Psychological navigation: Xiaohua finished reading 16×5=80 (pages) in 5 days, because 3/5 of the whole book has not been read after 5 days, which means that 80 pages that have been read account for 1-3/5 = 2/5 of this book.
Solution: 16× 5 ÷ (1-3/5) = 200 (page)
This book has 200 pages.
How much is 2.25 less than 30? How much is 30 more than 25?
Psychological navigation: 1, how much is 25 less than 30?
25 is less than 30-25 = 5, and 5 is the score of 30?
At this time, 30 is "unit 1", that is, 5÷30= 1/6.
How much is 2.30 more than 25?
30 is more than 25. 30-25 = 5.5 is a fraction of 25?
At this time, 25 is "unit 1", that is, 5÷25= 1/5.
Answer: 25 is smaller than 30 1/6, and 30 is larger than 25 1/5.
3. There are 3/5 more male workers than female workers in a workshop, and fewer female workers than male workers.
Thinking navigation: The number of male employees is 3/5 more than that of female employees. Here, the number of female employees is regarded as "1 unit".
Then the number of male employees is 1+3/5=8/5.
How many fewer female workers are there than male workers? Here, the number of male workers is regarded as "unit 1"
That is, the number of female workers is less than that of male workers.
(8/5— 1)÷8/5=3/8。
A batch of rice was sent from the canteen. I ate 2/5 on the first day, 1/3 on the second day and 3/4 on the third day. At this time, there is 15 kg left. How many Jin of rice did the canteen send?
Mind navigation: the last remaining15kg is "leftover".
(1-3/4 = 1/4), the quantity of rice delivered from the canteen can be calculated by this method.
15 ÷ (1-3/4) ÷ (1-kloc-0//3) ÷ (1-2/5) =150 (.
A: The canteen sent 150 Jin of rice.
Xiaohua read a story book. On the first day, he read six pages more than 1/6 of this book. The next day, he read eight pages less than 1/8, leaving 172 pages. How many pages does this story book have?
Mental navigation: 6 more pages, 8 less pages, leaving 172 pages. The relationship between these quantities and the inclusion or exclusion of scores is the key to solve this problem. The drawing shows that this quantitative relationship is very clear.
The number of pages corresponding to 1- 1/6- 1/8 is obviously (172+6-8).
Solution: (172+6-8) ÷ (1-1/6-1/8) = 240 (page).
This story book has 240 pages.
Thinking training:
1, a car traveled 60 kilometers in an hour, and after five hours, it traveled the whole distance 1/3. How many kilometers is the whole journey?
Two engineering teams, Team A and Team B, jointly built a road. Team A builds 35 meters every day, while Team B builds 50 meters every day. Three days later, three-quarters of the road was completed. How long is this road?
3. The number of A is more than that of B 1/3, and the number of B is less than that of A?
4, a pot of goldfish, red fish is 3/8 more than black fish, and black fish is less than red fish?
According to the census of a certain year, the rural population is 3/7 more than the urban population, and the urban population is less than the rural population.
6. Students from a school took part in a math contest, accounting for 2/25 of the whole school, and those who didn't win the prize accounted for 3/4 of the participants, among which the first prize accounted for 1/5 of the winners. There are two people in the first prize. How many students are there in the school?
7. Mom bought some apples. On the first day, she ate 1/3 and 1/3. On the second day, she ate the remaining 1/4 and 1/4. On the third day, she ate the remaining 1/3. How many apples do you eat every day?
8. The water tank is full in the morning. Use 1/5 during the day, 27 liters at night, and the remaining water110 at night. The last remaining water is half a tank 1 liter. How many liters of water do you put in the morning?
Second, the cuboid:
1. In a cuboid, the sum of the lengths of three sides intersecting at a vertex is 27 cm. How long is its side?
Mental navigation: in a cuboid, there are four lengths, four widths and four heights, and the three sides intersecting at the same vertex are length, width and height respectively. Known: length+width+height = 27cm.
Then: 4 length +4 width +4 height =4× (length+width+height) =4×27= 108 cm.
2. A rectangular carton without a lid, 35cm long, 30cm wide and 12cm high. What is the surface area of this carton?
Mind navigation: This rectangular box has no cover, only five faces, and the surface area is the sum of these five areas. Finally, pay attention to the unity of the unit.
35×30+35× 12×2+30× 12×2
= 1050+840+720
=26 10 (square centimeter)
=26. 1 (square decimeter)
3. Dig a hole in the center of each face of a cube with a side length of 5 cm. The hole is square with side length 1 cm and hole depth 1 cm. What is the surface area of the wood block after digging?
Mind navigation: There are holes in all six sides of the cube. We only need to calculate the surface area of a face multiplied by 6 to calculate the surface area of a cube. We dug a square with an area of 1× 1= 1 (square centimeter) on a surface, but added five areas of 1 square centimeter.
1. The school has a reception room, which is10m long, 8m wide and 3m high. Ceiling and wall painting, after deducting the area of doors and windows, the painting area is 22 square meters.
There is a cuboid block with a length of 7 cm, a width of 3 cm and a height of 5 cm. Cut it into two identical cuboids, how many square centimeters will the surface area increase at most?
3.▲ How many square centimeters does it take to make an iron chimney with a height of 120 cm and a length of 10 cm?
4.▲ A swimming pool, 50 meters long, 20 meters wide and 2 meters deep. What is the area of the four walls and the bottom to be tiled? Draw a straight line with red paint on the four walls of the swimming pool at a depth of 1 m. How long is this straight line?
1, a, b two cars are coming from two opposite directions at the same time. A car travels 27 kilometers per hour, and B car travels 29 kilometers per hour. Will the two cars meet in 3/5 hours?
Thinking navigation: According to the fourth grade knowledge, students know:
Distance traveled = speed and time
Countable formula (27+29) × 3/5 = 33.6 (km)
Through analysis and discussion, students find that they didn't tell the distance between A and B, so there are two situations:
Third, fractional multiplication.
1. If the distance between A and B exceeds 33.6 kilometers, two cars can't meet.
2. If the distance between A and B is less than or equal to 33.6 kilometers, two cars can meet.
This topic is the application of fractional multiplication in real life. Combined with specific problems, the results are different when analyzing different situations.
2. 36 tons of chemical fertilizer. After using 1/4, use 1/4 tons. How many tons are left?
Mental navigation: The key to this problem is to understand "1/4" and "1/4 tons".
"1/4" refers to 1/4 of the total fertilizer, that is, 36 tons of 1/4, that is, 36× 1/4.
"1/4 tons" refers to the quantity actually used.
Solution: 36—36× 1/4— 1/4.
=36-9— 1/4
=26 3/4 tons
A: There are 26 3/4 tons left.
3. There was a sheet piling, *** 120, which was used for 3/5 for the first time and 1/6 for the second time. * * * How many sheets were used twice?
Thinking navigation: find out "unit 1" and clarify the quantitative relationship.
"Use 3/5 of it for the first time" means "What is 3/5 of 120?"
"1/6 used for the second time" means "What is 1/6 of 120?"
Scheme 1: Number of sheets used for the first time+Number of sheets used for the second time = Total number of sheets used.
120×3/5+ 120× 1/6
=72+20
=92 (sheets)
A: Two times * * * with 92 sheets of paper.
Scheme 2: Total number of sheets × (number of copies used for the first time+number of copies used for the second time) = total number of sheets.
120×(3/5+ 1/6)
= 120×23/30
=92 (sheets)
A: Two times * * * with 92 sheets of paper.
4. Judges; A rope, cut off 3/4, leaving 1/4 meters, is that right?
Psychological navigation: There are three situations.
The length of a rope is 1 m, and it is correct to cut off 3/4, leaving1/4 m.
The length of the second rope is greater than 1 m, 3/4 is cut off, and the rest is greater than 1/4 m.
The length of three ropes is less than 1m, 3/4 of them are cut off, and the rest are less than 1/4m.
Thinking training:
1, Xiao Wang and Xiao Zhang typed the manuscript together, Xiao Li typed 70 words 1 minute and Xiao Zhang typed 1 minute. Can they finish typing in 3/4 hours?
Team a and team b will jointly build a road. Team A will build 65 meters a day, and Team B will build 75 meters a day. Can the two teams complete the journey in 7/ 15 months?
3. For a 9-meter-long rope, cut 1/2 for the first time and 1/2 for the second time. How many meters are left?
There are 30 boxes of soap, each box weighs 1/2 tons, and 1/3 of these soaps are transported by car. How many tons of soap did the car transport?
5. A 4-meter-long wood, cut off its 1/2 for the first time, cut off the remaining 1/2 for the second time, and cut off 1/2 for the third time. How many meters are left?
6. A road team built a 240-meter road. 1/3 was built on the first day, and 1/4 was built on the second day. How many meters were built on the first day than on the second?
I bought two bags of potatoes in the canteen. The first bag weighs 23 kilograms, and the second bag weighs 25 kilograms. I ate 5/ 12 of the total at noon. How many kilograms did I eat?
8. A school participated in the National Hard Pen Calligraphy Competition. There are 65,438+020 participants in the lower grades, 96 participants in the middle grades and 64 participants in the upper grades. Among them, 1/7 participants won the prize. How many people won the prize?