First, method guidance.
The problem of sum and multiple is to find the sum of two numbers and the multiple relationship between two numbers. Its main features are: ① the sum of two numbers is known; ② It is known that one of the two numbers is "multiple" of the other. The main quantitative relations of the sum-times problem are:
Multiples of two numbers and multiples of sum of two numbers = 1 (decimal)
1 multiple× multiple = multiple (large number)
When solving this kind of application problems, a smaller number is often taken as the standard number (multiple of 1), and then the sum of multiples is obtained according to the multiple relationship between other numbers and this smaller number (standard number). Finally, sum (multiple of 1) = standard number (decimal), and standard number × multiple = another number (standard number× multiple).
Second, typical cases
Example 1: My sister has 40 picture books and my sister has 50 picture books. Q: How many picture books did my sister give her, so that my sister had twice as many picture books as her sister?
Analysis: According to the known conditions, my sister has 40 comic books and my sister has 50 comic books. We can find out the number of comic books of them. Knowing that my sister gave some to my sister, my sister's number was 1 time, and my sister's number was twice that of my sister. According to the relationship between sum and times, we can find out how many books my sister has at this time, and finally get the question.
Solution:
After my sister gave it to my sister, my sister had:
(40+50)÷( 1+2)
=90÷3
= 30 (Ben)
Sister to sister:
40-30 = 10 (Ben)
Answer: My sister gave my sister 10 picture book, so my sister's picture book is twice as big as my sister's.
Example 2: Grade 4 and Grade 5 students in a school 165, and the number of grade 4 students is twice as small as that of grade 5. Q: How many students are there in grades four and five?
Analysis: From "the number of students in grade four is twice that of grade five", it can be seen that the number of students in grade five is regarded as a multiple of 1, while the number of students in grade four is twice that of grade five. From this, it can be concluded that the number of students in grade four is twice that in grade five, so we can know the sum of two numbers and the multiple of two numbers, and we can find out these two numbers.
Solution:
Fifth grade:
( 165+6)÷(2+ 1)
= 17 1÷3
= 57 (person)
Fourth grade:
57× 2-6 = 108 (person)
A: There are 0/08 students in Grade Four and 57 students in Grade Five.
Example 3: There are 52 original cars in Station A and 32 original cars in bilibili ... If 28 cars drive from Station A to bilibili and 24 cars drive from bilibili to Station A every day, the number of cars in bilibili will be twice that of Station A in a few days.
Analysis: There are 28 cars from Station A to bilibili and 24 cars from bilibili to Station A every day, which is equivalent to 28-24 cars from Station A to bilibili every day. After a few days, the number of vehicles at Station A was regarded as 1 time. At this time, the number of vehicles in bilibili is twice, and the total number of vehicles in two stations (52+32) is equivalent to (2+ 1) times. Then, a few days later, the number of vehicles at Station A was reduced to (52+32) ÷ (2+65438).
Solution:
(52+32) ÷ (2+ 1) = 28 (vehicle)
(52-28) ÷ (28-24) = 6 (days)
A: After 6 days, the number of vehicles in bilibili is twice that of Station A. ..
Example 4: The sum of the numbers A, B and C is 170. The number B is four times less than the number A, and the number C is six times more than the number A. Find out what these three numbers are.
Analysis: The numbers B and C are directly related to the number A, so the number A is regarded as 1 time. Because the number B is 4 less than twice that of the number A, adding 4 to the number B will make the number B twice that of the number A. Because the number C is 6 times that of the number A, subtracting 6 from the number C becomes 3 times that of the number A. At this time, (170+4-6) is equivalent to (1+2+3) times that of a number.
Solution:
A number: (170+4-6)+(1+2+3) = 28.
Number B: 28× 2-4 = 52
Number c: 28× 3+6 = 90
A: The number A is 28, the number B is 52 and the number C is 90.
Third, actual combat drills.
Question 1: Apples and pears have12kg, which is three times that of pears. How many kilograms are apples and pears?
Question 2: Two boxes of oranges, box A weighs 180 kg, and box B weighs 120 kg. Take some oranges from box B and put them in box A. At this time, there are twice as many oranges in box A as in box B. How many kilograms of oranges did you take from box B and put them in box A?
Question 3: There are 80 people digging and 52 people moving earth on the construction site. According to the needs of the construction site, how many people should be raised from the earth-moving truck to dig, so that the number of people digging can reach three times that of the earth-moving truck?
Question 4: A and B have two barrels of gasoline * * * 84kg. If the gasoline in barrel B is poured into barrel A (15kg), the gasoline in barrel A is equal to 3 times that in barrel B. How many kilograms of raw gasoline are there in barrel A and barrel B respectively?
Question 5: Three pieces of cloth are 546 meters long, the second piece is twice as long as the first piece, and the third piece is less than the third piece 14 meter. How long are these three pieces of cloth?