1. Read the text and translate it into Ukrainian. The Real Number System

The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers, or sometimes the counting numbers.

Natural numbers or counting numbers1, 2, 3, 4, 5 . . . The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever.

At some point, the idea of “zero” came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers.

Even more abstract than zero is the idea of negative numbers. If, in addition to not having any sheep, the farmer owes someone 3 sheep, you could say that the number of sheep that the farmer owns is negative 3. It took longer for the idea of negative numbers to be accepted, but eventually they came to be seen as something we could call “numbers.” The expanded set of numbers that we get by including negative versions of the counting numbers is called the integers. So, integers involve whole numbers plus negatives:. . . –4, –3, –2, –1, 0, 1, 2, 3, 4, . . .

The next generalization that we can make is to include the idea of fractions. While it is unlikely that a farmer owns a fractional number of sheep, many other things in real life are measured in fractions, like a half-cup of sugar. If we add fractions to the set of integers, we get the set of rational numbers.

In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number.

2. Translate into Ukrainian.

1. Спочатку слово «число» означало щось, що можна порахувати.

2. Цілі числа включають натуральні числа та число «нуль».

3. Негативне число – це будь-яке реальне число, яке є менше за 0.

4. Дріб представляє частину цілого .або певну кількість рівних частин.

3. Say if the statements are true or false. Correct the false sentences.

1. Natural numbers or counting numbers include -1, -2, 3, -4,- 5 . . .

2. At first, “number” meant something you could count.

3. We call the set of natural numbers plus the number zero the rational numbers.

4. Integers involve whole numbers plus negatives.

5. A rational number is any number that can be expressed as the fraction a/b of two integers, with the denominator b equal to zero.

Література:

1. Барановська Т.В. Граматика англійської мови. Збірник вправ: Навч. посібник. Видання друге, виправлене та доповненею – Мова англ., укр. – Київ: ТОВ “ВП Логос-М», 2007. – 384с.

2. Л.В. Мисик, А.Л. Арцишевська, Л.Р. Кузнєцова, Л.Л. Поплавська. Англійська мова. Комунікативний аспект. / За ред. доц. Мисик Л.В. – Підручник. – К.: Атіка, 2000. – 368с.

3. Гужва Т. М. Англійська мова: Розмовні теми: Навч. посіб. Для студентів фак. Інозем. Філології, університетів, ліцеїв, гімназій та коледжів. – Харків: Фоліо, 2005. – 414с.

4. Бессонова І. В. Англійська мова (за професійним спрямуванням). Навчальний посібник для дистанційного навчання. – К.: Університет «Україна», 2005. – 263с.

Практичне заняття 2

Тема: У ресторані (кафе).

Three of the restaurants are real places, but one is invented. Which one do you think isn't real?

DRACULA'S RESTAURANT • Melbourne, Australia

Dinner is different at Dracula's. Start your evening with an interesting cocktail in the Graveyard Bar, then get on the ghost train for the dark, terrifying journey into Dracula's Restaurant. There you can enjoy a four-course meal and a two-hour cabaret, followed by dancing in the Graveyard Disco. Dracula's is great for just two people but also for birthday parties, office parties - even wedding parties. Dress: black is best!

RED SEA STAR RESTAURANT • Éclat, Israel

Do you enjoy eating by the sea? How about under the sea? The Red Sea Star Restaurant lies seven metres under the sea and 35 metres from land, and is surrounded by coral and colourful fish. The restaurant is lovely inside, too, with its strange, flowing windows, and fantastic fishy furniture. This is a wonderful place to have a meal. And the best thing on the menu? The fish, of course.

COLOURS RESTAURANT • London, England

Colours Restaurant has a different colour for each night of the week. Friday is Yellow Night, and all the food is yellow or orange. You might have carrot soup, then fish in a lemon sauce, then a fruit salad. Other things change, too. On Saturday the food is red, and so are the waiters' jackets, the tablecloths and even the flowers. On Wednesdays, everything is blue and purple. So find out the day's colour before you go, as most guests like to choose clothes that go with their meal.

^{TWINS RESTAURANT • New York, usa}

All 80 people who work at Twins Restaurant are identical twins. They work together at the same tables, and they wear the same clothes. The owners are twins, too. Lots of other things here are in pairs: there are double lamps, double mirrors and, of course, double bar stools. You don't have to be a twin to eat here, but if you are, come along together: you can sign our twin guest book, we'll put your photo on the wall - and you get two drinks for the price of one!

ІІ Робота з граматичним матеріалом

Ex. 2. Change the following statements into indirect speech.

1. I often play tennis. 2. She is staying with her aunt. 3. She went to Moscow alone. 4. He has gone home. 5. I will go with Anna. 6. She wrote another romantic novel. 7. He will write a detective story next. 8. Mary was speking with her relatives in the evening yesterday. 9. They are hapy now. 10. He studies at the university in the USA. 11. He travelled to Africa last year. 12. I know Spanish a little. 13. He often takes part in differenet sports competitions. 14. She went to Kyiv on holiday. 15. I told you about it yesterday.

Ex. 3. Change the following questions into indirect speech.

1. Did you go home early yesterday? 2. Will you write to me next week? 3. Will you go to the sea this year? 4. Did you take your Literature examination? 5. Have you ever visited Africa? 6. Are you married? 7. Are you going to the library today? 8. When will you stop asking me the same question? 9. Where did they meet? 10. How long do you want to stay in the country? 11. When did they return? 12. Who told you that? 13. How well does he know English? 14. Where are they going to stay in London? 15. Did I forget about anything? 16. Where does he study? 17. How often do they invite him for dinners? 18. Do you know anything about Mr Jones? 19. How did you get to the station? 20. Have you heard the news? 21. Did she sing that beautiful song? 22. What will you watch? 23. Are they going to leave soon? 24. Did they speak about you?

III.Робота над текстом за професійним спрямуванням