Sum and difference problem formula
(sum+difference) ÷2= larger number;
(sum and difference) ÷2= smaller number.
Sum-multiple problem formula
And present (multiple+1)= a multiple;
Multiple x multiple = another number,
Or sum-a multiple = another number.
Formula of differential multiple problems
Difference ÷ (multiple-1)= smaller number;
Smaller number x multiple = larger number,
Or decimal+difference = large number.
Average problem formula
Total quantity/total number of copies = average value.
General travel problem formula
Average speed × time = distance;
Distance/time = average speed;
Distance-average speed = time.
The formula of reverse travel problem can be divided into "encounter problem" (two people start from two places and walk in opposite directions) and "separation problem" (two people walk with their backs to each other). Both of these problems can be solved by the following formula:
(speed sum) × meeting (leaving) time = meeting (leaving) distance;
Meet (leave) distance ÷ (speed sum) = meet (leave) time;
Meet (leave) distance-meet (leave) time = speed and.
Formula of the problem of traveling in the same direction
Catch-up (pull-out) distance ÷ (speed difference) = catch-up (pull-out) time;
Catch up (pull away) the distance; Catch-up (pull-away) time = speed difference;
(speed difference) × catching (pulling) time = catching (pulling) distance.
Formula of train crossing bridge problem
(bridge length+conductor) ÷ speed = crossing time;
(Bridge length+conductor) ÷ Crossing time = speed;
Speed × crossing time = sum of bridge and vehicle length.
Navigation problem formula
(1) general formula:
Still water speed (ship speed)+current speed (water speed) = downstream speed;
Ship speed-water speed = water flow speed;
(downstream speed+upstream speed) ÷2= ship speed;
(downstream speed-upstream speed) ÷2= water flow speed.
(2) Formula for two ships sailing in opposite directions:
Downstream speed of ship A+downstream speed of ship B = still water speed of ship A+still water speed of ship B.
(3) Formula for two ships sailing in the same direction:
Hydrostatic speed of rear (front) ship-Hydrostatic speed of front (rear) ship = the speed of narrowing (expanding) the distance between two ships.
(Find out the speed of narrowing or widening the distance between the two ships, and then solve it according to the relevant formula above).
Engineering problem formula
(1) general formula:
Efficiency × working hours = total workload;
Total workload ÷ working time = working efficiency;
Total amount of work ÷ efficiency = working hours.
(2) Assuming that the total workload is "1", the formula for solving engineering problems is:
1÷ working time = the fraction of the total amount of work completed in unit time;
1What is the score that can be completed per unit time = working time.
1. Each copy × number of copies = total.
Total copies/number of copies = number of copies
Total copies/number of copies = number of copies
2. 1 multiple× multiple = multiple
Multiply1Multiply = Multiply
Multiply/Multiply = 1 Multiply
3. Speed × time = distance
Distance/speed = time
Distance/time = speed
4. Unit price × quantity = total price
Total price/unit price = quantity
Total price ÷ quantity = unit price
5. Work efficiency × working hours = total workload.
Total amount of work ÷ work efficiency = working hours
Total workload ÷ working time = working efficiency
6 addend+addend = sum
And-one addend = another addend
7 minuend-minuend = difference
Negative difference = negative
Difference+Minus = Minus
8 factor × factor = product
Product ÷ One factor = another factor
Dividend = quotient
Dividend = divisor
Quotient × Divider = Divider
Calculation formula of mathematical graphics in primary schools
1. square
Perimeter area side length
Perimeter = side length ×4
C=4a
Area = side length × side length
S=a×a
2. Cubic
Volume a: edge length
Surface area = side length × side length ×6
S table =a×a×6
Volume = side length × side length × side length
V=a×a×a
3. Rectangular shape
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 = (length× width+length× height+width× height) ×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×∈
9. Cylinder
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
Formula of sum and difference problem;
Total number ÷ Total number of copies = average value
(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 mainly 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
Profit and loss issues:
(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.
Encountered problems:
Meeting distance = speed × meeting time
Meeting time = meeting distance/speed and
Speed Sum = Meeting Distance/Meeting Time
Follow up questions:
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
Centralized question:
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 issues:
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%)
Should this be enough?