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)
Progress rate between the length, area, volume and their similarities of compound application problems
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 Block = 10 Angle 1 Integer Meaning: … Numbers like -4, -3, -2,-1, 0, 1, 2, 3, … are called integers.
2 natural numbers: when we count objects, 1, 2, 3, 4 ... the numbers used to represent the number of objects are called natural numbers. There is no object, which is represented by 0, and 0 is also a natural number.
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.
32. Time of a day: there are 24 hours in a day, one hour and 60 minutes, 1 minute and 60 seconds 1, and each copy × number of copies = total number of copies/number of copies = number of copies/number of copies = number of copies.
2. 1 multiple× multiple = multiple1multiple = multiple/multiple = 1 multiple
3. Speed × time = distance/speed = time/distance/time = speed.
4. Unit price × quantity = total price ÷ unit price = total quantity ÷ quantity = unit price
5. Work efficiency × working hours = total workload ÷ work efficiency = working hours ÷ total workload ÷ working hours = work efficiency.
6. Appendix+Appendix = sum, and-one addend = another addend.
7. Minus-Minus = Minus-Minus = Minus+Minus = Minus
8. Factor × factor = product ÷ one factor = another factor.
9. Divider/Divider = quotient dividend/quotient = divisor quotient × divisor = dividend 1, squared (c: perimeter s: area a: side length)
Perimeter = side length ×4 C=4a
Area = side length × side length s = a× a 2, cube (v: volume a: side length)
Surface area = side length × side length× ×6 S Table =a×a×6
Volume = side length × side length × side length v = a× a× a.
3. rectangle (c: perimeter s: area a: side length)
Circumference = (length+width) ×2 C=2(a+b)
Area = length × width S=ab
4. Cuboid (V: volume S: area A: length B: width C: height)
(1) surface area (length× width+length× height+width× height )× 2s = 2 (AB+BC+CA)
(2) volume = length× width× height V=abc
5. triangle (s: area a: bottom h: height) area = bottom× height ÷2 s=ah÷2.
Height of triangle = area ×2÷ base of triangle = area ×2÷ height
6. parallelogram (s: area a: bottom h: height) area = bottom x height s=ah
7. Trapezoidal (s: area a: upper bottom b: lower bottom h: height) area = (upper bottom+lower bottom) × height ÷2 s=(a+b)× h÷2.
8. Circle (s: area c: perimeter л d= diameter r= radius) (1) perimeter = diameter× л = 2×л× radius C=лd=2лr (2) area = radius× radius×л.
9. Cylinder (v: volume h: height s: bottom area r: bottom radius c: bottom perimeter) (1) lateral area = bottom perimeter × height =ch(2лr or лd) (2) surface area = lateral area+bottom area × 2.
(3) Volume = bottom area × height (4) Volume = lateral area ÷2× radius.
10, cone (v: volume h: height s: bottom area r: bottom radius) volume = bottom area × height ÷3 length unit conversion1km =1000 m1m =10 mm. Area unit conversion 1 km2 =100ha10000m21m2 =100m21m2 =
Volume (capacity) product unit conversion 1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1 cubic decimeter = 1 liter 1 cubic centimeter = 1 ml/kloc. Kg 1 kg = 1000g 1 kg RMB unit conversion 1 yuan = 10 angle1angle =10 minute1yuan =/kloc.
The time unit is converted into 1 century = 100 1 year =1February (3 1 day):1\ 3 \ 5 \ 7 \ 8 \/kloc-0.
1 hour = 60min 1 minute = 60s 1 hour = 3600s 1. Additive commutative law: Two numbers add and exchange addends, and the same position. 2. The law of addition and association: When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and then the third number is added, and the sum remains unchanged. 3. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged. 4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied, or the second two numbers are multiplied first, and then the third number is multiplied, and the product remains unchanged. 5. Multiplication and distribution law: When two numbers are multiplied by the same number, you can multiply the two addends by this number respectively, and then add the two products, and the result remains unchanged. Such as: (2+4)×5=2×5+4×5. 6. Nature of division: In division, the dividend and divisor are expanded (or reduced) by the same multiple at the same time, and the quotient remains unchanged. Divide 0 by any number other than 0 to get 0. 7. Equation: An equation in which the value on the left of the equal sign equals the value on the right of the equal sign is called an equation. Basic properties of the equation: When both sides of the equation are multiplied (or divided) by the same number at the same time, the equation is still valid. 8. Equations: Equations with unknowns are called equations. 9. One-dimensional linear equation: An equation with an unknown number of 1 is called a one-dimensional linear equation. Example method and calculation of learning linear equation of one variable. That is, an example is given to illustrate that the formula is replaced by χ and calculated. 10. Score: divide the unit "1" into several parts on average, and the number representing such a part or points is called a score. 1 1. Addition and subtraction of fractions: add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains unchanged. Fractions of different denominators are added and subtracted, first divided, then added and subtracted. 12. Comparison of fraction size: Compared with the fraction of denominator, the numerator is large and the numerator is small. Compare the scores of different denominators, divide them first and then compare them; If the numerator is the same, the denominator is big and small. 13. Fractions are multiplied by integers, and the product of the multiplication of fractions and integers is a numerator, and the denominator remains unchanged. 14. Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator. 15. Fraction divided by integer (except 0) equals fraction multiplied by the reciprocal of the integer. 16. True fraction: The fraction with numerator less than denominator is called true fraction. 17. False fraction: the fraction with numerator greater than denominator or numerator equal to denominator is called false fraction. False score is greater than or equal to 1. 18. With score: write the false score as an integer, and the true score is called with score. 19. The basic nature of the fraction: the numerator and denominator of the fraction are multiplied or divided by the same number at the same time (except 0), and the size of the fraction remains unchanged. 20. A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction. 2 1.A divided by b (except 0) equals the reciprocal of a multiplied by b.