Topic 3

Text

Fractions, Decimals and Percentage

Topic 2

Mathematical Expressions. Four Simple Rules of Arithmetic

Topic 1

Unit 2 Essential Course

Addition: 6 + 2 = 8

+ is plus sign.

You read this “six and two are (or is) eight”

or “six plus two equal (or equals) eight”

or “six plus two make(s) eight”.

6 and 2 are components; 8 is the sum.

Subtraction: 11 – 7 = 4

- is minus sign.

You read this “seven from eleven are (is) four”

or “eleven minus seven are (is) four”

or “eleven minus seven leave(s) four”

or “eleven minus seven equal(s) four”.

11 is minuend; 7 is subtrahend; 4 is the difference.

Multiplication: 9 x 3 = 27

x is multiplication sign.

You read this “nine times three is twenty-seven”

or “nine multiplied by three is twenty-seven”

or “nine times three make twenty-seven”.

9 is multiplicand; 3 is multiplier (9 and 3 are factors); 27 is the product.

Division: 56: 8 = 7

: is division sign.

You read this “eight into fifty-six goes seven times”

or “fifty-six divided by eight is seven”

or “fifty-six divided by eight equals seven”.

56 is dividend; 8 is divisor; 7 is the quotient.

= is called the sign of equality or “the equals sign”.

Exercises:

1 Name the arithmetical signs:

+; -; x;:; =.

2 Translate into English:

сложение, сложить, слагаемое, сумма; вычитание, вычесть, уменьшаемое, вычитаемое, разность;

умножение, умножить, множимое, множитель, произведение; деление, делить, делимое,

делитель, частное.

3 Read the numerals in English:

4, 11, 49, 208, 5119; 3-й, 13-й, 51-й, 178-й, 3020-й.

4 Read the following expressions in English:

29 – 13 = 16; 15 + 27 = 42;

6 x 8 =48; 17 – 3 = 14;

4 + 4 = 8; 9 x 2 = 18;

54: 6 = 9; 30: 5 = 6.

5 Write down the mathematical expressions in English:

4 + 27 = 31; 8 x 9 = 72;

69 – 11 = 58; 45: 5 = 9;

5 x 7 = 35; 16 – 4 = 12;

49: 7 = 7; 6 + 16 = 22;

17 + 8 = 25; 63: 3 = 21;

(7 x 4) + (15: 5) – 11 = 20.

6 Translate the sentences into English:

6.1 Аудитория № 403 находится на 4-ом этаже.

6.2 Вам следует знать основные правила арифметики.

6.3 Откройте учебник на странице 218.

6.4 Разделите смесь на 8 равных частей.

6.5 В чём различие между этими тремя приборами?

7 Answer the following questions:

7.1 What rules of arithmetic do you know?

7.2 How do you call the numbers which you multiply?

7.3 What is the result of subtraction?

7.4 How do you call the numbers which you add?

7.5 What is the result of division?

A unit or an aggregate of units is called a whole number or an integer; a part of a unit is called a fractional number.

Arithmetical numbers are represented by symbols called numerals, as the Arabic figures (1, 2, 3, etc.) and the Roman figures (I, V, X).

Every fraction must contain two numbers, a denominator and a numerator. The denominator tells into how many equal parts the unit is divided. The numerator shows how many of these parts are taken. The fraction 4 ½ is read four and one half.

A decimal fraction is a fraction having a denominator of 10, 100, 1000, or some similar multiple of 10. All figures to the left of the decimal point are whole numbers, everything that comes after the decimal point (to the right of it) is a fraction, or part of a unit.

0.2 is read two tenths; 52.23 is read fifty-two and (or: point) twenty-three hundredths.

Percentage is a particular kind of a decimal fraction, of which the denominator is always 100. Instead of writing the denominator we use the term “per cent” to indicate that the denominator is 100.

When we speak of “6 per cent” we mean 6/100 or 0.06. These all mean the same thing; namely, 6 parts out

of 100. Instead of writing out the words “per cent” we more often use the sign % after the number, as for instance 6%, which means “six per cent”.

Exercises:

1 Find the English equivalents to the following words and word-combinations in the text:

1.1 целое число

1.2 дробное число

1.3 десятичная дробь

1.4 числитель

1.5 знаменатель

1.6 арифметические числа

1.7 быть представленным символами

1.8 разделить число на равные части

1.9 десятичный знак

1.10 процентное отношение

1.11 особый вид десятичной дроби

2 Read the fractions and decimals in English:

1/8; 0.5; 3.72; 4 1/6; 1.17; 7/12; 0.235; 2/3; 0.2; 6.35; 3/8

3 Write down the following fractions and decimals in English:

½; 3 1/3; 34.01; 0.04; 5/7; 8 1/6; 13.092; 1.25; 1.8; ¾; 0.7

4 Read in English:

3%; 18%; 100%; 10.2%; 4.8%

5 Answer the questions:

5.1 What is an integer?

5.2 How is a part of a unit called?

5.3 What are arithmetical numbers represented by?

5.4 How do you call the numbers which every fraction must contain?

5.5 What is a denominator?

5.6 What does a numerator show?

5.7 What fraction is called a decimal one?

5.8 What can you say about percentage?

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