straw hats. There are 25 people in the first workshop, with an average production of 203 per person; The average person in the second workshop produces 170 straw hats. How many people are there in workshop 2?