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

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.