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3.1. Математический факультет

Four Basic Operations of Arithmetic

There are four basic operations of arithmetic. They are addition, subtraction, multiplication and division. An equation like 3 + 5 = 8 represents an operation of addition. Here you add three and five and get eight as a result. 3 and 5 are addends (or summands) and 8 is the sum. There is also a plus (+) sign and a sign of equality (=). They are mathematical symbols.

An equation like 7 – 2 = 5 represents an operation of subtraction. Here seven is the minuend and two is the subtrahend. As a result of the operation you get five. It is the difference. We may say that subtraction is the inverse operation of addition since 7 – 2 = 5 and 5 + 2 = 7.

In multiplication there is a number that must be multiplied. It is the multiplicand. There is also a multiplier. It is the number by which we multiply. We get the product as a result. When two or more numbers are multiplied, each of them is called a factor.

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. We get the quotient as a result. However, suppose you are dividing 10 by 3. In this case you will get a part of the dividend left over. This part is called the remainder. In our case, the remainder will be one. Since multiplication and division are inverse operations, you may check division by using multiplication.

1. Choose the right statement.

1. Plus, minus, equality sign and remainder are mathematical symbols.

2. You may check subtraction by using addition.

3. If you divide the dividend by the divisor you’ll get the product.

2. Match the definitions with their explanations.

1) The process of taking a number or amount from larger number or amount. 2) The process of finding out how many times one number is contained in another. A method of calculating in which you add a number to itself a particular number of times. The process of calculating the total of numbers or amounts.

Addition Subtraction Multiplication Division

3.2. Филологический факультет

Indo-European Languages

By Indo-European languages is meant the family of languages with the greatest number of speakers, spoken in most of Europe and areas of European settlement and in southwestern and southern Asia.

They are descended (произошли) from a single unrecorded language believed to have been spoken more than 5000 years ago in the steppe regions north of the Black Sea and to have split into a number of dialects by 3000 BC. Carried by migrating tribes (племена) to Europe and Asia, these developed over time into separate languages. The main branches are Anatolian, IndoIranian, Greek, Italic, Romanic, Germanic, Baltic, Slavic, Armenian, Celtic, Albanian, and the extinct Tocharian languages.

The study of Indo-European began in 1786 with Sir William Jones’s proposal that Greek, Latin, Sanskrit, Germanic, and Celtic were all derived from a “common source.” In the 19th century linguists added other languages to the Indo-European family, and scholars such as Franz Bopp, Jacob Grimm, Rasmus Rask established a system of sound correspondences and founded the science of comparative linguistics. Since then Proto-Indo-European language has been partially reconstructed via identification of roots common to its descendants and analysis of shared grammatical patterns.

1. True, false or no information?

1. Indo-European language family has more than 10 branches of languages and the greatest number of speakers.

2. There are only living languages belonging to Indo-European family.

3. They are descended from Proto-Indo-European language that was spoken by 3000 BC in the steppe regions north of the Black Sea.

4. Scholars such as Franz Bopp, Jacob Grimm, Rasmus Rask were first linguists who began to study Indo-European languages.

5. The objects of analysis in comparative linguistics are corresponding sounds, common roots of words and shared grammatical patterns.

6. Indo-European languages are spoken only in Europe and Asia.

2. Find the terms in the text that mean:

1. a system of communication by written or spoken words, which is used by the people of a particular country or area.

2. a form of a language which is spoken in a particular part of a country and contains some different words, grammar and pronunciation.

3. a branch of historical linguistics that is concerned with comparing languages to establish their historical relatedness.