3 1x27、53x32、57x4 1、22x79、50x67、92x37、43x82、 164、63x72、2 1x58、22x80、24x35、 19x66、30x54、79x20、83x43、7 1x67

First, multiplication skills:

1, multiplicative commutative law: a * b = b * a

2. Multiplicative associative law: a*b*c=(a*b)*c=a*(b*c)

3. Multiplicative distribution law: (a+b) * c = a * c+b * c; (a-b)*c=a*c-b*c

Two, vertical calculation multiplication should pay attention to four issues:

1, the last digit of two numbers should be aligned.

2. Write as many numbers as possible above, and write as few numbers as possible below to reduce the times of multiplication.

3. If there is a "0" at the end of both numbers, the last digit of the number can only be aligned before the "0" when writing vertically, and finally the number "0" owned by the two numbers after vertical product is added.

4. Decimal multiplication should determine the position of the decimal point of the product according to the multiple of the decimal.

Extended data:

Each letter in the multiplication formula can generally represent a number, a single item, a polynomial, and some can also be extended to fractions and roots. Multiplication formula is an important content of algebraic expression multiplication. Mastering the multiplication formula accurately and skillfully is of great significance for learning the multiplication of algebraic expressions and even other operations of algebraic expressions. Multiplication formula is the most commonly used and basic formula, from which other formulas can be derived.

The square of a polynomial is equal to the sum of the squares of the terms, plus twice the product of every two terms. Most formulas can be used not only smoothly (polynomial multiplication) but also reversibly (factorization).

Edited in March and May, 2020

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The calculation of 120 double digit

28×29= 77×67= 37×50= 17×3 1= 87×74= 15× 1 1= 7 1×3 1= 56×4 1= 59×49= 96×95= 26×83= 1 7×68= 98×52= 40×26= 6 1×72= 48×93= 56×25= 49×5 1= 93×3 1= 97×8 1= 98×25= 18×72= 47×22= 12×38= 78×89= 7 / kloc-0/×39= 69×54= 64×78= 34×43= 49× 15= 33×2 1= 50×40= 97×76= 77×64= 37× 16= 45×37= 63×25= 67×24= 76×23= 19× 1 / kloc-0/= 90×83= 22×95= 58×2 1= 66×95= 78×50= 62×94= 57×53= 84×26= 60×93= 43×29= 27×76= 64×62= 13×83= 69×74= 4 1×46= 96×9 / kloc-0/= 87×20= 95×28= 54×97= 33×34= 72× 15= 13×49= 65 438+04×76= 12×3 1= 87×48= 10×29= 23×80= 52×8 1= / kloc-0/9×48= 10×24= 78×89= 24×34= 55×6 1= 69×30= 68×4 1= 66×74= 4 5×20= 3 1×42= 60×48= 83×74= 29× 1 2= 92×73= 45×63= 54×43= 36×20= 23×94= 3 1×58= 50×44= 5 1×92= 12×54= 16×38= 73×69= 28×6 5= 30×5 1= 1 / kloc-0/× 17= 58×60= 86×60= 27×84= 5 1×28= 49×47= 53×68= 35×37= 27×73= 98×40= 75×32= 67×74= 79×80= 77×47= 12×77= 1 8×47= 3 1× 19= 27×64= 23×75= 35×98= 54×80= 72×44= 20×85= 69×50= 4 1×28= 27×55= 66×80= 55×3 1= 34×79= 3 1×40= 7 / kloc-0/×6 8= 64× 10= 8 1× 17= 10× 10= 63×79= 39×89= 75×43= 2 1×43= 6 1× 17= 10× / kloc-0/4= 3 1×29= 84×25= 96543 8+0×35= 76×53= 75×79= 97×48= 39×39= 15×68= 39×50= 67×39= 1 4×57= 24×26= 63×62= 66×73= 20×98= 62×42= 72×52= 26× 19= 68×7 1= 52×50= 57×55= 13×88= 63×55= 84×5 1 = 82×69= 90×98= 32×22= 14×79= 85×80= 53×53= 82×9 1= 7 1×53= 62×65= 4 1×42= 54×48= 7 1×4 3= 95×80= 1 2×59= 42×29= 62×87= 48×49= 94×70= 98× 13= 79×68= 13×65= 88× 10= 68× 18= 25×86= 56×7 1 = 40× 45 = 80× 98 = 58× 72 = 34× 29 = 81× 33 = 9/kloc-0 /× 34 = 3/kloc-0 /× 85 = 93× 49 = 5/kloc-0 /× 33. It is widely used in scientific development and modern life production, and is an essential basic tool for studying and studying modern science and technology. Mathematics (hanyu pinyin: shùXué；; ; Greek: μ α θ η μ α κ; English: Mathematics/Math) comes from the ancient Greek word μθξμα(máthēma), which means learning, learning and science, and has a narrow and technical meaning-"mathematical research". Even in its etymology, its adjective meaning and learning-related will be used to refer to mathematics. Its plural form in English and as the plural form of mathématiques in French +es can be traced back to the Latin neutral plural (Mathematica), which is Cicero's plural from Greek τ α α θ ι α τ κ? (ta mathē matiká). In ancient China, mathematics was called arithmetic, also called arithmetic, and finally changed to mathematics. Mathematics is divided into two parts, one is geometry and the other is algebra. [2] Mathematics is a subject that studies concepts such as quantity, structure, change and spatial model with symbolic language. Mathematics, as an expression of human thinking, embodies people's aggressive will, meticulous logical reasoning and pursuit of perfection. Although different traditional schools can emphasize different aspects, it is the interaction of these opposing forces and their comprehensive efforts that constitute the vitality, availability and lofty value of mathematical science. The knowledge and application of object-based mathematics is an indispensable part of individual and group life. The refinement of its basic concepts can be found in ancient mathematical documents of ancient Egypt, Mesopotamia and ancient India. Since then, its development has made small progress. Until the Renaissance in16th century, the mathematical innovation generated by the interaction with new scientific discoveries led to the acceleration of knowledge. Mathematics is used in different fields of the world, including science, engineering, medicine and economics. The application of mathematics in these fields is usually called applied mathematics, and sometimes it will lead to new mathematical discoveries and the development of new disciplines. Mathematicians also study pure mathematics, that is, mathematics itself, without any practical application. Although many studies started from pure mathematics, many applications will be found later. The French Bourbaki School, founded in 1930s, believes that mathematics, at least pure mathematics, is a theory to study abstract structures. Structure is a deductive system based on initial concepts and axioms. According to Boone School, there are three basic abstract structures: algebraic structure (group, ring, field, lattice …), ordered structure (partial order, total order …) and topological structure (neighborhood, limit, connectivity, dimension …). [3] The needs of commercial calculation in the field of mathematics, the systematic understanding between numbers, the concepts of measuring land area and predicting astronomy. These four requirements are generally related to a wide range of mathematical fields (namely, arithmetic, algebra, geometry, analysis) such as quantity, structure, space and change. In addition to the above-mentioned main concerns, there are sub-fields used to explore the relationship between the core of mathematics and other fields: to logic, to set theory (foundation), to empirical mathematics in different sciences (applied mathematics), and to the rigorous study of uncertainty in modern times. The phrase mathematics; ; Mathematics; TEACMSES [span] mathematical analysis [number] mathematical analysis; Analysis; Mathematical analysis; Matematic analyst【span] mathematical programming [number] mathematical programming; Mathematical planning; MP； [Number] Mathematical Slave ogramming Mathematical Concept: The learning of the number of pi begins with the number. At first, it is the familiar natural number and integer as well as the rational number and irrational number described in arithmetic. Another research field is its size, which leads to cardinality and another infinite concept: Alev number, which allows meaningful comparison between the sizes of infinite sets. The first person to find the value of pi by scientific method was Archimedes, and he got the π value accurate to two decimal places. When Liu Hui, a mathematician, annotated Nine Chapters Arithmetic, he used the secant circle method to find the approximate value of π. Zu Chongzhi, a mathematician and astronomer, calculated the value of pi (∏) to seven decimal places for the first time in the history of mathematics in the world, that is, between 3. 14 15926 and 3.64 15927. π is an infinite acyclic decimal, an irrational number and a transcendental number. Structure Many mathematical objects, such as sets of numbers and functions, have embedded structures. The structural properties of these objects are discussed in groups, rings, bodies and other abstract systems that are themselves objects. This is the field of abstract algebra. Here is a very important concept, that is, vector, which is extended to vector space and studied in linear algebra. The study of vector combines three basic fields of mathematics: quantity, structure and space. Vector analysis extends it to the fourth basic field, namely change. The study of space comes from geometry, especially Euclidean geometry. Trigonometry combines space and numbers and contains a very famous Pythagorean theorem. Now the research on space is extended to high-dimensional geometry, non-Euclidean geometry and topology. Numbers and spaces play an important role in analytic geometry, differential geometry and algebraic geometry. In differential geometry, there are concepts such as fiber bundle and calculation on manifold. In algebraic geometry, there are descriptions of geometric objects such as polynomial equation solution sets, which combine the concepts of number and space; There is also the study of topological groups, which combines structure and space. Lie groups are used to study space, structure and change. In order to understand the basis of mathematics, the German mathematician Georg Cantor (1845- 19 18) developed mathematical logic and set theory, which boldly marched into infinity, provided a solid foundation for all branches of mathematics, and its own content was quite rich, which put forward the existence of real infinity and made immeasurable contributions to the future development of mathematics. Cantor's work has brought a revolution to the development of mathematics. Because his theory transcended intuition, it was opposed by some great mathematicians at that time. Poincare also compared set theory to an interesting "morbid situation", and Poincare retorted that Cantor was "neurotic" and "went into a hell beyond numbers". Cantor is still full of confidence in these criticisms and accusations. He said: "My theory is as firm as a rock, and anyone who opposes it will shoot himself in the foot." Set theory gradually penetrated into all branches of mathematics at the beginning of the 20th century, and became an indispensable tool in analytical theory, measurement theory, topology and mathematical science. Hilbert, the greatest mathematician in the world in the early 20th century, spread Cantor's thoughts in Germany, calling him "a mathematician's paradise" and "the most amazing product of mathematical thoughts". British philosopher Bertrand Russell praised Cantor's works as "the greatest works that can be boasted in this era". Logic Mathematical logic focuses on putting mathematics on a solid axiomatic framework and studying the results of this framework. It is the birthplace of Godel's second incomplete theorem, which is perhaps the most widely spread achievement in logic-there is always a true theorem that cannot be proved. Modern logic is divided into recursion theory, model theory and proof theory, which are closely related to theoretical computer science. In modern symbols, simple expressions can describe complex concepts. This image is generated by a simple equation. Most of the mathematical symbols we use today were invented after16th century. Before that, mathematics was written in words, which was a hard procedure that would limit the development of mathematics. Today's symbols make mathematics easier to be controlled by experts, but beginners are often afraid of it. It is extremely compressed: several symbols contain a lot of information. Like music, today's mathematical symbols have clear grammar and difficulty.