Правила чтения знаков, символов и формул

Английские знаки и символы (ENGLISH SIGNS AND SYMBOLS)

Signs and symbols in Mathematics are international in majority, but there are some signs peculiar to the English language of mathematics, physics and technology which should be learnt:
+, / - the signs of division corresponding to the Russian signs /, -,:, ∟ __,:
·, - the signs of multiplication.
The sign (x) can also have the meaning “from … to”, “up to” (от и до) – 1 x 1.1; 1.2 is read – from one to one point one, one point two (от одной до 1.1; 1,2); ½ x ¼ inch – from one half up to one fourth inch (от ½ до ¼ дюйма). Sometimes this sign (x) is substituted by the sign @
. (point) - the sign is used in decimal fractions and corresponds to the Russian sign, - comma.
2.2 is read two point two (2,2 – две целых две десятых). The sign is used in writing dates, hours and minutes (see above). In this case. (point) is not pronounced
, (comma) - is used to denote the position of every three numbers: 15,000,000 – fifteen million; 1,000 books – a thousand books
: - the sign of ratio and proportion. In this case it is read: “is to”. A: B = C: D A is to B as C is to D
:: - the sign denotes the equality of two ratios (proportions) and can be substituted by the sign of equality = 2: 4:: 3: 6 – two is to four equals (as) three is to six
* - a star, an asterisk

- the sign means: to vary proportionally
+ - the sign of addition – plus

- the sign of subtraction – minus or negative

± - plus or minus – плюс-минус
- minus or plus – минус-плюс
= - the sign of equality, it is read: is, is equal to…, equals, makes - равно
≠ - is read: is not equal to…, is not – не равно
– - a dash – тире
/ - a slash – наклонная черта
≈, - the signs means: approximately equals, is approximately equal to… - приблизительно, почти равен…
> - is greater than, includes – более чем, больше; включает
≤ - is not greater than… - не более чем
< - is less than, is included – менее чем, меньше; включено
≥ - is not less than … - не менее чем
≥ - is equal to… or greater than … - равно или более
≤ - is equal to … or less than … - равно или менее
- the sign denotes infinity – бесконечность
→ - the signs mean: approaches, tends to – достигает, стремится к…
- it means parallel to – параллельно к
∆ - triangle – треугольник
- element of (a set) – элемент (множества)
- is not an element of (a set) – не элемент (множества)
- is an empty set – пустое множество
- intersection – пересечение
- union – соединение
- subset of – подмножество (чего-то)
- implies; see – подразумевается, предполагается; смотри, см.
B - pi [paI] – B – окружность
r - [Rr] – radius of circle – радиус круга
Br² - pi r squared – Br² – формула площади круга
- belongs to – принадлежит к
- doesn’t belong to – не принадлежит к
- is contained – содержится;
(a b) a is contained in b
- doesn’t contain – не содержит (a b) a is not contained in b
- the intersection - пересечение; () – the intersection of A and A prime)
- the union ( the union of A and A prime) – связь, союз
┴ - perpendicular to – перпендикулярно к
' - the sign denotes:
1) minutes - минуты;
2) foot, feet – фут, футы;
3) with numerals expressed by letters a'-prime ['eI 'praIm] - прим
" - the sign denotes:
1) second(s) – секунды(ы);
2) inches – дюймы;
3) double prime – два прим, два штриха
"' - third prime, triple-prime – три штриха
a"' - a third prime or a triple prime – a три штриха
- the sign of integral of – знак: интеграл от
- the integral between the limits a and b – интеграл в пределах а и b
- конгруэнтный
AB - length of line from A to B – длина линии AB
< > - broken brackets – скобки угловые
() - parentheses, round brackets (opening and closing) – круглые скобки
[ ] - brackets, square brackets – квадратные скобки
{ } - braces – фигурные скобки
/ / - slash brackets – наклонные скобки
° - degree(s), grade(s) – градус(ы)
0 - null, nought, zero, o [ou] – нуль, ноль, часто читается как алфавитная буква O [ou]
% - per cent – процент
Σ - the sum, summation of – сумма, знак суммирования
, - is called the sign of the root or the radical sign. It is read: square root, cube root – корень квадратный, кубический
- the fourth root – корень 4-ой степени
- the n -th root – корень n –ой степени
Ø - diameter – диаметр
", & - and – и
& c - etc (et cetera) – и т.д.; и проч.
- circle, circumference – круг, окружность
dy - differential of y – дифференциал от y
- derivative of y with respect to x – обычная производная y по x
- partial derivative of y with respect to x – частная производная y по x
- absolute value of (x) – абсолютная величина x
F(x), f(x) - function of x – функция от x
Єx - increment of x – приращение x
t° - temperature – температура
- centre line – центральная линия, линия центров
µ - micron – микрон = 0,001 mm (10^-3 мм)
mµ - millimicron – миллимикрон = 0,001 µ (10^-7 мм)
~ - similar to – подобный
- equivalent to – эквивалентно (чему-то)
- angle – угол
∟ - right angle – прямой угол
k, c - constant – константа
- varies (directly, inversely) – изменяется прямо, обратно пропорционально
a₁ - a sub one, a first – а первое
a_n - a sub n, a n-th – a n-ое – (а -энное)
… - and so on – и так далее
- round – круглый
- square – квадрат
- a “barred” – a с черточкой
- a tilted – a с тильдой
a* - a star, asterisk – a со звездочкой
@ - at

Математические действия (OPERATIONS IN MATHEMATICS)

Сложение (Addition)
a + b + c is read: a plus b equals c; a and b is equal to c; a added to b makes c; a plus b is c.

a, b are called “addends” or “summands” (слагаемые);
c is the “sum”.
Вычитание (Subtraction)
4 – 3 = 1 is read: three from four is one; four minus three is one; four minus three is equal to one; four minus three makes one; the difference between four and three is one; three from four leave(s) one.
4 is called “a minuend” (уменьшаемое);
3 is “a subtrahend” (вычитаемое);
1 is “a difference” (разность).
Умножение (Multiplication)
2 х 3 = 6; 2 ∙ 3 = 6 is read: two multiplied by three is six; twice three is six; three times two is six; two times three make(s) six.
5 ∙ 3 = 15 is read: five threes is (are) fifteen.

2, 5 are “multiplicands” (множимое);
3 is “a multiplier” or “factor” (множитель);
6, 15 are “products” (результат).
Деление (Division)
35 ÷ 5 - 7 is read: thirty five divided by five is 7; five into thirty five goes seven times; 35 divided by 5 equals 7.
35 is “a dividend” (делимое);
5 is “a divisor (делитель);
7 is “a quotient” (частное).
Возведение в степень (Involution or Raise to power)
3² is read: three to the second power; 3 squared.
5³ is read: five cubed; 5 to the third power; 5 to power three.
x² – x is called the “base of the power”;
2 is called “an exponent or index of the power”.
Извлечение из корня (Evolution)
is read:
the square root of nine is three.
is read:
the cube root of twenty seven is three.
is called “the radical sign” or “the sign of the root”.
To extract the root of … - извлекать корень из…
ДРОБИ (FRACTIONS)
Простые дроби (Common Fractions)
Common (simple, vulgar) fractions nowadays more often than not are written on one line: 1/2, 3/5, 4/7, 1/3 in printing. But there are printed works where traditional writing is used:

Common fractions are read in the same way as we, Russians do, i.e.: the numerator is read as a cardinal number and the denominator as an ordinal number. If the numerator is greater than one the nominator takes the plural ending –s:
1/9 - a ninth, one ninth
3/7 – three sevenths
5/8 – five eighths,
- two one hundred and twenty-thirds
- three quarters, three fourths
- thirty-four seventy-eighths
- two-thirds, etc.
In mixed numbers the integer is read as a cardinal number and fraction must be added with “and”. E.g.:
3 2/5 – three and two fifths
10 2/7 – ten and two sevenths
5 1/2 - five and a half
7 1/3 - seven and a third
247 86/93 - two hundred and forty-seven and eighty-six ninety-thirds
347/1000 - three hundred and forty-seven thousandths
The reading of small fractions is often simplified:
1/2 - a half, one half
1/3 - a third, one third
1/4 - a quarter, one quarter, a fourth, one fourth
instead of: one the second, one the third, one the fourth.
Decimal Fractions
0.5 1) o [ou] point five 2) nought point five 3) zero point five
.5 point five
0.05 1) o [ou] point o [ou] five 2) nought point nought five 3) zero point zero five
1.3 one point three
4.7 four point seven
10.35 ten point three five
247.864 two hundred and forty-seven point eight hundred and sixty-four

Отношение (Ratio)
a: b is read: the ratio of a to b;
10: 5 is read: the ratio of ten to five
4: 2 = 2 is read: the ratio of four to two is two
is read: the ratio of twenty to five equals the ratio of sixteen to twenty four; twenty is to five as sixteen is to four.
Proportion (Пропорция)
In proportion we have two equal ratios. The equality is expressed by the sign:: which may be substituted by the international sign of equality =.
a: b:: c: d or a: b = c: d is read a is to b as c is to d
2: 3:: 4: 6 or 2: 3 = 4: 6 is read two is to three as four is to six.
The extreme terms of proportion are called “extremes”, the mean terms are called “means”. The proportion can vary directly (изменяться прямо пропорционально) and it can vary inversely (изменяться обратно пропорционально):
x y: x varies directly as y; x is directly proportional to y;
x = k/y: x varies inversely as y; x is inversely proportional to y.
Уравнения и тождества (Equations and Identities)
There are different kinds of equations. In general the equation is an equality with one or several unknown variable(s). The reading of equations is the same as in Russian:
30 + 15 + x² + x³ = 90 is read: thirty plus fifteen plus x squared plus x cubed is equal to ninety.
2 + b + + b⁴ = 160 is read: two plus b plus the square root of six plus b to the fourth power is equal one hundred and sixty.
The identity is an equality, valid at all admissible values of its variables.
The identities are read: a + b = b + a - a plus b equals b plus a:
sin²x + cos²x = 1 - sine squared x plus cosine squared x is equal to one.
Чтение формул (READING FORMULAS)

a b = c a divided by b is equal to c
2 x 2 = 4 twice two is four
c x d = b c multiplied by d equals b
dx differential of x
the definite integral of f(x) with respect to
x from a to b (between limits a and b)
c(s) = K _ab c of s is equal to K sub ab
x_a-b = c x sub a minus b is equal to c
a b a varies directly as b
10 ÷ 2 = 5 1) ten divided by two is equal to five;
2) ten over two is five
a squared over c equals b
1) a raised to the fifth power is c;
2) a to the fifth degree is equal to c
a³ = log_cb a cubed is equal to the logarithm of b to the base c
the logarithm of b to the base a is equal to c
x sub a minus b is equal to c
= 0 the second partial derivative of u w with respect to t equals zero
c: d = e: 1 c is to d as e is to 1
15: 3 = 45: 9 1) fifteen is to three as forty five is to nine;
2) the ratio of fifteen to three is equal to the ratio of forty five to nine
= 3 the fourth root of 81 is equal to three
c d c varies directly as d
sin = a sine angle is equal to a
a b 1) a is not equal to b;
2) a differs from b;
3) a is different from b
1) a approximately equals b;
2) a is approximately equal to b
p plus (or) minus q
m > n m is greater than n
m < n m is less than n
1) a is greater than or equal to b;
2) a is greater than or equals to b
B = capital B is equal to infinity
1) the modulus of a;
2) the absolute value of a;
3) the numerical value of a
the modulus of the quantity x minus b is greater than zero and less than or equal to capital C
the interval a to b
28^o 28 degrees (angular measure and temperature measure)
56' 1) 56 minutes (angular measure); 2) 56 feet (linear measure)
45'' 1) 45 seconds (angular measure); 2) 45 inches (linear measure)
the square root (out) of 7
5% 5 per cent
2/9 % 1) two ninths per cent; 2) two ninths of one per cent
½ % 1) a half per cent; 2) a half of one per cent
0.47% 1) point four seven per cent; 2) zero point forty-seven per cent; 3) nought point forty-seven per cent; 4) o point four seven of one per cent
7 %₀ 7%₀ seven per mille
c is equal to (dash, line of division) a over (divided by, by) b
sin (arc sin a) the sine of the angle whose sine is a
sin 23º the sine of 23º
cos 47º the cosine of 47º
sec 80º the secant of 80º
the tangent of a (one) half (of) A
sin α the sine of (the angle) α
the cosine of the angle of one half A minus B (the difference of A and B) [19].