1. Interesting Olympiad in the fourth grade of primary school
Let a and b both represent numbers, and specify a△b=3×a-2×b, ① find 3△2, 2 △ 3;
(2) Is there a commutative law for this operation "△"?
③ Find (17△6)△2,17 △ (6 △ 2);
(4) Is there an associative law for this operation "△"?
⑤ If 4△b=2 is known, find b. ..
Solution: The key to analyze and solve the problem of defining new operations is to grasp the essence of definition. The essence of the operation specified in this question is: subtract the 2 times after the symbol from the 3 times before the operation symbol. Solution: ①3△2=3×3-2×2=9-4=5.
2△3=3×2-2×3=6-6=0。
② From the example of ①, it can be seen that "△" has no commutative law.
③ To calculate (17△6)△2, first calculate the number in brackets, that is,17 △ 6 = 3×17-2× 6 = 39; Recalculate the second step
39△2=3×39-2×2= 1 13,
So (17 △ 6) △ 2 =113.
For 17△(6△2), the number in brackets is also calculated first, 6△2=3×6-2×2= 14, and then
17△ 14=3× 17-2× 14=23,
So 17△(6△2)=23.
(4) From the example of (3), it can be seen that "△" has no associative law. ⑤ Because 4△b=3×4-2×b= 12-2b, then 12-2b=2 and b=5.
2. Interesting Olympiad math problems in the fourth grade of primary school
1, colored stationery 19 yuan each, ordinary stationery 1 1 Yuan each. I bought 16 sets of these two kinds of stationery and spent 280 yuan. Q: How many sets of two kinds of stationery did you buy? Analysis: We imagine a strange chicken with 1 head 1 feet and a strange rabbit with1head 19 feet. They * * * have 16 heads, 280 feet. In this way, the problem of buying stationery will turn into the problem that chickens and rabbits are in the same cage.
Suppose you buy 16 sets of colored stationery, then * * needs 19× 16=304 yuan, which is 304-280 = 24 yuan more than the actual situation. Now, if ordinary stationery is replaced by colored stationery, each set needs less 19.
2, children divide candy, if each person divides 4, there will be 9 more; If each person is divided into 5 capsules, there are 6 capsules missing. Q: How many sweets are given to how many children?
Analysis: According to the topic conditions, the number of children and the number of sugar grains remain unchanged. Comparing the two distribution schemes, the first scheme has 9 more capsules when each person is divided into 4 capsules, and the second scheme has 6 fewer capsules when each person is divided into 5 capsules. The difference between the two different schemes is 9+6= 15 capsules. The reason for the difference is that the allocation numbers of the two schemes are different. The first scheme is divided into 4 capsules, and the second scheme is divided into 5 capsules. The difference between the two distribution numbers is 5-4= 1 (capsule). Everyone's difference is 1, and how many people are 15? It is concluded that the number of children is 15÷ 1= 15 (people) and the number of candy granules is 4× 15+9=69 (granules).
Solution: (9+6)÷(5-4)= 15 (person), 4× 15+9=69 (particle).
A: There are 15 children, divided into 69 pieces of sugar.
3. Interesting Olympiad math problems in the fourth grade of primary school
1. One road is long 100 meters. From beginning to end, plant 10 meter/plane tree. How many trees have been planted? Answer: The roads are divided into 100 ÷ 10 = 10, * * * plants10+1=1tree.
2. 12 willows are arranged in a row, and 3 peach trees are planted between every two willows. How many peach trees have been planted?
Answer: 3× (12- 1) = 33 trees.
3. How many times does it take to saw a 200 cm long piece of wood into 10 cm long pieces?
Answer: 200 ÷ 10 = 20 paragraphs, 20- 1 = 19 times.
4. It takes 10 seconds for ants to climb branches. How many minutes does it take to climb from the first section to the 13 section?
Answer: It takes10× (13-1) =120 seconds, 120 ÷ 60 = 2 points.
5. Plant chrysanthemums around the garden and plant them every 1 meter 1 potted flower. * * * The flower bed is 20 meters long. How many pots of chrysanthemums do you need?
Answer: 20 ÷ 1× 1 = 20 pots.
4. Interesting Olympiad math problems in the fourth grade of primary school
1, share the oil equally (an interesting topic of Olympic Mathematics) There is a big barrel filled with 8 liters of gasoline, and there are two empty barrels, one can hold 5 liters and the other can hold 3 liters. Now, it takes eight times at most to pour gasoline back and forth in these three barrels and divide 8 liters of gasoline into two 4 liters. Children, this is not an easy task. You should think more and do something!
2. Be careful to answer the wrong questions (interesting questions in Olympic Mathematics)
In order to recycle soda bottles, a store stipulated that three empty bottles should be replaced by one soda bottle. A man bought 10 bottles of soda, changed the empty bottles into soda after drinking them, and asked him how many bottles of soda he could drink.
3. Guess the color skillfully (the interesting question of Olympic Mathematics)
There is a cube with six colors on each side: red, green, yellow, blue, black and white. Three people look at it from different angles. A sees that the front of the building block is white, the top is red and the right side is green. B sees that the front of the building block is yellow, the top is blue and the right is white; C sees that the front of the building block is green, the top is black and the right is yellow. Each side of the cube is painted with only one color.
Children, guess what color is opposite to each color of this cube?
5. Interesting Olympiad math problems in the fourth grade of primary school
1, Wang Dong has deposits in 50 yuan, Zhang Hua has deposits in 30 yuan, and Zhang Hua wants to catch up with Wang Dong. Wang Dong deposits in 5 yuan and Zhang Hua deposits in 9 yuan every month. It will take () months to catch up with Wang Dong. 2. There are 164 students in the third grade, and 28 people participate in art interest groups. The number of people who participate in music interest groups is twice that of art groups, and the number of people who participate in sports interest groups is twice that of music groups. If everyone participates in at least one interest group and at most two interest group activities, then at least () people will participate in two interest groups.
One of the three students, Zhang San, Li Si and Wang Wu, did a good thing for the group when others were away. Afterwards, the teacher asked who did the good deed. Zhang San said it was Li Si, Li Si said it wasn't him, and Wang Wu said it wasn't him. One of them told the truth, and the one who did good was ().
4. Li finished a story book in 12 days, but must finish it in 2 days. Li Ming reads four more pages than Wang Fang every day. This story book has () pages.
5, a three-digit number, the sum of the numbers on each digit is 15, and the number on the 100th digit is 5 less than the number on the single digit; If the unit and the hundred digits are reversed, the new number is 39 times less than the original number. Then the original three digits are ().