Four basic operation of arithmetic
1) We cannot live a day without numerals. Number and numerals are everywhere.
2) The numbers used in our numeration system are called digits.
3) In our Hindu-Arabic system we use only ten digits 0,1,2,3,4,5,6,7,8,9 to represent any number.
6) The digits may be used in various combinations to make different numbers 123,321,231 and so on.
7) One and the same number can be represented in various ways.
8) For example, take 8.It can be represented as the sum of 3 and 5;the difference between 10 and 2; the quotient of 80 and 10; and the product of 2 and 4.
9) For example 2 multiplied by 4 equal 8.
7) This is an equation. An equation is a mathematical sentence.
8) There are four basic operations on arithmetic.
9) They are addition, subtraction, multiplication and division.
10) In arithmetic an operation is a way of transforming two numbers into one number.
11) An equation 2+3=5 represents an operation of addition. Here 2 is an addend, 3 is a summand. When we add 2 to 3 we get a sum. It is 5.
12) An equation 5-3=2 represents an operation of subtraction. Here 5 is a minuend, 3 is a subtrahend. When we subtract 3 from 5 we get 2 as a result. It is difference.
13) Addition and subtraction are inverse operation.
14) An equation 3x2=6 represents an operation of multiplication. Here 3 is a multiplicand, 2 is a multiplier. When we multiply 3 by 2 we get a result 6. It is a product.
15) An equation 6:3=2 represents an operation of division. Here 6 is a dividend,3 is a divisor. When we divide 6 by 3 we get 2 as a result. It is a quotient. When we divide 10 by 3 we will get a part of a dividend left over.
16) Multiplication and division are inverse operations, so we can check division by multiplication and vice versa.
17) There are two important facts that we must remember about division:
* The quotient is 0 whenever the dividend is 0.That is 0 divided by n is equal to 0
for all values of n except 0.
* Division by 0 is impossible.
number-Число
numeral-Цифра
Place-value system- Позиційна система розрядів
Addition-Додавання
Addend-Перший доданок
Summand-Другий доданок
Sum-Сума
Plus-Знак «+»
Subtraction-Віднімання
Minuend-Зменшуване
Subtrahend-Від’ємник
Difference-Різниця
Minus-Знак «-«
Multiplication-Множення
Multiplicand-Перший множник
Multiplier-Другий множник
Product-Добуток
Division-Ділення
Dividend-Ділене
Divisor-Дільник
Quotient-Частка
The history of geometry
1) Engineers, architects and people of many other professions use lines and figures in their daily work.
2) Geometry is the branch of mathematics which investigates solids, surfaces, lines and angles.
3) Geometry is the Greek name for the science which the early Egyptians began and developed about 5000 years ago for building pyramids.
4) The word GEOMETRY is derived from two Greek words: GEO meaning earth and METRON meaning measure.
5) After a time Greek philosophers and teachers developed and perfected the proofs of the Egyptians.
6) The most important of the early Greek teachers was Pythagoras.
7) He founded a school in Italy.
8) Plato lived more than a hundred years later than Pythagoras and he was interesting in geometry, because of the logic contained in the proofs.
9) Euclid was a teacher of geometry in Alexandria.
10) The Elements of Euclid has been used as a basic for all textbooks on geometry since his time.
11) Archimedes lives in Sicily.
12) He discovered many laws of mathematics.
13) For over twenty centuries Euclidean geometry was the ruling theory.
14) In the 19th century the Russian mathematician Lobachevsky founded non-Euclidean geometry of two dimensions.
15) The third system of geometry was developed by Riemann and is called elliptic geometry.
Engineer-Інженер
Architect-Архітектор
Line-Лінія
Figure-Фігура
Geometry-Геометрія
Solid-Тіло
Surface-Поверхня
Angle-Кут
Measure-Міра
Area-Площа
Volume-Об’єм
Proofs-Доведення
Mathematician-Математик