(1) Find out the range of the original data, and what are the maximum and minimum values respectively;
(2) According to the needs of statistics and the specific situation of data range, the data range is divided into several groups, arranged in a certain order, and made into tables;
(3) Count the number of original data in each group and fill in the statistical table. Unit 2 ● The edge where two faces intersect is called an edge. The point where three sides intersect is called a vertex. A cuboid is a three-dimensional figure surrounded by six rectangles (in special cases, two opposite faces are squares). In a rectangular body, the opposite faces are exactly the same, and the opposite sides are equal in length. There are 6 faces, 12 edges and 8 vertices. The length of three sides intersecting at a vertex is called the length, width and height of a cuboid. ● 12 edges can be divided into three groups. The first group has parallel and equal opposite edges. A cube is a three-dimensional figure surrounded by six identical squares. A cube also has 12 sides, all of which have the same length. A cube also has eight vertices. The number of faces, edges and vertices of cubes and cuboids is the same; Only the edges of the cube are all equal. A cube can be said to be a cuboid with equal length, width and height. It is a special cuboid. The total area of six faces of a cuboid or cube is called its surface area. The size of the space occupied by an object is called its volume. Unit of volume is used to measure volume, and commonly used unit of volume is cubic centimeter, cubic decimeter and cubic meter. ● A cube with a side length of 1cm and a volume of 1cm. ● A cube with a side length of 1 decimeter has a volume of 1 cubic decimeter. A cube with a side length of 1m and a volume of 1m3. ● cuboid volume = length× width× height ● cube volume = side length× side length× side length ● cuboid (or cube) volume = bottom area× height ● 1 cubic decimeter = 1000 cubic centimeter ● 1 cubic meter = 1000. 100 The propulsion rate between two adjacent unit of volume is 1000 ● The volume is measured, so unit of volume is generally used. The common units of volume are liters and milliliters ● 1 liter = 1000 ml/liter = 1 cubic meter 1 milliliter = 1 cubic centimeter The third unit ● Integer A divided by Integer b(b≠0). Suppose A is divisible by B (or B is divisible by A) ● If A is divisible by B (b≠0), then A is called a multiple of B, and B is called a divisor of A (or a factor of A). The divisors of multiples are interdependent ● The divisor of a number is finite, in which the smallest divisor is 1 and the largest divisor is itself. The number of multiples of a number is infinite, and the smallest multiple is itself. ● Numbers that are divisible by 2 are called even numbers, and numbers that are not divisible by 2 are called odd numbers.
Natural numbers are divided into even numbers and odd numbers. Because 0 can also be divisible by 2, 0 is even. A number with a bit of 0 or 5 can be divisible by 5. The sum of the numbers on each digit of a number can be divisible by 3, and this number can be divisible by 3. And a number. If 1 and itself have only two divisors, such numbers are called prime numbers. A number is called a composite number if there are other divisors besides 1 and itself. ● 1 is neither a prime number nor a composite number. ● 100 Internal Quality Table: 235711319 23 29 3137 4143 47 53 59 6167 765438+ Every prime number is a factor of this composite number, which is called the prime factor of this composite number. When a composite number is expressed by multiplying a prime factor, it is called prime factor decomposition. ● Decompose a composite number into prime factors, first divide it by a prime number that can divide the composite number evenly (generally starting from the smallest). If the quotient is prime, write the divisor and quotient as multiplication; If the quotient is a composite number, continue to divide by the above method until the quotient is a prime number, and then write each divisor and the final quotient in the form of multiplication. The common divisor of several numbers is called the common divisor of these numbers; The largest one is called the greatest common divisor of these numbers. The common divisor is only 1, which is called a prime number. To find the greatest common divisor of two numbers, the common prime factor of these two numbers is generally used to divide them continuously until the quotient obtained is a prime number. Then multiply all the divisors. In the process of division, sometimes you can divide by the common divisor of two numbers. If the smaller number is the divisor of the larger number, then the smaller number is the greatest common divisor of these two numbers. ● If two numbers are prime numbers, their biggest convention is 1. The common multiple of several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers. Find the least common multiple of two numbers. Divide these two numbers by the common prime factor (usually starting from the smallest) until the quotient is a prime number, and then multiply all the divisors by the last two quotients. If the larger number is a multiple of the smaller number, the larger number is the least common multiple of the two numbers. If two numbers are prime numbers, then the product of these two numbers is their least common multiple.
Unit 4 ● An object, a unit of measurement or a whole composed of many objects can be expressed by a natural number 1, which we usually call the unit "1". ● Divide the unit "1" into several parts on average, and the number representing such a part or parts is called a fraction. ● In the score, the horizontal line in the middle is called the score line; The number below the fractional line is called the denominator, indicating how many copies the unit "1" is divided into on average; The number above the fractional line is called numerator, indicating how many copies there are. ● Divide the unit "1" into several parts on average, and the number representing one part is called decimal unit. ● Fractions can represent the quotient of integer division. When expressing the quotient of integer division, the divisor should be the denominator and the dividend the numerator. In integer division, the divisor cannot be 0. The denominator in the score cannot be 0 either. ● For two fractions with the same denominator, the fraction with larger numerator is larger. ● For two fractions with the same numerator, the fraction with the smaller denominator is larger. ● Fractions with numerator less than denominator are called true fractions. The true score is less than 1. ● Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions. The error score is greater than 1 or both are equal to 1. A false score can be written as a number consisting of an integer and a true score, which is usually called a score. ● To turn a false fraction into an integer or a fraction, use the denominator to remove the numerator. Divisible, quotient is an integer; If it is not divisible, the quotient is the integer part with a fraction, the remainder is the numerator of the fraction part, and the denominator remains unchanged. ● Integers (except 0) can be divisible into false fractions whose mother is 1, 2, 3, 4, 5, …. Turn an integer (except 0) into a false fraction, use the specified denominator (except 0) as the denominator, and use the product of the denominator and the integer (except 0) as the numerator. Turn the band fraction into a false fraction, use the original denominator as the denominator, and use the product of denominator and integer plus the sum of the original molecules as the numerator. ● The numerator and denominator of a fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged. ● Applying the basic properties of fractions, a fraction can be divided into fractions with different parents and equal size. ● Changing a fraction into a fraction equal to it, but with smaller numerator and denominator, is called a reduced fraction. A fraction whose numerator and denominator are prime numbers is called simplest fraction. ● Note: Try to calculate the score by mouth, and generally use the common divisor of the numerator and denominator (except 1) to remove the numerator and denominator of the score; Usually, we have to separate it until we get the simplest score. ● In order to compare or calculate scores, it is sometimes necessary to divide scores with different denominators into scores with the same mother number according to their basic properties. ● Changing scores of different denominators into scores of the same denominator is equal to the original score, which is called the total score. ● The general method of general division is: first find the least common multiple of the original denominator, and then take this least common multiple as the denominator to turn each fraction into a fraction. ● Decimal represents the number of components. There are several decimals. Just write a few zeros after 1 as the denominator and remove the decimal point of the original decimal as the numerator; After the number of components, the number of quotation points can be reduced. ● The denominator is fractional decimal 10, 100, 1000, … You can directly remove the denominator, and look at the zero after 1 in the denominator, just count a few numbers to the left from the last digit in the numerator and point the decimal point. ● Denominator is not fractional decimal 10, 100, 1000 ..., and numerator should be removed by denominator; If the numerator is divided by the denominator, you can keep several decimal places according to the rounding method as needed. A simplest fraction, if the denominator does not contain other prime factors except 2 and 5, this fraction can be reduced to a finite decimal; If the denominator contains prime factors other than 2 and 5, the fraction cannot be reduced to a finite decimal.
Unit 5 ● Fractional addition has the same meaning as integer addition, and it is an operation that combines two numbers into one number. ● Fractional subtraction means the same as divisible subtraction, and it is an operation to find the other addend by knowing the sum of two addends and one of them. ● Fractions with the same denominator are added and subtracted, and the denominator remains the same, only the numerator is added and subtracted. ● Add and subtract fractions with different denominators, and divide another addend first. The commutative law and associative law of integer addition are also applicable to fractional addition.