Additive commutative law: A+B = B+A Addition Law: (A+B)+C = A+(B+C)
Multiplicative commutative law: ab=ba Multiplicative associative law: (ab)c=a(bc) Multiplicative distributive law: A (B+C) = AB+AC.
2. Geometric figure calculation formula
(1) circumference: the length of a circle around an object.
① Rectangular perimeter = (length+width) ×2 C=(a+b)×2 ② Square perimeter = side length× 4c = 4a.
③ Circumference = pi× diameter = pi× radius× 2c = π dc = 2π r.
(2) area: that is, the size of the surface or closed figure of an object.
① area of rectangle = length× width S=ab ② area of square = side length× side length S=a? a=a2
③ area of parallelogram = base × height S=ah ④ area of triangle = base × height ÷2 S=ah÷2.
⑤ trapezoidal area = (upper bottom+lower bottom) × height ÷ 2s = (a+b) h ÷ 26 circular area = pi × radius S=πr2.
⑦ Diameter d=2r Radius = Diameter ÷2 r= d÷2 ⑧ Annular area = outer circle area-inner circle area S-ring =S outside -S inside.
The area formula of related plane graphics is based on the rectangular area calculation formula. For example, two identical triangles and trapezoids can be combined into a parallelogram. The length of a circle is 1/2C and the width is r 。
(3) Surface area: The sum of the areas of all faces of a solid figure is called its surface area.
① The surface area of a cuboid = (length× width+length× height+width× height )× 2s = 2 (AB+AH+BH).
② Surface area of cube = side length× side length× 6s = a× a× 6 = 6a2.
③ lateral area of cylinder = bottom circumference x height S=Ch =2πrh.
④ Surface area of cylinder = lateral area+bottom area× 2s = CH+2π R2 = 2π RH+2π R2.
Note: When the circumference of the cylinder bottom is equal to the height, the lateral expansion is square, and c = H2 π r = h..
(4) Volume: The size of the space occupied by an object is called volume.
① cuboid volume = length× width× height v = abh2 cuboid volume = side length× side length× side length V=a×a×a=a3.
③ Cylinder volume = bottom area × height v = SH = π r2h4 Cone volume = bottom area × height ÷ 3v =1/3sh =1/3π r2h.
The volume formula of cuboid, cube and cylinder which are interrelated can be unified as: V=sh, that is, the bottom area × height.
Long, positive, equal volume and equal bottom cylinders and cones, the height of which is three times that of cuboids, cubes and cylinders.
Three. magnitude relation
65438+ 0× number of shares per share = total number of shares = total number of shares = number of shares = number of shares.
2 unit price × quantity = total price/total price = total quantity/quantity = unit price
3 speed × time = distance distance ÷ speed = time distance ÷ time = speed
4 working efficiency × working time = total workload ÷ working efficiency = total working time ÷ working time = working efficiency
5. Appendix+Appendix = sum, and-one addend = another addend.
6. Minus-Minus = Minus-Minus = Minus+Minus = Minus
7, factor × factor = product product ÷ one factor = another factor
8. Dividend = quotient dividend = quotient × divisor = dividend = divisor × quotient+remainder
Note: 0.3÷0.2= 1. . . The divisor and dividend of 0. 1 are expanded by 100 times at the same time, the quotient is unchanged, and the remainder is also expanded by 100 times.
9 average = total number of copies/average speed of total number of copies = total distance/total time
10. Encounter problem Encounter distance = speed and× encounter time Meet time = meet distance/speed sum.
Sum of speeds = meeting distance/meeting time One person's speed = meeting distance/meeting time-another person's speed.
1 1. Average speed problem Average speed = total distance ÷ (downstream time+countercurrent time) Note: Return (to) = distance ×2.
12. concentration problem: solute (drug)+solvent (water) = solution (drug) solute (drug) ÷ solution (drug) = concentration.
Solution (drug) × concentration = solute (drug) Solute (drug) ÷ concentration = solution (drug)
13. discount: discount = current price ÷ original price (discount < 1) current price = original price × discount original price = current price ÷ discount.
Interest = principal× annual interest rate× time (year) = principal× monthly interest rate× time (month)
14 scale = distance on the map ÷ actual distance = distance on the map ÷ distance on the scale map = actual distance × scale.
After-tax interest = principal × interest rate × time × (1-5%)
15 tracking problem tracking distance = speed difference × tracking time = tracking distance ÷ speed difference.
Speed difference = catching distance ÷ catching time
Error-prone question: 1, perimeter and area are not equal. 2. The area of a circle is out of proportion to its radius. 3. The difference between increasing and expanding, narrowing and decreasing. 4. Calculation of the number and area of floor tiles. 5. The time rate is 60, and the square meter hectare rate 10000. 6. A three-dimensional figure is converted into another three-dimensional figure with the same volume. 7. Fill in the blanks, and pay attention to the unity of the unit (error-prone) in application questions; When asking for a reservation, you don't need to use any method, but use "rounding" or "one-in-one method" according to the actual situation. 8. When calculating the surface area, find out which surfaces should be combined with the actual situation. 9. The forward distance between the wheel and the drum is circumference × revolution. 10, rewrite the decimal point for the number, and then add the unit; Accurate to the next place (when reserved) and expressed by "rounding" method, and then add the unit. 1 1, a triangle with equal base and equal height is half the area of a parallelogram; The volume of a cylinder with equal base and equal height is three times that of a cone. 12, the distance is certain, and the speed is inversely proportional to the time. For example, the time ratio of A and B walking together is 5: 4, and the speed ratio of A and B is 4: 5. The total workload is similar. 13, when you see the height and vertical line, you think of right angles (symbols). 14, the straight line between two points is the shortest, and the vertical line between points is the shortest; Rotating around a point is to take this point as the vertex, make the perpendicular lines on both sides related to this point, and determine the other two points. When rotating counterclockwise, turn left. 15. Pay attention to observation points when determining the direction. 16, pay attention to the number that is a little different from the integer when calculating, such as 9.9; 10. 1。 17, pay attention to * * * equal or invariant analysis when analyzing application problems. Such as the actual and planned total number, the number of girls when boys transfer; Replace tiles with different side lengths in the same area. 18, the area ratio of two circles is the square of the radius ratio; The multiple of graphic area expansion is the square of side length expansion.