Разговорный английский

скобка, 12 минус 8; за­

multiplied by two; enclose in

крыть круглую скобку и

a square bracket.

помножить на 2; закрыть квадратную скобку.

6 + [9 - (12

- 8) х 2]

61

 

Doing Sums

 

Addition

471

⁺ 54

39

564

9 plus 4 are 13, and 1 are 14; put down the 4 and carry (transfer) 1; 1 plus 3 are 4, and 5 are 9, and 7 are 16; put down the 6 and carry 1; 1 plus 4 are 5. The total is 564.

Subtraction

6003

4879

1124

9 from 3 won’t go; borrow 10 (from the preceding column); 9 from 13 leaves 4; carry the 1 over to the 7, making it 8; 8 from nought won’t go; borrow 10; 8 from 10 leaves 2; carry the 1 over to the 8, making it 9; 9 from nought won’t go; borrow 10; 9 from 10 leaves 1; carry the 1 over to the 4, making it 5; 5 from 6 leaves 1. The difference (remainder) is 1124.

 

Multiplication

234

^x      56

1404

1170

13104

Begin with the units; 6 times 4 equals 24; put down the 4; carry 2; 6 times 3 is 18, and 2 are 20; put down the nought and carry 2; 6 times 2 is 12, and 2 are 14; go over to the tens; 5 times 4 equals 20; put down the nought and carry 2; 5 times 3 is 15, and 2 are 17; put down the 7; carry 1; 5 times 2 is 10, and 1 are 11. Now add. Carry down the 4; nought plus nought gives nought; 7 plus 4 are 11; put down 1 and carry 1; 1 plus 1 are 2, and 1 are 3; carry down 1. The product is 13104.

 

Division

15 ] 1387 [ 92      15 into 13 won’t go; 15 into 138 goes 9 times;

135      9 times 15 are 135; 135 from 138 leaves 3; bring

37      down the 7; 15 into 37 goes twice; 2 times 15 are

30      30; 30 from 37 leaves 7. The quotient is 92 and

7      the remainder 7.

 

Fractions

3      2

4 ⁺ 5

First reduce the denominators to a common one by multiplying 4 by 5; 4 times 5 makes 20; 20 divided by the denominator 4 gives 5; carry the 5 over to the numerator of the first fraction and multiply it by 3; 5 times 3 are 15; 20 divided by the denominator 5 gives 4; 4 times 2 is 8; 15 plus 23      3

8 are 23. The answer is — or 1—.

20      20

62

Consider these 3 expressions:

2      1

(!)      6:5X5

/2      1\

(2)

2      1

<3>      6:-of J

In (1), since there are no brackets, the sign of division or

multiplication affects only the number that immediately follows it.

Thus 6 : | = 6 x | and 6:jx|=6x|x|.

If we first multiply | by | and divide 6 by the result, we make the

division sign affect both j and |. That is the case (2).

If two numbers are connected by the word of, the product is

regarded as a single number. Thus (3) is the same as (2).

State the following in brackets and prove it:

“Take any number, double it, subtract the result from 120, divide

by 3, subtract this result from 40, add half of what you get. The

answer is the number with which you have started.”

What is the difference between 39-17 + 21 and 39- (17 + 21)?

The Multiplication Table

1x1=1 Once one is one.

1x2=2 Once two is two.

1 x 12 = 12 Once twelve is twelve.

2 x 1=2 Twice one is two.

2x2=4 Twice two is four.

2 x 12 = 24 Twice twelve is twenty-four.

3 x 1=3 Three times one (three ones) are three.

3 x 2=6 Three times two (three twos) are six.

3x12= 36 Three times twelve (three twelves) are thirty-six.

12 x 1 = 12 Twelve times one (twelve ones) are twelve.

12 x 12 = 144 Twelve times twelve (twelve twelves) is a hundred

and forty-four.

¹ В российском стандарте вместо точки в десятичных дробях используется за­

пятая, а вместо знаков < и > используются знаки и

63

 

Mathematical Signs

Математические знаки¹

+

Plus; a sign of addition

Плюс; знак сложения

—

Minus; a sign of subtraction

Минус; знак вычитания

±

Plus or minus

Плюс или минус

X

Times (by); a sign of multi­plication

-жды; раз; знак умножения

 

Decimal point

Точка в десятичных дробях

 

Divided by; a sign of divi­sion

Деленное на; знак деления

*

Is to; a ratio sign

Относится к; знак отношения

=

Equals; is equal to

Равняется; равно

 

Not equal

Не равно

 

Approximately equals

Приблизительно равняется

>

Greater than

Больше (чем)

>

Equal or greater than

Больше или равно (чем)

<

Less than

Меньше (чем)

<

Equal or less than

Меньше или равно (чем)

00

Infinity

Бесконечность

yj~

Square root of

Корень квадратный из

 

Cube root of

Корень кубический из

V

nth root of

Корень n-й степени из

[]

Brackets (square brackets)

Квадратные (или прямые) скобки

Parentheses (round brack­ets)

Круглые (или овальные) скобки

{}

Braces

Фигурные скобки

AB Length of line from A to В

Длина линии от А до В

II

Parallel

Параллельный; параллель

Z

Angle

Угол

L

Right angle

Прямой угол

±

Perpendicular

Перпендикулярный; перпен­дикуляр

%

Percent (per cent)

Процент

64

2. HIGHER SCHOOL

2. ВЫСШАЯ ШКОЛА

a) Studies

а) Занятия

What Institute do you study at?

She is at the University and is studying to become a teacher.

He is a student of law (medicine).

He studies for a degree.

I am fresh from school.

More than a thousand freshmen arrive at the Institute every year.

I got my higher education in 19—.

We all looked forward to the studies at the University.