1. There are four basic operations of arithmetic: addition, subtraction, multiplication and division. In arithmetic an operation is a way of thinking of two numbers and getting one number. Numbers are represented by numerals and digits. In the Arabic numeration system there are only ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent any number. These digits may be used in various combinations. Thus, for example, 1, 2 and 3 are used to write 123, 213, 132 and so on. Any operation in arithmetic is written as an equation – a mathematical sentence that has an equal sign (=) between its parts. There is a plus (+) sign, minus (-) sign and a sign of equality (=). They are mathematical symbols.
2. An example of addition is 2+5=7 (two plus five is equal to seven). Here we add 2 and 5 and get 7. In this example 2 and 5 are addends or summands and 7 is a sum. An operation of subtraction may be represented by an equation like 7-2=5 (seven minus two equals five). In the example seven is the minuend and two is the subtrahend and five is the difference. We may say that subtraction is the inverse operation of addition since 2+5=7 and 7-2=5.
3. Multiplication and division are also inverse operations. In multiplication there is a number that must be multiplied (multiplicand) and a number by which we multiply (multiplier). When numbers are multiplied, each of them is called a factor. An example of multiplication is 5x2=10 (five multiplied by two is equal to ten). The numbers 5 and 2 are factors and ten is the product. In the operation of division there is a number that is divided and it is called the dividend; the number by which we divide is called the divisor. When we divide the dividend by the divisor, we get the quotient. For example, in the equation 12:3=4 (twelve divided by three is equal to four) 12 is the dividend, 3 is the divisor and 4 is the quotient. There are two important facts about division: 1) the quotient is 0 if the dividend is 0; 2) division by 0 is meaningless.
Ex.2 Disagree with the following statements:
1. There are five digits in the Arabic numeration system.
2. The result of multiplication is called the difference.
3. We get the sum as a result of subtraction.
4. Division and subtraction are inverse operations.
5. In addition the order of addends is important.
6. In division we use a plus sign.
7. Only 2 and 6 can be divided by 0.
8. In the equation 2+3=5 2 and 3 are factors.
9. In the equation 12-9=3 3 is the minuend.
10. If we multiply 12 by 4, we’ll get 50 as a product.
Ex. 3Answer the following questions:
1. What are the operations in arithmetic?
2. How can numbers be represented?
3. How many digits are there in Arabic system? Name them.
4. How is any operation in arithmetic written?
5. What are the parts of the operation of addition? Give your example.
6. What are the parts of the operation of subtraction? Give your example.
7. What are the parts of the operation of multiplication? Give your example.
8. What are the parts of the operation of division? Give your example.
9. What are the important facts about division?
Ex. 4. Speak on basic operations of arithmetic using your answers to questions from exercise 3.
ТЕМА4
GREATMATHEMATICIANS
Vocabulary
| To measure | Измерять |
| To count | Считать |
| Mathematician | Математик |
| Different | Различный |
| Contribution | Вклад |
| Field | Область |
| To be known | Быть известным |
| Weight | Вес |
| To divide | Делить |
| Volume | Объем |
| To displace | Заменять |
| Density | Плотность |
| Discovery | Открытие |
| Researcher | Исследователь |
| Scientist | Ученый |
| To consider | Полагать, думать |
| To be renowned | Быть известным |
| Ratio | Соотношение |
| To find out | Обнаружить |
| Circumference | Окружность |
| Circle | Круг |
| Non-recursive number | Нерекурсивное число |
| To derive a theorem | Вывести теорему |
| Root | Корень |
| Law of motion | Закон движения |
| Gravitational attraction | Гравитационное притяжение |
| Dispersion of light | Распространение света |
| Partialdifferentialequations | Уравнениясчастнымипроизводными |
| Theory of probability | Теория вероятности |
| Number theory | Теория чисел |
| Applied mathematics | Прикладная математика |
| Differential equations | Дифференциальные уравнения |
| To develop the foundation | Заложить основу |
| To contradict | Выступать против |
| To view | Рассматривать |
| Explanation | Объяснение |
| To recognize a theory | Признавать теорию |
