5/7 — five sevenths
пять седьмых
4— — four and one twentieth
20
четыре целых и одна двадца
тая
0.5 — nought point five (о [эо]
ноль целых и пять десятых
point five) .5 — point five
ноль целых и пять десятых
0.05 — nought point nought five
ноль целых и пять сотых
(о [эи] point о [эи] five) 0.005 — nought point nought
ноль целых и пять тысячных
nought five
3.05 — three point о [эи]
три целых и пять сотых
(nought) five
Brackets
Скобки
Well, now, write down this sum
А теперь запишите следую
and do it:
щую задачу и решите ее:
Six plus square bracket, nine
Шесть плюс квадратная
minus, twelve minus eight
скобка, 9 минус, круглая
enclosed in parentheses,
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