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All primary educate to junior high school numbers
formula


1, each = absolute number of shares × ; ÷ absolute number of copies of each number =
÷ total number of shares = each
2, 1 factor × factor = number of times the number of ÷ 1 times multiple = multiple
factor = 1 ÷ the number of times a multiple of
3, speed × time = distance speed = distance ÷ time
time = distance ÷ speed
4, unit price × quantity = total ; price = ÷ total number of
= total price ÷ number

5, the efficiency of the total work × hours = volume
÷ efficiency = total work hours
÷ total hours of work = efficiency
; 6,GHD Hair Straighteners, addend + addend = and and - a one addend = addend
; 7, minuend - subtrahend = difference minuend - subtrahend = difference ;
difference = minuend subtrahend +
8, factor × Factor = a factor = ÷ contrive contrive distinct element
9, dividend ÷ divisor = commerce = Business dividend ÷ divisor
provider × divisor = dividend


primary numerical formula graphics

1, square: C perimeter area of ​​a side perimeter S = side × 4C = 4a
area = side × side length S = a × a
2, cube: V: Volume a: surface area = edge long edge long edge long × × 6
S chart = a × a × 6
Volume = length × edge × edge long edge long V = a × a × a
3, rectangular:
C perimeter area of ​​a side length S ; perimeter = (length + width) × 2 C = 2 (a + b)
area = length × width S = ab
4, rectangular
V: volume s: size a: long b: W h: high
; (1) surface area (length × width + height + length × width × height) × 2 S = 2 (ab + ah + bh)
(2) Volume = length × width × height V = abh
5, an area of ​​a triangle
s high-end h area = base × height ÷ 2 s = ah ÷ 2
triangle = area × 2 ÷ high end
; triangle = district × 2 ÷ by the end of tall
6, parallelogram: s area of ​​a high-end h ; area = base × height s = ah
7, trapezoid: s on the area of ​​a base b h below the high-end
area = (base + down on the base) × height ÷ 2 s = (a + b) × h ÷ 2
; 8 round: S side perimeter Π d = diameter of C r = radius
(1) circumference = diameter × Π = 2 × Π × radius ; C = Πd = 2Πr
(2) area = radius × radius × Π
; 9, cylinder: v volume h: high-s: basal area
r: the radius c: bottom perimeter
; (1) side of the bottom area = circumference × height
(2) surface area = side area + base area × 2
(3) Volume = base area × height
(4) volume = side area ÷ 2 × radius
10, cone: v s at the end of an area of ​​high volume h
r the radius volume = bottom area × elevation ÷ 3


÷ total number of shares =
average

and needy problem formulation
(and + poor) ÷ 2 = large number
(and - aggravate) ÷ 2 = decimal

and fold problem
and ÷ (factor -1) = decimal
; decimal × multiplier = massive mathematics
(or and - decimals = large numbers)

wrong times worse problem
÷ (factor -1) = decimal
; decimal × multiplier = large numbers
(or decimal + SD = large numbers)

planting answers
1, non-closure of the main line of the tree planting issue can be divided into the following three scenarios:
⑴ closed if the non-planting both ends of the line, then:
; number of trees = number of segments + 1 = length ÷ spacing -1
; length = spacing × (number of plant -1)
spacing = length ÷ (number of plant -1)
; ⑵ If the non-closed circle at one end to vegetation trees, not planted the other end, then:
number of trees = number of segments = length ÷ spacing
length = spacing × number of trees
spacing = length ÷ number of trees
⑶ If the line ends in a non-closed are not trees, then:
number of trees = number of segments -1 = length ÷ spacing -1
length = spacing × (number of trees +1)
spacing = length ÷ (number of trees +1)

2, closed the line on the publish of the relationship between the number of tree planting as
number of trees = number of segments = length ÷ spacing
length = spacing × digit of trees
spacing = length ÷ number of trees

profit and loss issues
(profit + loss) ÷ volume of distribution of the difference between the two = to participate in the distribution of copies
(large extra - a small profit) ÷ = ​​twice the difference between the amount allocated to participate in the distribution of copies
(burned - small detriment) ÷ = ​​twice the feud between the quantity apportioned to partake in the distribution of copies

meet problems
encounter distance = speed × time
meet encounter time = distance ÷ speed and
encounter the speed and distance ÷ = meet meet Time

to catch problems
distance = speed chase and chase and the time difference ×
; chase and chase and time = distance ÷ speed difference
speed difference = distance ÷ pursue and chase and period

downstream water problems
hydrostatic speed + speed = flow rate
hydrostatic upstream speed = speed - flow rate
hydrostatic speed = (speed + upstream downstream speed) ÷ 2
stream rate = (downstream speed - upwards rate) ÷ 2

solute concentration problems
weight + weight of solvent = solution weight
÷ solution of the weight of the solute weight × 100% = weight × concentration of solution concentration
= weight of the solute concentration
solute = solution weight ÷ weight

profit and discounts
profit = selling price - cost
margin = Profit ÷ Cost × 100% = (selling price ÷ cost -1) × 100%
; Change Change amount = principal × the percentage of the actual selling price = ÷
deduct the original price × 100% (deduct <1)
Interest = headmaster × rate × time
after-tax amuse = principal × rate × time × (1-20%)

length unit converter
1 km = 1000 m 1 meter = 10 decimeter
1 decimeter = 10 cm 1 measure = 100 centimeters
; 1 cm = 10 mm

area element conversion
1 square km = 100 hectares
; 1 hectare = 10,000 square meters
1 square meter = 100 square decimetres
; 1 square decimeter = 100 cm2
1 平方 cm = 100 mm2

body (content) product unit conversion
1 cubic meter = 1000
1 cubic decimeter cubic decimeter = 1000 cubic centimeters
1 cubic decimeter = 1 liter
1 立方厘米 = 1 ml
1 cubic meter = 1000 l

Weight unit conversion

1 ton = 1000 kg
; 1 kg = 1000 g = 1 kg
1 千克

RMB unit conversion
1 yuan = 10 jiao
; an angle = 10
1 dollar = 100 cents

time unit conversion
1 century = 100 years 1 year = December
big month (31 days): 1 3 5 7 8 10 December
Satsuki (30 days) are: 4 6 9 November
; non-leap year February 28 days, a leap year bound year February 29 天
365 days a year ; leap year 366 days
1 daytime = 24 hours 1 hour = 60
1 min = 60 seconds, 1 hour = 3600 seconds

Primary Mathematics geometry perimeter area volume formula

1, the rectangular perimeter = (length + width) × 2 C = (a + b) × 2
; 2, the perimeter of the square side length × 4 = ; C = 4a
3, rectangular area = length × width ; S = ab
4, area = side of square length × side length S = aa = a
5, the area of ​​the triangle = base × height ÷ 2 S = ah ÷ 2
6, the area of ​​parallelogram = base × height ; S = ah
7, the area of ​​trapezoid = (bottom + down on the base) × height ÷ 2 ; S = (a + b) h ÷ 2
8, diameter = radius × 2 d = 2r ; Radius = diameter ÷ 2 r = d ÷ 2
9, circumference of a circle = pi × pi × diameter = radius × 2 c = πd = 2πr
10, the circle area = pi × radius × radius

general navel school math

1 and only had two points a straight line
; 2 the shortest line between two points with the angle or isometric
3 of the additional angle equal
4 with the complementary angle equal to angle or isometric
5 and only a little over a straight line and understood straight line perpendicular to
6 point outside the points joined with straight line segments in all, the shortest vertical segment
7 point outside a straight line through the parallel axiom,GHD Diamond National Flag,
and only a straight line parallel with this line if two lines are
8 and a third line parallel to the two lines are parallel to each other
9 corresponding angles are equal, the two straight lines parallel to the
; 10 interior angles are equal, the two straight lines parallel to the
11 with the afterward complementary angles, 2 straight lines parallel to the
; 12 two parallel lines, corresponding angles are equal
13 two parallel lines, within the two angles are equal
14 straight line parallel with the contiguous complementary angles on both sides of the triangle theorems
15 and greater than the third side
16 inference on both sides of the triangle is fewer than the third side
17 angles of a triangle and three angles of a triangle theorems and equal to 180 °
; 18 Corollary 1 The two right-angled triangle acute angle than
19 each inference exterior angle of a triangle is equal to 2 and It is not adjacent to two angles and
20 Corollary 3 is greater than the exterior angle of a triangle and it is not adjacent to any one of the angles
21 congruent triangles correspond to edges, corresponding angles are equal
22 corners meantime axiom (SAS)
both sides and their angles are equal to the corresponding two triangles congruent angle corner axiom
23 (ASA)
with corners and edges corresponding to the same folder they are two triangles congruent
24 Corollary (AAS)
have corners and edges which correspond to the same corner of the two triangles congruent
25 Collage while axiom (SSS) with the corresponding three sides of two triangles congruent equal
26 bevel, right angle side axiom (HL)
a bevel corner and a corresponding right-angle triangle equal two congruent
27 Theorem 1 the angle bisector of the angle on both sides point to the same distance from
28 Theorem 2-1 from the corner on both sides of the same point, in this corner bisector
29 angle to the angle bisector is equidistant from both sides of the set of all points
30 isosceles triangle isosceles triangle theorem of the nature of the two bottom corners are equal
(that is, on the other side isometric)
31 Corollary 1 isosceles triangle angle bisector split the base and the bottom
32 isosceles triangle is perpendicular to the angle bisector, the bottom edge of the center line and the bottom edge of the high overlap with each other
33 Corollary 3 of the corners of an equilateral triangle are equal, and each angle is equal to 60 °
; Theorem 34 to determine if an isosceles triangle has two angles are equal,
then the two angles are also equal to the edge (isometric to the other side)
35 inference 1 three angles are equal triangle is an equilateral triangle
36 Corollary 2 has an angle of an isosceles triangle is equal to 60 ° equilateral triangle
37 In the right triangle, if one acute angle equal to 30 °
then it is equal to the hypotenuse of a right-angle side of half
38 on the hypotenuse of the midline on the hypotenuse is equal to half the
39 Theorem perpendicular bisector of the line point and the two endpoints of this segment equidistant
; 40 converse and a line equidistant from the two end points,
in this segment of the vertical bisector
41 perpendicular bisector of line segment and the segment can be seen as equidistant from the two end points of the set of all points of Theorem 1
42 symmetrical about a straight line plot is congruent shape
two 43 Theorem 2 If two graphics on a straight-line symmetry,GHD Leopard Grain Straighteners,
then the corresponding point of the connection axis of symmetry is the vertical bisector
44 Theorem 3 on two graphics a linear symmetry,
if their corresponding segments or extend the lines across, then the intersection of the axis of symmetry
45 converse ; if the two graphs corresponding to the point of connection is a straight line with the vertical,
then the two graphics on this line symmetry
46 two right-angle triangle the Pythagorean theorem sides a, b of the square and,
equal to the square of the hypotenuse c, ie a ^ 2 + b ^ 2 = c ^ 2
47 Pythagorean theorem converse
If the triangle triangular
long a, b, c a relationship a ^ 2 + b ^ 2 = c ^ 2,
then the triangle is right triangle
48 Theorem quadrilateral interior angle equal to 360 °
49 quadrilateral Waijiao and equivalent to 360 °
50 polygon angles Theorem n-gon angles and equivalent (n-2) × 180 °
51 deduction equal to any multilateral exterior angle and 360 °
52 parallelogram parallelogram of the nature of Theorem 1 is equal to the angular nature of
53 parallelogram parallelogram's Theorem 2 from the opposite side
54 inference sandwiched between two parallel line segments parallel to the nature of a parallelogram equal
55 Theorem 3 diagonal parallelogram bisect each other
Theorem 56 to determine the parallelogram 1
two diagonal are equal quadrilateral is a parallelogram parallelogram
57 Theorem 2 to determine
two sides were equal to the quadrilateral is a parallelogram parallelogram
58 Judgement Theorem 3
diagonals bisect each other the quadrilateral is a parallelogram parallelogram
59 Judgement Theorem 4
a set of edges parallel to the quadrilateral is a parallelogram equal to the rectangular nature of Theorem 1
60 the four corners of the rectangle are right angles
61 rectangular nature of Theorem 2 ; rectangle diagonal equal
62 rectangles to determine the 3 angles is Theorem 1 right-angled quadrilateral is a rectangle
63 Theorem 2 to decide the diagonal of the rectangle equal to the parallelogram is a rectangle
64 diamond diamond nature of the Theorem 1 of the 4 sides are equal
65 diamond diamond diagonal nature of Theorem 2 perpendicular to each other,
and each diagonal split a diamond-shaped area on the turn
66 = product of the diagonal half, or S = (a × b) ÷ 2
67 diamond Theorem 1 to determine the four sides of the quadrilateral is a rhombus are equal
; 68 diamond Theorem 2 to determine the diagonal of the parallelogram are perpendicular to each other diamond
69 square nature of the Theorem 1 the four corners of a square are right angles, four sides are equal
70 square nature of Theorem 2 a square equal to two diagonal ,
and perpendicular to each other equally, and each diagonal split a diagonal
71 Theorem 1 on centrosymmetric two graphics are congruent
72 Theorem 2 on the center of symmetry of the two graphics,
symmetrical connections have been the center of symmetry, and is a center of symmetry converse equally
73 ; if the two graphs corresponding to the point of connection is through a decisive point,
and was this split, then the two graphics on this isosceles symmetry
74 isosceles trapezoid trapezoidal nature of the Theorem on the same end of the two angles are equal
75 of the two diagonals are equal isosceles trapezoid
Theorem 76 to determine the isosceles trapezoid
the same at the end of the two angles are equal isosceles trapezoid is equal to the diagonal stepladder
77 The trapezoid is isosceles trapezoid
78 equal parts parallel segments Theorem
If a set of parallel lines in a straight line intercepted on the same line,
then intercepted on the other line segments are equal
79 Corollary 1 after the midpoint and trapezoidal behind end of a parallel line, will split the other waist
80 Corollary 2 through the side of the midpoint of the triangle parallel with the other side of the line,
will split the third side
81 triangle theorem of the triangle median line median line parallel to the the third side,
and equal to its half of the centre line
82 trapezoid trapezoid theorems parallel to the median line two at the end,
and equal to half and two at the end
; L = (a + b) ÷ 2 S = L × h
83 (1) proportion of the elementary nature of the
If a: b = c: d, then ad = bc if ad = bc,
then a: b = c: d
84 (2) the nature of cooperation than if a / b = c / d,GHD, then (a ± b) / b = (c ± d) / d
85 (3) If the geometric nature of the a / b = c / d = ... = m / n (b + d + ... + n ≠ 0),
then (a + c + ... + m) / (b + d + ... + n) = a / b
86 parallel line segments proportional to the theorem of three sub-parallel lines cut two straight,GHD Precious Gift Set,
from the corresponding proportion
87 section inference straight line parallel apt the tear the additional side of the triangle aboard either sides
(or both sides of the extension cord), the proceeds of the line ought be proportional to
88 Theorem If a line cut both sides of a triangle
(or both sides of the enhancement cable) from the corresponding line segments proportional,
then this line parallel to the triangle's third side
89 parallel to the side of the triangle, and, and other on both sides of the intersection of a straight line,
intercepted by the triangle's three sides and the corresponding sides of a triangle is proportional to the original
90 Theorem straight line parallel to the side of the triangle and the other side
(or both sides of the extension line) intersect, a triangle formed by the triangle similar to the incipient Judgement theorem of similar triangles
91 1 corresponds to the same corners, the two triangles are similar (ASA)
92 is the hypotenuse of a right triangle into two right-angled triangle and high raw triangle similar
93 to determine the proportion corresponding to Theorem 2 and the angle between the two sides are equal,GHD IV Mini Straighteners,
two triangles are similar (SAS)
94 to determine the corresponding Theorem 3 into a trilateral percentage, the two triangles are similar (SSS)
95 Theorem If the hypotenuse of a right triangle and a right angle with another side of the hypotenuse of a right triangle and a right angle is proportional to the corresponding side, then the two triangles are similar
96 triangles correspond to the nature of Theorem 1 is similar to the high ratio corresponds to the center line than the corresponding angle bisector is equal to the ratio of similar nature than
97 is similar to Theorem 2 is similar to a triangle is equal to the ratio of the circumference than
98 properties similar to Theorem 3 is similar to the triangle area ratio is equal to the square of
99 than the sine of any acute angle is equal to the cosine of its complementary angle, any the cosine of an acute angle equal to its complementary angle of the sine
100 acute angle of the tangent is equal to any of its complementary angle of the cotangent, any acute angle equal to the cotangent its complementary angle of the tangent
101 circle is a nailed distance equal to the length of the set of points
102 inside the circle can be seen as the distance is less than the radius of the center point of the set
103 outside the circle tin be discerned as the distance is greater than the radius of the center point of the set
104 know next to nothing of round the same circle of radius equal
105 to a fixed distance equal to the length of the locus of points , is designated as the center, fixed-length circle of radius
106 and the known line equidistant from the two ends of the locus of points is the perpendicular bisector of segment
107 to a known angular distance equal points on both sides of the pathway, is the angle bisector
108-2 parallel lines equidistant from the locus of points, and it is these two parallel lines and parallel to a straight line from the period of the Theorem
109 not in the same three points determine a straight line a circle.
110 vertical diameter Theorem
diameter perpendicular to the string split this string by string and split on the two arcs
111 Corollary 1.
① split string (not diameter) of the diameter perpendicular to the string,
and split the string by two arcs of string
② vertical bisector through the center of the circle, and split the string by two arcs of split strings
③ the diameter of an arc, vertical split string,
and split the string by another one on the arc
112 Corollary 2 round mow of two parallel strings of arc equal
113 round center for the center of symmetry is the center of symmetry
114 theorems in the same circle or other circuitous , the equivalent of the arc of the chief angle is equal,
the equal of the chord, the chord of the center strings of equal
115 deduced from the and round the same circle or, if the two central angle, two arcs, two string or two strings of the heart strings in a set amount from the same so that they correspond to the amount of the other groups are equal
Theorem 116 of the circumference of an arc of the angle of the central angle is equal to its half
117 Corollary 1 with the arc alternatively so the arc of the circuit of the angles are equal; and round the same circle or in equal circumferential angle of the arbitrage of Corollary 2 is also equal
118 semicircle (or diameter) of the right the circumference of the angle is right angle; 90 ° circumferential angle of the diameter of the string is
119 Corollary 3 If the center line on the side of a triangle is equal to half the side, then the triangle is theorem of right triangle
120 quadrilateral inscribed circle of the complementary angle, and any appearance angle is equal to its angle within
; 121 ① ⊙ O line L and intersects the d r
; 122 Tangent Theorem to determine the radius of the outer end and through the vertical radius of this circle tangent line is tangent to the nature of Theorem
123 ; circle tangent perpendicular to the radius through the cut-off point through the center
124 Corollary 1 and vertical to the tangent line will pass through cut-off point
Corollary 2 after 125 cut-off point and perpendicular to the tangent line will pass through the centre
126 long Theorem from outside the circle tangent point guide round two tangent, so they are tangent Zhang Xiang, the center point of connection and split the angle between two tangent
127 round circumscribed quadrilateral two of the side and equal
128 Xian Qiejiao Theorem Xian Qiejiao equal to its arc on the circumference of the clip angle
; 129 deduction if the direcotry two Xianqie Jiao arc equal,
then the two Xianqie Jiao also equal
130 intersect within the circle theorem of two strings intersection string,
intersection divided along the production of two equal length segments
131 deduction if the strings intersect with the vertical diameter,
then string it points to half the diameter into two segments of cutting the proportion of items in the
132 Theorem from the point appearance line round the circle tangent and secant cited,
tangent to the secant long is this intersection of two line segments and circle the proportion of long-term
133 deduced from outside the circle round the two secant point lead, which is secant to each intersection of two circles with long product segment equal
134 If the tangent to two circles, then cut point have to be in line with the heart outside the circle
135 ① two from d> R + r
② two round exo d = R + r
③ two circles intersect Rr r)
④ two circle cut d = Rr (R> r) ;
⑤ two circles involving d r)
136 Theorem ; intersection of two circles with the center line perpendicular bisector of two circles theorems public string
137 into the circular n (n ≥ 3):
; ⑴ in rotate correlate the points from the polygon is the circle inscribed regular n-gon