- •Сборник текстОв для самостоятельного чтения и экзаменационные темы
- •Contents
- •Выписка из программы курса "Иностранные языки для неязыковых факультетов и вузов"
- •Требования, предъявляемые к студенту по окончании курса
- •О работе с англо-русским словарем
- •Term 1 my working day Learn the following words and expressions:
- •Read and translate the text “My Working Day”
- •Our university Learn the following words and expressions:
- •Practise the pronunciation of the following words:
- •Read and translate the text “Our University”.
- •Answer the questions:
- •Great britain Learn the following words and expressions:
- •Practise the pronunciation of the following words:
- •Mind some proper names:
- •Loch Lomond – озеро Ломонд
- •House of Commons – Палата Общин
- •Conservative party – консервативная партия
- •Read and translate the text “Great Britain”
- •What languages are spoken in the uk?
- •Read the texts about some British sights
- •Term 2 london Learn the following words and expressions:
- •Mind some proper names:
- •Practice the pronunciation of the following words:
- •Read and translate the text “ London”
- •Read the texts about some London sights
- •My future profession Learn the following words and expressions:
- •Practise the pronunciation of the following words:
- •Read and translate the text “My Future Profession”
- •Answer the questions:
- •Read about some school policies of one of the English schools
- •Heinrich pestalozzi
- •Learn the following words and expressions:
- •Practise the pronunciation of the following words:
- •Read and understand the text “Heinrich Pestalozzi”
- •Answer the questions:
- •Read the text about Friedrich Froebel
- •Term 3
- •The faculty of primary schooling
- •The faculty of pre-school psychology and pedagogics
- •Higher Education
- •Elementary and Secondary Education
- •Adult and Continuing Education
- •The faculty of mathematics The Whole Numbers
- •Addition of Whole Numbers
- •Subtraction of Whole Numbers
- •Multiplication of Whole Numbers
- •Division of Whole Numbers
- •Fractions
- •Addition of Fractions
- •Subtraction of Fractions
- •Multiplication of Fractions
- •Division of Fractions
- •Addition and Subtraction of Decimal Fractions
- •We discard the digits 2 and 3. But we do not simply ignore these discarded digits. They may cause a change in one of the digits we intend to use. If we have 45.6723
- •Multiplication of Decimal Fractions
- •Division of Decimal Fractions
- •Quotients with Repeated Decimals
- •The faculty of biology The Cell
- •Some Familiar Proteins
- •Enzymes and Genes
- •The faculty of geography a Country Across the Channel
- •The faculty of physical culture Sports and Recreation
- •Term iy
- •The faculty of primary schooling
- •The faculty of pre-school psychology and pedagogics
- •Standards
- •The United States Educational Structure
- •Reform and Progress
- •Examining Schools
- •The faculty of mathematics Numbers
- •The faculty of biology What Is a Mutation?
- •Evolution and Heredity
- •Animal Behaviour
- •The faculty of geograpgy The Face of Britain
- •The faculty of physical culture Sports and Money
- •Leisure Sports
- •Anything That Has Wheels
- •Список литературы
- •Сборник текстОв для самостоятельного чтения и экзаменационные темы по английскому языку
- •614990, Г. Пермь, ул. Сибирская, 24, корп. 2, оф. 71,
- •614990, Г. Пермь, ул. Сибирская, 24, корп. 1, оф. 11
Division of Decimal Fractions
The only difference between the division of whole numbers and that of numbers containing decimal fractions is that we must take into consideration the fact that some portion of either the dividend or the divisor or of both is fractional, as is indicated by the decimal point.
Furthermore, when we perform division with whole numbers, we often cannot complete this operation as we obtain a remainder. Thus, we have before us two questions:
1. Where shall we locate the decimal point in the quotient?
2. What shall we do in the case of a remainder?
We have examined the effect of moving of the decimal point. Let’s first examine the division of a decimal fraction by a whole number. For example 111.78 : 9. We shall proceed as in the division of whole numbers:
111.78 I 9
- 9 12
21
- 18
3
Note that the division of the whole part leaves a remainder 3, and that we have a fractional part 0.78. That is we are left with 3.78. From this point on we can't expect anything else but some fraction in the quotient if we continue the division. If now we bring down the next digit, that is 7, we shall have 3,7 or 370 tenths. If we divide 37 tenths by 9, we shall have a certain number of tenths in the quotient. We shall, therefore, place a decimal point after the 2 in the obtained
quotient and continue the division as usual. Then we shall have:
111.78 I 9 Check: I2.42
-9 12.42 x 9
21 111.78
-18
37
-36
18
-18
Thus we observe that division of a decimal fraction by a whole number is performed in the same manner as division of a whole number by a whole number.
The whole part of the decimal fraction will give the whole part of the quotient. As soon as we bring down the first digit from the decimal part of the dividend, we shall begin to obtain the decimal part (the fractional part) of the quotient. This procedure always serves for the division of decimal numbers by whole numbers.
Now we shall apply the results just obtained to the division of decimal fractions by decimal fractions. Let’s perform the division 176.28 : 2.6. We know that the multiplication of the dividend and of the divisor by the same number does not produce any change in the quotient. When we multiply the dividend by some number, the quotient is multiplied by the same number, but when we multiply the divisor by some number, the quotient is divided by the same number. This fact enables us to change the dividend 2.6 into a whole number. This change is accomplished by moving both decimal points one place to the right; thus, both the divisor and the dividend 176.28 and 2.6 are multiplied by 10. The divisor 2.6 becomes 26, and the dividend 176.28 becomes 1,762.8.