First of all, a brief analysis of the topic:
Some differential multiple problems are complex and cannot be solved directly by formulas. At this time, children need to carefully examine the problem, pay special attention to some hidden conditions, and help us understand the meaning of the problem with the help of line segment diagrams, so as to find a solution.
For more complex differential application problems, the quantitative relationship is hidden. First draw a line graph according to the meaning of the question, and the quantitative relationship will be clearly displayed. Then, with the help of the line graph, find out the difference between two numbers and the corresponding multiple, and then use the formula to solve it.
Second, be concise.
Example 1: There are two bags of corn, and the big bag is 56 kilograms more than the small bag. If you eat 4 kilograms of corn in a small bag, the weight of corn in a big bag is 4 times that in a small bag. How many kilograms do these two bags of corn weigh?
Third, the main points of knowledge:
In front of us, we have initially mastered the characteristics and solving methods of the "sum-multiplication problem". If we know the difference between two numbers and the multiple relationship between the two numbers, we call it the "difference multiple problem".
Solving differential multiple problem is similar to solving sum multiple problem. You should first find the multiple corresponding to the business trip, first find the multiple of 1, and then find the multiple. In addition, we should make full use of the line chart to help analyze the quantitative relationship.
This relationship can be expressed as follows:
Difference between two numbers ÷ (multiple-1)= smaller number (multiple 1)
Smaller number × multiple = larger number (multiple)
Exercise 1
1, there are two boxes of toys, the first box is 60 more than the second box. If you take three out of the second box, the number of the first box is eight times that of the second box. How many toys are there in two boxes?
There are some books on a bookshelf, and there are more books on the second floor than on the first floor 12. If you take six books from the first floor, the number of books on the second floor is four times that on the first floor. How many books are there on the first and second floors?
Example 2: There are two barrels of salad oil, A and B. If you pour 8 kilograms into one barrel, the weight of the two barrels of salad oil is the same. If 12kg is poured into barrel B, the salad oil in barrel B is five times that in barrel A. How many kilograms of salad oil did A and B eat respectively?
Exercise 2
1. There are two buckets of water, A and B. If you pour 10 kg of water into bucket A, the two buckets of water are the same. If you pour 4 kilograms of water into bucket B, the water in bucket B is three times as much as that in bucket A. How many kilograms of water are there in each bucket of A and B?
2. Students from Class Three (1) take part in the English contest. If there are fewer boys 1, the number of men and women participating in the competition is equal; If 1 girl is missing, then there are twice as many boys as girls taking part in the competition. How many boys and girls took part in the English contest in Class Three (1)?
Example 3: A has three times as much money as B. After buying a set of encyclopedias of 180 yuan, B has the same amount of money left. A how much is it?
Exercise 3
1. The amount of money of Party A is four times that of Party B. After Party A bought a schoolbag from 30 yuan and a pen from 6 yuan, both of them have the same amount of money. A how much is it?
Dandan's money is five times that of Xiao Min. Dandan bought a suit, 1 15 yuan. After Xiao Min bought a pair of shoes at the price of 15 yuan, they had the same amount of money left. How much money does Dandan have?
Example 4: The number of boxes of white chalk in school is four times that of colored chalk. If you buy 12 boxes of white chalk and colored chalk respectively, the number of boxes of white chalk is three times that of colored chalk. How many boxes of white chalk and colored chalk are there?
Exercise 4
1. There are two baskets of apples, A and B. The number of kilograms in the first basket is three times that in the second basket. If the apples in the second basket are increased by eight kilograms each, the number of kilograms of apples in the first basket is twice that in the second basket. How many kilograms of apples are there in baskets A and B?
Xiaoming and Cong Cong each have some colored pens, and Xiaoming has five times as many colored pens as Cong Cong. If everyone buys four more markers, the number of Xiaoming is four times that of Cong Cong. How many colored pens did Xiao Ming and Cong Cong have at first?
Example 5: Tian Tian Primary School bought a batch of basketball and football. The number of basketball is four times more than football, five more, and basketball is 26 more than football. How many basketballs and footballs are there?
Exercise 5
1. There are some red balls and white balls in the shop. The number of red balls is 3 times more than that of white balls, and there are 24 more red balls than white balls. How many red and white balls are there?
There are two bags of flour. The flour in bag A is five times more than that in bag B, 12kg, and the flour in bag B is less than that in bag A 132kg ... How many kilograms are there in two bags of flour?
Third, homework after class.
1.two barrels of oil, a and b, each have several kilograms of oil. The oil in barrel A is 20 kilograms less than that in barrel B. If 5 kilograms are poured from barrel A and put into barrel B, the weight of barrel B is four times that of barrel A. How many kilograms of oil are there in barrels A and B?
Xiao Min and Xiaowen each have some glass balls. If Xiao Min gives Xiaowen three pills, they will have the same number of glass balls. If Xiaowen gave Xiao Min 1 pill, Xiao Min's glass ball was five times that of Xiaowen. How many primitive glass balls do Xiao Min and Xiaowen have?
Yun Yun's money is four times that of Xiaoyue. Yun Yun bought a set of watercolor pens and spent 19 yuan. After Xiaoyue bought an eraser with 1 yuan, they both had as much money left. How much money does Yun Yun have?
There are two barrels of oil, A and B. The weight of one barrel of oil is five times that of B.. If 8 kilograms of oil is poured into each barrel, the weight of oil in barrel A is three times that of oil in barrel B.. How many kilograms of oil are there in barrels A and B?
There are some story books and comic books in the library. The number of storybooks is four times less than that of comics, and storybooks are 28 more than comics. How many story books and comic books are there in the library?