Post-Reading Activity

Ex. 8. Answer the following questions.

1. What numerals were used in Europe until XVI century? 2. Who introduced the symbol 0? 3. Is the Hindu-Arabic system a decimal system or a binary one? 4. What does the value which a digit represents depend on? 5. What are the signs most used in arithmetic? 6. What are the fundamental operations of arithmetic? 7. Are division and multiplication inverse operations? 8. Are subtraction and multiplication inverse operations? 9. What must you remember about multiplication? 10. What important facts about division must be remembered?

Ex. 9. Find the Russian equivalents for the following English word combinations.

1. to use the same numbers; 2. to represent numbers; 3. present notation; 4. numeration system; 5. decimal system; 6. to be based on tens; 7. inverse operation; 8. capital letters; 9. arithmetic sentence; 10. to measure the distance

a. основываться на десятках; b. обратная операция; c. заглавные буквы; d. измерять расстояние; e. десятичная система; f. представить числа; g. использовать одни и те же числа; h.система счисления; i. арифметичес­кое выражение; j. современная система записи

Ex. 10. Mark the following as True or False.

1. People used numbers thousands of years ago. 2. The decimal number system was invented by the Romans. 3. The Roman system of numbers is based upon the letters A, B, C, D, E, F and G. 4. The symbol 0 was introduced by the Arabs. 5. The work of a zero is to keep the other nine symbols in their proper place. 6. Our decimal number system is positional. 7. We go from right to left in forming larger and larger units of ten, hundred, thousand and so on. 8. We work both with positive and negative numbers in arithmetic. 9. The product of any number multiplied by one is the same number. 10. The quotient is 0 whenever the divisor is 0.

Ex. 11. Fill in the blanks with necessary words and word combinations from the box.

the sum, the quotient, the multiplication sign, to divide, the difference, subtraction, factors, addends, the subtrahend, a remainder, to be added, a numeral, division

1. We get … as a result of addition. 2. The numbers to be added are called …. 3. You may check … by multiplication. 4. Will there be … if you divide 25 by 7? 5. If you are … two numbers, you must remember that division by 0 is meaningless. 6. To find the minuend … and the subtrahend must be known. 7. Addition and … are inverse operations. 8. The multiplicand and multiplier are the names for the … . 9. The result of division is known as …. 10. The difference is the number that when added to the … gives the minuend. 11. The plus sign between two numbers means that these numbers are … . 12. A dot placed between two numbers is used as … . 13. A symbol used to represent a number is called … .

Ex. 12. Make the sentences negative and interrogative.

1. We can add numbers in any order. 2. You should discuss the rules of multiplication at the next lesson. 3. Mathematicians were able to discover another fundamental law of nature. 4. The result must be checked immediately. 5. You have to decide on the subject of your thesis. 6. They may misunderstand the theoretical character of the problem. 7. We were allowed to work on our experiment out of class. 8. They will be able to use some symbols instead of words. 9. We need to use special methods to obtain necessary results. 10. You ought to study carefully the definitions given above.

Ex. 13. Ask special questions.

1. Scientists should develop this important branch of mathematics. (What) 2. In antiquity people could count using positive integers. (When) 3. We are not allowed to use zero as a divisor. (Who) 4. Natural numbers may be divided into two classes: even and odd. (How many) 5. She was able to obtain the solution by multiplying two numbers. (How) 6. He had to speak English at the international conference. (Where) 7. I must discuss the details of my dissertation with the science adviser. (Who(m)) 8. You need to follow your teacher’s instructions during the test. (Whose) 9. You ought to do your best and fulfil the task. (What) 10. First you are to perform the operation of division and then multiply the quotients. (Which)

Ex. 14. Choose the phrase closest in meaning to the given statement.

1. Dan can’t be a teacher.

a) I’m sure Dan isn’t a teacher.

b) I think Dan isn’t a teacher.

2. Need I take the tablets every day?

a) Is it a good idea to take the tablets every day?

b) Is it necessary to take the tablets every day?

3. If it is hot tomorrow, we may go to the beach.

a) We will definitely go to the beach tomorrow.

b) It is possible that we will go to the beach tomorrow.

4. You mustn’t steal.

a) It is against the law to steal.

b) It isn’t necessary to steal.

5. Alison has to work on Saturday. Her boss told her so.

a) Alison wants to work on Saturday.

b) Alison’s boss wants her to work on Saturday.

6. Late-comers are to report to the dean’s office.

a) It’s a good idea.

b) It’s the rule.

7. Astronauts must feel afraid sometimes.

a) They are supposed to.

b) It’s only natural.

8. You can’t come in here.

a) It isn’t allowed.

b) I don’t believe it.

9. We should be there soon.

a) I expect so.

b) It’s absolutely certain.

10. All motorcyclists have to wear crash helmets.

a) It’s a good idea.

b) It’s the rule.

Ex. 15. Choose the correct modal verb or its equivalent.

1. You (may/ought to/are to) take care of your parents. 2. My sight is getting worse. Next year, I’m afraid I (cannot/may not/won’t be able to) read without glasses. 3. Twelve delegates from several countries (can/have to/are to) meet at the end of February. 4. Excuse me, (could/may/must) you tell me the way to the Houses of Parliament? 5. The weather is getting worse. It (must/is likely/may) rain. 6. There are no people in the hall, we (must/can/need) have a talk there. 7. Although he felt ill, he (could/was able to/may) finish all the paperwork. 8. You (can/must/ought to) go and see that movie. It’s very interesting. 9. Don’t worry, you (don’t have to/mustn’t/may not) pay now.10 When we were at school, we (had to/ought to/must) wear a uniform.

Ex. 16. Give the proper English equivalents for the Russian expressions.

1. Нам пришлось perform the operation of addition to find the answer. 2. Ему предстоит specify the conditions of the experiment. 3. Им разрешают use a dictionary if necessary. 4. Я в состоянии solve this difficult problem myself. 5. Вам следует remember that multiplication is associative. 6. Ей не надо use this theorem. 7. Они могут apply their theories in practice. 8. Вы обязаны remember several rules about division. 9. Можно мне start the calculations now? 10. Вам следует to accept everything your parents say as an axiom.

Ex. 17. Translate from English into Russian.

1. Everyone studying mathematics must have a good understanding of the meaning of each symbol. 2. These expressions may contain numbers and letters. 3. Multiplication can be distributed over addition, e.g. 14x12 = (14x10)+(14x2) 4. A prime number is a number that can be divided evenly by only 1 and itself. 5. No multiplication sign is to be used between two letters or a letter and a number written side by side. 6. The plus sign should be understood when there is no sign before the number. 7. Will you be able to name other factors of 18 except nine and two? 8. In some cases, when we have to name a whole number in a factored form, more than two factors can be used. 9. A positive number can be indicated by placing a plus sign (+) before the number. 10. When the minus sign is placed between any two numbers, it indicates that the difference of the two numbers is to be found. 11. Division may be indicated also by writing the dividend above the divisor with a line between them.

Ex. 18. Translate from Russian into English.

1. Числа, которые нужно сложить, называются слагаемыми, а результат сложения называется суммой. 2. Эти числа предстоит перемножить. 3. Мы должны записывать результат справа от знака равно. 4. Число можно поделить на два без остатка (точно), если это четное число. 5. Деление обратно умножению. 6. Произведение любого числа, умноженного на ноль, равно нулю. 7. Никто не может сказать, когда люди начали считать. 8. Они обозначили (указали) операцию сложения знаком плюс. 9. Ни один студент не мог решить задачу, заданную профессором. 10. Им придется использовать двоичную систему счисления. 11. Данный элемент может быть обозначен тем же символом.

UNIT 5

Grammar: Present, Past, Future Perfect (Active Voice)

The Present Perfect Tense	The Past Perfect Tense	The Future Perfect Tense
have/ haven’t + V3 has/ hasn’t + V3	had/ hadn’t + V3	shall/ will have + V3 shan’t/ won’t have + V3
Resultative Perfect just, yet, already, ever, never, lately, recently, today, this week, this month, etc. They have not done it yet. Они еще это не сделали. Durative Perfect (to be, to have, to know) for, since, how long How long have you known him? Как давно ты его знаешь?	by 6 o’clock yesterday, by that time, by the end of last year, before he came They had done it by the time we came. Они сделали это к нашему приходу. They hadn’t done it by the time he came. Had they done it by the time you came?	by 6 o’clock tomorrow, by this time tomorrow, by the end of next year, before he comes They will have done it by 6 o’clock tomorrow. Они сделают это завтра к шести часам. They won’t have done it by 6 o’clock tomorrow. Will they have done it by 6 o’clock tomorrow?

Ex. 1. Compare Russian and English Tense forms.