Prime numbers and prime numbers:
There is no connection between these two concepts. Two prime numbers are not necessarily prime numbers, such as 5 and 5. Only two different prime numbers can be sure to be prime numbers. In addition, two composite numbers may or may not be prime numbers, but it cannot be said that two composite numbers must not be prime numbers.
Prime factor: decompose a composite number into the form of multiplication of several prime numbers. Such prime numbers are called prime factors.
Prime factor decomposition: the form of decomposing a composite number into several prime numbers is called prime factor decomposition.
Common multiple: A multiple shared by several numbers. It is called a common multiple, and its number is infinite, only the smallest, not the largest.
Greatest common factor: Among the factors shared by several numbers, the largest one is called the greatest common factor of these numbers.
Least common multiple: among the infinite multiples shared by several numbers, the smallest one is called the least common multiple of these numbers.
Characteristics of multiples of 2:
Numbers in units of 0, 2, 4, 6 and 8 are multiples of 2. Numbers that are multiples of 2 are called even numbers, and numbers that are not multiples of 2 are called odd numbers.
Characteristics of multiples of 5: A number of 0 or 5 digits is a multiple of 5.
Characteristics of multiples of 3: the sum of digits of a number is a multiple of 3, and this number is a multiple of 3.
It is a multiple of 2, 3 and 5 at the same time: the unit must be 0. The minimum two digits that are multiples of 2, 3 and 5 at the same time are 30, and the minimum three digits are 120.
How to judge whether a fraction can be converted into a finite decimal: A simplest fraction can only be converted into a finite decimal if its denominator is a prime factor "2 or 5". If it contains prime factors other than 2 and 5, it cannot be reduced to a finite decimal.
General score and reduced score (according to the basic nature of the score):
Total score: Divide several scores with different denominators into scores with the same number and size, which is called total score.
Approximate fraction: Changing a fraction into an equal fraction with smaller numerator and denominator is called approximate fraction.
Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentage is also called percentage or percentage. The percentage cannot exceed 100%.
Ordinary year and leap year of Gregorian calendar year:
Average year: when the Gregorian calendar year is divided by 4 (here, it is not 100 whole Gregorian calendar years) and there is a remainder, it is called a 365-day average year. February has 28 days.
Leap year: when the Gregorian calendar year is divided by 4 (here is not a full 100 Gregorian calendar years) and there is no remainder, this year is called leap year. 366 days. February has 29 days. If the year is whole hundred, divide it by 400 and see the remainder. The judgment method is the same as above.
Ratio and ratio:
Ratio: The division of two numbers is also called the ratio of two numbers. The number A divided by the number b(b≠0) can be called the ratio of A: B. A/b, which can also be expressed in fractional form.
Ratio: the quotient obtained by dividing the former term by the latter term is called ratio. Comparison and comparison are different. For example, 5/7 can be regarded as both ratio and ratio. But the score can only represent a proportion. The ratio has no company name.
The basic property of ratio: When the first term and the last term of the ratio are multiplied or divided by the same number (except 0), the ratio remains unchanged.
Simplify ratio: Simplify a ratio to the simplest integer ratio, which is called ratio simplification. Usually, the basic properties of ratio are used to simplify the ratio, and the ratio can also be calculated. In general, the ratio after simplification and the two terms before and after simplification are prime numbers.
Proportion: Two expressions with equal proportions are called proportions.
Basic property of proportion: In proportion, the product of two external terms equals the product of two internal terms, which is called the basic property of proportion.
Scale: The ratio of the distance on the map to the actual distance is called the scale of this map. A scale is a ratio. There are two scales: numerical scale and line scale, which can be converted to each other.
Proportional ratio: two related quantities, one change and the other change. If the ratio (that is, quotient) of the corresponding two numbers in these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. Expressed in letters: y/x = k (certain)
Inverse proportion: two related quantities, one of which changes and the other changes accordingly. If the product of the corresponding two numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. Use letters to indicate y x=k (certain)
Equation: An equation with an unknown number is called an equation. (Note: It is not "an equation with unknowns is called an equation")
Solution of the equation: the value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation.
Solving equations: The process of solving equations is called solving equations.
Features of bar graphs: The number of each bar graph needs to be clearly displayed.
Features of folded statistical chart: When using broken-line statistical chart, not only the quantity of various quantities should be displayed, but also the changes of various quantities can be clearly seen.
The characteristics of fan-shaped statistical chart: clearly show the percentage of each part in the whole.
Average value: the average value represents the "average level" of this group of data. When calculating the average value, divide the sum of all data by the number of data, and the number is the average value of this group of data. In most cases, the average value is used, but it cannot be used if it is affected by very small data.
Median: The median represents the "medium level" of this set of data. To find the median, we must first sort (from small to large or from large to small), and then according to the number of data, when the data is odd, the middle number is the median; When the data is even, the average of the middle two numbers is the median. It can be used when the average value cannot be used because the data has little influence.
Mode: The number with the highest frequency in a set of data is called the mode of this set of data. Majority stands for "majority level". Available when the number of public data accounts for the majority of the total number. Straight line: it has no end points and can extend to both ends indefinitely.
Straight line: it has no end points and can extend to both ends indefinitely.
Ray: Only one endpoint can extend to one end indefinitely. A straight line and a ray cannot be compared in length.
Line segment: There are two endpoints. Both ray and line segment are part of a straight line. Between two points, the line segment is the shortest.
Parallel lines: Two straight lines that do not intersect the same plane are called parallel lines.
Vertical line and vertical foot: When two lines intersect and an angle is right, they are said to be perpendicular to each other. One of the straight lines is called the perpendicular of the other straight line, and its intersection point is called the vertical foot. In the line segment drawn from a point outside the line to the line, the vertical line is the shortest.
Angle: acute angle (greater than 0 and less than 90), right angle (equal to 90), obtuse angle (greater than 90 and less than 180), right angle (equal to 180), rounded corner (equal to 360).
Characteristics of cuboids and cubes: cuboids and cubes have 6 faces, 12 sides and 8 vertices; The difference between them is that at least four faces of a cuboid are rectangles, while six faces of a cube are squares. A cube can be regarded as a special cuboid.
Characteristics of cylinders and cones:
A cylinder has three faces, the upper and lower faces are called bottom faces, and the other face is called side faces. A cone has two faces, the west is round and the side is fan-shaped. In the case of equal bottom and equal height, the volume of a cylinder is three times that of a cone, and the volume of a cone is one third of that of a cylinder.
Area and occupied area: area is used to indicate the size of the surface of an object; The floor space is the size of the floor space (the area at the bottom of the three-dimensional figure).
Volume and volume (capacity):? Volume measures data from the outside, and volume measures data from the inside.
Volume: The size of the space occupied by an object is called the volume of the object.
Volume: The volume of the object that a container can hold is called volume.
Axisymmetric graphics: If a graphic is folded in half along a straight line, the graphics on both sides can completely overlap. This figure is called an axisymmetric figure, and this straight line is called an axis of symmetry. When you draw the symmetry axis, you should draw a dotted line, and both sides should stand out (this is because the symmetry axis is a straight line).
Surface area: The area of all the surfaces of a three-dimensional figure is called its surface area.
Formula:
1, square:? Perimeter = side length× 4c = 4a Area = side length× side length s = a2
2. rectangle:? Circumference = (length+width) × 2 c = 2 (a+b)
Area = length × width s = ab
3. parallelogram: area = base × height S = AH height = area ÷ base = area ÷ height.
4. Triangle:
Area = bottom × height ÷ 2s = ah ÷ 2
Height of triangle = area ×2÷ base.
Triangle base: area ×2÷ height
5, trapezoidal:
Area = (upper bottom+lower bottom) × height ÷ 2s = (a+b )× h ÷ 2.
Find the height: list the solution of the equation according to the area formula.
6, round:
Circumference = diameter× π c = π d or circumference = 2× radius× π c = 2 π r.
Area = pi × radius× radius s = π r?
7. Cube:
Surface area = side length × side length× ×6 S table = 6a?
Volume = side length x side length x side length v = a3
8. Cuboid:
Surface area (length× width+length× height+width× height )× 2s = 2 (AB+AH+BH)
Volume = length× width× height v = abh
9. Cylinder:
(1) lateral area = bottom circumference × height s = 2π rh.
(2) surface area = lateral area+bottom area s = 2π RH+2π r?
(3) volume = bottom area × height v = π r? h
10, cone: volume = bottom area × height ÷ 3 V = 1/3sh.
Find the height: list the solution of the equation according to the volume formula.
1 1, interest = principal × interest rate× after-tax time interest = principal × interest rate× time × (1-5%)
Taxable amount = turnover × tax rate net income = turnover-taxable amount
Prepayment rate:
Length:
1km1000m1m = l0 decimeter? 1 decimeter =10cm
1cm = 10mm 1m = 100cm
Area (building area):
1 km2 = 100 hectares l hectares = 10000 square meters.
1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter
Volume (Volume):
L cubic meter = 1000 cubic decimeter
1 cubic decimeter = 1000 cubic centimeter
L l = 1000 ml
1 cubic decimeter = 1 liter l cubic centimeter = L ml.
Mass:1t =1000 kg1kg =1000 mg.
Time: l century = 100 1 year = 12 months.
The big moon (1, 3, 5, 7, 8, 10, 12) has 3l days; Abortion (4, 6, 9, 1 1) lasts for 30 days; There are 28 days in February in a normal year and 29 days in February in a leap year.
1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds.
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