Number:
Integer, natural number, positive number, negative number, fraction, decimal number.
Counting units and numbers
Counting units, numbers and decimal counting methods.
Rewrite Numbers (Omit)
1. Rewrite multiple numbers into "10,000" and "100 million".
Direct rewrite:
First, move the decimal point of the original number to the left by 4 or 8 places (the end of the decimal part is 0 to be crossed out), then add 10000 or 10000 million, and add "=" in the middle.
The omitted mantissa is rewritten as a divisor:
Omit the mantissa after 10,000 digits or 100 million digits by rounding, then add 10,000 digits or 100 million digits after the digit to get the approximate number, and add "√" in the middle.
2. Find the decimal approximation.
According to the requirements, wherever decimal places are reserved, the mantissa after this digit should be omitted by rounding, such as 1.5 ≈ 2, 1.4 ≈ 1. Use ""in the middle.
3. Reciprocity between false fraction and band fraction or integer.
1. Turn a false fraction into a fraction: the denominator is unchanged, the integer obtained by dividing the numerator by the denominator is the integer part with the fraction on the left, and the remainder is the numerator.
2. Turn the band fraction into a false fraction: the denominator is unchanged, and the numerator is the product of the sum of the integer part and the denominator plus the original molecule.
3. Divide the band into integers: divider ÷ divider = divider/divider, and the divisible band is an integer.
Interoperability among fractions, decimals and percentages.
Fractional decimals, that is, numerator divided by denominator, are decimals. When converted into percentages, it is to multiply decimals by 100 and then add a% sign after it, and vice versa.
For example, 1/4 is converted into decimal, that is, 1 divided by 4=0.25 is decimal, and then converted into percentage, that is, 0.25* 100=25 plus% is 25%.
If 25% is converted into a decimal, that is, the percentage sign is removed, now it is divided by 100 25/ 100=0.25.
The component number of 0.25 is 25/ 100 and then simplified to 1/4.
Digital comparison:
Integer size comparison, decimal size comparison and fractional size comparison.
The essence of numbers:
The basic properties of fractions and decimals and the changing law of decimal size caused by the movement of decimal position.
Understanding of numbers:
Factor, multiple, odd number (jρ), even number, prime number (prime number), composite number, factorization prime factor, greatest common factor, least common multiple.
The significance and counting method of four operations;
Addition meaning, subtraction meaning, multiplication meaning, division meaning, addition, subtraction, division, multiplication and check calculation.
Algorithms and simple methods, elementary arithmetic;
Additive commutative law (a+b=b+a), additive associative law (a+(b+c)=(a+b)+c), multiplicative commutative law (a*b=b*a), multiplicative associative law (a*(b*c)=(a*b)*c), and multiplicative distributive law.
Subtraction property: a-(b+c) = a-b-ca-(b-c) = a-b+c.
Classification of operations: addition and subtraction are called first-order operations; Multiplication and division are called two-stage operations (abbreviated).
Composite application problem:
Formulas and equations:
Equation.
Unit of measurement:
The speed of progress between length, area and volume, and their similarities.
Quality units and the progress between them
1 ton = 1000 kg = 1000 g.
Time unit exchange rate
1 hour =60 minutes 1 minute =60 seconds
1 = 10.
Ratio and proportion:
Positive proportion, inverse proportion, simplified proportion, ratio, ratio and fraction, division, ratio, proportion, solving application problems with proportion
Graphics and space:
Graph, space, perimeter, area, lateral area, surface area, graph transformation, graph and position, graph understanding and measurement.
Statistics and possibilities:
Statistical table, statistical chart, average, median, mode, possibility
(1) Integer:
Meaning of integer 1: … Numbers like -4, -3, -2,-1, 0, 1, 2, 3, … are called integers.
2 natural numbers: when we count objects, 1, 2, 3 ... the numbers used to represent the number of objects are called natural numbers. There is no object, which is represented by 0.
3 Counting unit:
One, ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million ... are all counting units.
The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.
4 digits
Counting units are arranged in a certain order, and their positions are called numbers.
Divisibility of 5 numbers: the integer A is divisible by the integer B (b≠0), and the divisible quotient is an integer without remainder, so we say that A is divisible by B, or that B is divisible by A. ..
If the number A is divisible by the number B (b≠0), then A is called a multiple of B, and B is called a divisor of A (or a factor of A). Multiplication and divisor are interdependent.
Because 35 is divisible by 7, 35 is a multiple of 7, and 7 is a divisor of 35.
7. What is the ratio? The division of two numbers is called the ratio of two numbers. Such as: 2÷5 or 3:6 or 1/3.
The first and second items of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.
8. What is proportion? Two formulas with equal ratios are called proportions. For example, 3:6=9: 18
9. Basic properties of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.
10, solution ratio: the unknown term in the ratio is called the solution ratio. Such as 3:χ=9: 18.
Solution ratio is based on the basic nature of proportion.
1 1, ratio: two related quantities, one changes and the other changes. If the corresponding ratio (i.e. quotient k) of these two quantities is certain, these two quantities are called proportional quantities, and the relationship between them is called proportional relationship. For example: y/x=k(k must be) or kx = y.
12, inverse ratio: two related quantities, one changes and the other changes. If the product of two corresponding numbers in these two quantities is certain, these two quantities are called inverse proportional quantities, and their relationship is called inverse proportional relationship. For example: x×y=k(k must be) or k/x = y.
Percentage: a number that indicates that one number is a percentage of another number, which is called percentage. Percentages are also called percentages or percentages.
13. To convert decimals into percentages, just move the decimal point to the right by two places and add hundreds of semicolons. In fact, to convert a decimal into a percentage, just multiply this decimal by 100%.
To convert percentages to decimals, simply remove the percent sign and move the decimal point two places to the left.
14. When a fraction is converted into a percentage, it is generally converted into a decimal (except for the inexhaustible, three decimal places are generally reserved), and then the decimal is converted into a percentage. In fact, to turn a fraction into a percentage, you must first turn the fraction into a decimal and then multiply it by 100%.
Divide the percentage into components, and rewrite the percentage into components first, so that the quotation that can be lowered can be made into the simplest score.
15, we need to learn how to decimal the number of components and how to decimal fractions.
16, greatest common factor: several numbers can be divisible by the same number at the same time, and this number is called the greatest common factor of these numbers. (or the common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor. )
17, prime number: Two numbers whose common factor is only 1 are called prime numbers.
18, least common multiple: the multiple shared by several numbers is called the common multiple of these numbers, and the smallest is called the least common multiple of these numbers.
19. Comprehensive score: dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called comprehensive score. (Common divisor is the least common multiple)
20. Approximation: It is called approximation to change a fraction into a fraction equal to it, but with smaller numerator and denominator. (Use the greatest common factor in approximation points)
2 1, simplest fraction: The fraction whose numerator and denominator are prime numbers is called simplest fraction.
At the end of the score calculation, the score must be converted into the simplest score.
Numbers in units of 0, 2, 4, 6 and 8 can all be rounded by 2, that is, they can be rounded by 2.
About integrals. A number with a bit of 0 or 5 can be divisible by 5, that is, it can be subtracted by 5. Pay attention to the use of contracts.
22. Even and odd numbers: Numbers divisible by 2 are called even numbers. Numbers that are not divisible by 2 are called odd numbers.
23. Prime number (prime number): If a number only has 1 and its two divisors, it is called a prime number (or prime number).
24. Composite number: a number. If there are other divisors besides 1 and itself, such numbers are called composite numbers. 1 is neither prime nor composite.
28. Interest = principal × interest rate × time (time is generally in years or months, which should correspond to the unit of interest rate).
29. Interest rate: The ratio of interest to principal is called interest rate. The ratio of interest to principal for one year is called annual interest rate. The ratio of interest to principal in January is called monthly interest rate.
30. Natural number: An integer used to represent the number of objects is called a natural number. 0 is also a natural number.
3 1, Cyclic Decimal: a decimal, starting from a certain digit in the decimal part, and one or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals.