Integer times fraction, numerator is the molecular product of integer and fraction, and denominator remains unchanged.
Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.
Multiply three numbers. For simplicity, you can divide the numerator and denominator of all fractions first, and then multiply the divided numerator and denominator.
Two numbers whose product is 1 are reciprocal.
To find the reciprocal of a number (except 0), just switch the numerator and denominator of this number.
The significance of fractional division is the same as that of proof, that is, knowing the product of two factors and one of them to find the other factor.
A fraction divided by an integer (except 0) equals a fraction multiplied by the reciprocal of the integer.
A number indicating that one number is a percentage of another number is called a percentage. Percentages are also called percentages or percentages.
To convert decimals into percentages, move the decimal point two places to the right, followed by hundreds of semicolons (if the number of digits is not enough, use 0 to make it up).
To convert percentages to decimals, you should delete the percent sign and move the decimal point two places to the left.
When a fraction is converted into a percentage, it is generally converted into a decimal (three decimal places are generally reserved to prevent infinite division or large decimal places), and then the decimal is converted into a percentage.
Percentages are divided into numbers. First, rewrite the fraction with the letter 100, and then divide the divisor into the simplest fractions.
When drawing a circle, a fixed point is called the center of the circle, which is usually represented by the letter O; The line segment from the center of the circle to any point on the circle is called radius, which is usually represented by the letter r; The line segment passing through the center of the circle and having both ends on the circle is called the diameter, and the diameter is usually represented by the letter D.
If a plane figure is folded in half along a straight line, the figures on both sides can completely overlap, and this figure is a symmetrical axis figure. The straight line where the crease lies is called the symmetry axis.
The length of the curve forming a circle is the circumference of the circle.
For circles of different sizes, the circumference is always greater than 3 times the diameter. This multiple is a fixed number, which we call pi, and it is expressed by letters (pronounced pāi).
Germination rate = number of germinated seeds/total number of tested seeds * 100%
y = kx(k & gt； 0), y increases with the increase of x, then y is proportional to x,
y = k/x(k & gt； 0), y decreases with the increase of x, then y is inversely proportional to x,
1, number of copies × number of copies = total number of copies/number of copies = total number of copies/number of copies = number of copies.
2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple
3. Speed × time = distance/speed = time/distance/time = speed
4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price
5. Work efficiency × working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency.
6. Appendix+Appendix = sum, and-one addend = another addend.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor × factor = product ÷ one factor = another factor.
9. Dividend = quotient dividend = divisor quotient × divisor = dividend
Calculation formula of mathematical graphics in primary schools
1, square c perimeter s area a side length perimeter = side length× 4c = 4a area = side length× side length s = a× a.
2. Cube V: volume A: side surface area = side length × side length× 6s table =a×a×6 volume = side length× side length× side length V = a× a× a.
3. rectangular
Perimeter area side length
Circumference = (length+width) ×2
C=2(a+b)
Area = length × width
S=ab
4. Cuboid
V: volume s: area a: length b: width h: height.
(1) Surface area (L× W+L× H+W× H) ×2
S=2(ab+ah+bh)
(2) Volume = length × width × height
V=abh
5 triangle
S area a bottom h height
Area = bottom × height ÷2
s=ah÷2
Height of triangle = area ×2÷ base.
Triangle base = area ×2÷ height
6 parallelogram
S area a bottom h height
Area = bottom × height
S = ah
7 trapezoid
Height of upper bottom b and lower bottom h in s area a
Area = (upper bottom+lower bottom) × height ÷2
s=(a+b)× h÷2
8 laps
Area c perimeter d= diameter r= radius
(1) circumference = diameter ×∏=2×∏× radius
C=∏d=2∏r
(2) area = radius × radius×∈
Cylinder 9
V: volume h: height s; Bottom area r: bottom radius c: bottom perimeter
(1) lateral area = bottom circumference × height.
(2) Surface area = lateral area+bottom area ×2
(3) Volume = bottom area × height
(4) Volume = lateral area ÷2× radius.
10 cone
V: volume h: height s; Bottom area r: bottom radius
Volume = bottom area × height ÷3
Total number ÷ Total number of copies = average value
Formula of sum and difference problem
(sum+difference) ÷ 2 = large number
(sum and difference) ÷ 2 = decimal
And folding problems.
Sum \ (multiple-1) = decimal
Decimal × multiple = large number
(or sum-decimal = large number)
Difference problem
Difference ÷ (multiple-1) = decimal
Decimal × multiple = large number
(or decimal+difference = large number)
Tree planting problem
1 The problem of planting trees on unclosed lines can be divided into the following three situations:
(1) If trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes+1 = total length-1.
Total length = plant spacing × (number of plants-1)
Plant spacing = total length ÷ (number of plants-1)
2 If you want to plant trees at one end of the unclosed line and not at the other end, then:
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
(3) If no trees are planted at both ends of the non-closed line, then:
Number of plants = number of nodes-1 = total length-1.
Total length = plant spacing × (number of plants+1)
Plant spacing = total length ÷ (number of plants+1)
The quantitative relationship of planting trees on the closed line is as follows
Number of plants = number of segments = total length ÷ plant spacing
Total length = plant spacing × number of plants
Plant spacing = total length/number of plants
The question of profit and loss
(Profit+Loss) ÷ Difference between two distributions = number of shares participating in distribution.
(Big profit-small profit) ÷ Difference between two distributions = number of shares participating in distribution.
(big loss-small loss) ÷ The difference between two distributions = the number of shares participating in the distribution.
encounter a problem
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
Catch up with the problem
Catch-up distance = speed difference× catch-up time
Catch-up time = catch-up distance ÷ speed difference
Speed difference = catching distance ÷ catching time
Tap water problem
Downstream velocity = still water velocity+current velocity
Countercurrent velocity = still water velocity-current velocity
Still water velocity = (downstream velocity+countercurrent velocity) ÷2
Water velocity = (downstream velocity-countercurrent velocity) ÷2
Concentration problem
Solute weight+solvent weight = solution weight.
The weight of solute/solution × 100% = concentration.
Solution weight × concentration = solute weight
Solute weight-concentration = solution weight.
Profit and discount problem
Profit = selling price-cost
Profit rate = profit/cost × 100% = (selling price/cost-1) × 100%.
Up and down amount = principal × up and down percentage
Discount = actual selling price ÷ original selling price× 1 00% (discount <1)
Interest = principal × interest rate× time
After-tax interest = principal × interest rate × time × (1-20%)
Length unit conversion
1 km = 1 000m1m = 10 decimeter.
1 decimeter =10cm1m =10cm.
1 cm = 10/0mm
Area unit conversion
1 km2 = 100 hectare
1 ha = 1 10,000 m2
1 m2 = 100 square decimeter
1 square decimeter = 100 square centimeter
1 cm2 = 100 mm2
Volume (volume) unit conversion
1 m3 = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
1 cubic decimeter = 1 liter
1 cm3 = 1 ml
1 m3 = 1000 liter
Weight unit conversion
1 ton = 1000 kg
1 kg =1000g
1 kg = 1 kg
Rmb unit conversion
1 yuan = 10 angle.
1 angle = 10 point
1 yuan = 100 integral.
Time unit conversion
1 century = 100 1 year =65438+ February.
The big month (3 1 day) includes:1\ 3 \ 5 \ 7 \ 8 \10 \ 65438+February.
Abortion (30 days) includes: April \ June \ September \165438+1October.
February 28th in a normal year and February 29th in a leap year.
There are 365 days in a normal year and 366 days in a leap year.
1 day =24 hours 1 hour =60 minutes.
1 minute =60 seconds 1 hour =3600 seconds.
5. Angle
Straight line; A straight line is infinite.
Line segment: A segment between two points on a straight line is called a line segment. A line segment has two endpoints. A line segment is a part of a straight line.
Ray: Extend one end of a line infinitely, and you get a ray. A ray has only one endpoint.
Angle: The figure formed by two rays from a point is called an angle. This point is called the vertex of the angle. These two rays are called the edges of the angle. The angle is usually represented by the symbol "∞". As shown in the figure below:
edge
pinnacle
edge
Compare the sizes of angles: first overlap the vertices of two angles on one side, and then look at the position of the other side. Which corner has the other side outside, which corner is big. If the other side also coincides, the two angles are equal.
The size of the angle depends on the size of both sides. The bigger the fork, the bigger the angle. The size of the angle has nothing to do with the length drawn on both sides of the angle.
Measurement of angle: the unit of measurement of angle is "degree", which is represented by the symbol "0". Divide the semicircle into 180 equal parts, and the angle of each part is called 1 degree angle. Write 1. When measuring an angle with a protractor, place the protractor above the angle so that the center of the protractor coincides with the vertex of the angle. The 0 degree line coincides with one side of the angle, and the scale on the protractor on the other side of the angle is the degree of this angle.
Classification of angles: angles greater than 0 and less than 90 are called acute angles. An angle equal to 90 degrees is called a right angle. An angle greater than 90 and less than180 is called an obtuse angle. The two sides of an angle form a straight line, and the angle equal to 180 is called a right angle. The 360-degree angle formed by light rotating around its endpoint is called fillet.
Vertical line: When two lines intersect at right angles, they are called perpendicular to each other, one of which is called the vertical line of the other (as shown in the following figure 1), and the intersection of these two lines is called vertical foot.
Parallelism: Two straight lines that never intersect in the same plane are called parallel lines (Figure 2 below). It can also be said that these two straight lines are parallel to each other.
Vertical parallelism
A, B and C are walking by a round pond. Three people start from the same place at the same time. A and B walk clockwise and C walk counterclockwise. A walks 80 meters per minute, and B walks 65 meters per minute. Twenty minutes after departure, C meets A, and two minutes later, C meets B.. What is the circumference of this circular pond?
It takes 25 seconds for a train to pass through a 250-meter-long tunnel and 23 seconds to pass through a 2 10-meter-long tunnel. If the train and another conductor150m. How many seconds does it take for a 72-kilometer-per-hour train to meet and pass by by by mistake?
A tunnel is 360 meters long. It takes 8 seconds for a train to enter the tunnel from the front and 20 seconds from the front to the whole train. How long is this train?
On a path parallel to the railway, a group of people and cyclists are driving south at the same time. The pedestrian speed is 3.6 km/h and the cyclist speed is 10.8km/h when a train comes from behind them. It takes 22 seconds for a train to overtake a pedestrian and 26 seconds for a cyclist. What is the total length of the train?
4. There are two trains, one of which is 102 meters long and runs 20 meters per second; Column length120m, length17m/sec. Two cars are driving in the same direction. How many seconds does it take from the first train catching up with the second train to the two cars leaving?
Someone is walking at a speed of 2 meters per second. A train came from behind, and it took 10 seconds to overtake him. As we all know, this train is 90 meters long. Find the speed of the train.
6. At present, two trains run in the same direction at the same time. 12 seconds later, the express train overtook the local train. The express train runs18m per second, and the local train runs10m per second. If two trains travel in the same direction at the same time, the express train will overtake the local train in 9 seconds, and find the body length of the two trains.
7. It takes 40 seconds for a train to cross a 440m bridge and 30 seconds to cross a 3 10/0m tunnel at the same speed. What is the speed and length of this train?
Xiaoying and Xiao Min took two stopwatches to measure the speed and length of the passing train. Xiaoying used her watch to record that the train passed in front of her 15 seconds. Xiao Min used another watch to record that it took 20 seconds to cross the second pole from the front to the rear. It is known that the distance between two poles is 100 meters. Can you help Xiaoying and Xiao Min work out the total length and speed of the train?
9. It takes 40 seconds for a train to cross a 530-meter bridge and 30 seconds to cross a 380-meter cave at the same speed. Find out the speed and length of this train in meters.
10. The two started from these two places along the path next to the railway line and walked at the same speed. A train came, 10 seconds. The whole train passed by A. Three minutes later, B met the train, and the whole train only took 9 seconds to pass by B. How long did the two meet after the train left B?
1 1. Two trains, one with a length of 120m and a speed of 20m seconds per hour; The other train is160m long and runs at a speed of15m per second. The two cars are driving in opposite directions. How many seconds does it take from the front meeting to the back leaving?
12. Someone is walking at a speed of 2 meters per second. A train came from behind, and it took 10 seconds to overtake him. It is known that the length of the train is 90 meters. Find the speed of the train.
13. Party A and Party B walk along the railway at the same speed. It took 8 seconds for a train to pass by Party A, and only 7 seconds to pass by Party B after leaving Party A for 5 minutes. How many minutes after Party B met the train?
14. Express train length182m, 20 meters per second, slow train length1034m, 0/8m per second. The two cars are parallel in the same direction. How long does it take for the express train to cross the local train when the rear of the express train meets the rear of the local train?
15. Express train length182m, 20 meters per second, slow train length1034m, 0/8m per second. The two cars are parallel in the same direction. When the heads of the two cars are aligned, how many seconds can the express train pass the local train?
16. A person runs along the railway at a speed of 120m per minute. A 288-meter-long train came from the opposite side. It took him 8 seconds to find the speed of the train.
17. A train is 600 meters long. It passes through a 200-meter-long tunnel at a speed of 10 meter per second. How long does it take to leave the tunnel from the front to the rear?
18. A train is 200 meters long. It passes through a 200-meter-long tunnel at a speed of 10 meter per second. It takes _ _ _ _ _ _ _ time to leave the tunnel from the front to the rear.
19. Someone was walking on the sidewalk beside the railway, and a bus came from behind. The transit time is 15 second, the bus length is 105 meter, and the speed is 28.8 kilometers per hour. Require pedestrians to walk _ _ _ _ kilometers per hour?
20. A man was walking along the railway at a speed of 60 meters per minute when a bus with a length of 144 meters came head-on. It took him 8 seconds to pass, and the speed of the train was _ _ _ _ _ m/s.