When I entered the hall the
lecture was being listened to with great attention.
The prizes have already been
distributed.
Don’t worry. The sick child has
just been taken to hospital.
The driver had already been
sent for by that time.
All copies of Moscow News had
been sold out by half past nine.
Be sure, letters and newspapers
will have been brought by ten.
The latest news was being
listened to when Mike came in.
The new performance has been
much spoken about of late.
Упражнение 8
1) Thesumof 2 numbersis 15. If 2 is added to the
first number and the sum multiplied by 3, the product is 11 more than 7 times
the second. Find the numbers.
Сумма
двух чисел равна 15. Если прибавить 2 к первому числу и умножить сумму на 3, то
результат будет на 11 больше второго числа, умноженного на 7.
(x+
2)*3 = 7y + 11
x + y = 15
Ответ: x
= 11, y = 4
2) What happens with the sum if one of the
addends becomes some units greater (less)?
Что будет с суммой,
если одно из слагаемых станет не несколько единиц больше (меньше)?
The sum
will become some unites greater (less).
Сумма станет на несколько единиц больше (меньше)
3) Write down the number which is 2 less than
three times X.
Напишите число,
которое на 2 меньше, чем Х.
Если Х = 10, тогда 3*10 – 2 = 28
Если Х = х (переменная), тогда 3х – 2.
4) Find the number
such that when it is doubled and 6 added, the result is the same as when the
number is trebled (утроить) and 2 subtracted.
Найти такое число, что если его удвоить и к произведению прибавить 6,
то результат окажется равным разности исходного числа, умноженного на 3, и
2.
2x + 6 = 3x
-2
Ответ: х = 8
5) Find the number which is as much greater
than 25 as it is less than 93.
Найдите число, которое
на столько больше 25, на сколько меньше 93.
x+ 25 = 93 - х
х = 34
Число = 25 + 34 = 59
Ответ: 59
6) The number which is 5 more than X is 6 times
as big as the number which is 5 less than X. Find X.
Число, большее Х на 5,
в 6 раз больше числа, которое меньше Х на 5.
(x +
5)/6 = x - 5
Ответ: х = 7
7) Write down the three consecutive integers of
which "d” is the middle one (the smallest, the greatest).
Напишите три
последовательных целых числа, где "d” – средний элемент.
3, 4, 5
Упражнение 9.
Расположите следующие предложения в логической
последовательности.
I
Subtraction
is the process of finding the difference between 2 numbers by taking the
smaller of the two from the larger.
In
order to find the remainder the subtrahend is written under the minuend as
in addition.
When
the process is completed the third complete number below the subtrahend is
the desired remainder.
The
number which is subtracted is called the subtrahend, the other number is
called the minuend and their difference, the number which remains after
the subtrahend is subtracted from the minuend is called the remainder.
Beginning
at the right each figure in the subtrahend is subtracted from the figure
about it and the individual remainder written below in the same column.
As
a check the remainder and the subtrahend should be added.
If
the subtraction was correct the sum of this addition will be equal to the
minuend.
Ответ: 1, 4, 2, 5, 3, 6, 7.
II
When
either of these is placed between any two numbers it indicates
respectively that the sum, difference, product, or quotient of the two
numbers is to be found.
Another
sign sometimes used is the parentheses.
the
equality sign shows that any indicated operation or combination of numbers
written before it produces the result written after it.
The
signs most used in arithmetic to indicate operations with numbers are the
plus, minus, multiplication, and division signs. If any number oкcombination of numbers
is inclosed in parentheses the whole combinations, or the result of the
indicated operations, inside the parentheses is to be considered as a
single number.
Ответ: 4, 1, 3, 2, 5
III
Thus
6 is a divisor of 42, the quotient being 7.
A
divisor has already been defined.
Also,
3 is a divisor of 42, the quotient being 14.
It
is seen that a divisor is in reality a factor.
In
the sense in which we shall use it in this chapter, however, a divisor of
any number is another number which is contrained in that one a whole
number of times, that is, exactly and without a remainder.
This
was to be expected, since in division, the dividend is the product of the
devisor and the quotient.
Ответ: 2, 5, 6, 4, 1, 3
Упражнение 10. Выберите правильный ответ
1. Write down the number which is 3 times as
big (much) as a.
3a, 4-a, 5a
2. Write down the number which is 2 less than
x.
x-2, 2x, x + 2
3. Find 2 consecutive integers whose sum is
39.
20 and 19, 19 and 1, 17 and 18.
4. Using the letters x and y, write the
following: two numbers differ by 6 (note, y is greater than x)
y-x = 6, x – y = 6, y – x = 2
5. If a is a multiplier and иis the product, what is the
multiplicand equal to?
a:b, a – b, b:a
Упражнение 11.
Ответьте правильно
1. What laws does the operation of addition
obey?
1. There exists the law called the
distributive connecting the operation of addition and multiplication.
2. There
are two laws called the Commutative law and the Associative law holding good
for addition.
3. The Commutative law, the Associative law
and the Distributive law are the fundamental laws of arithmetic.
2. Is the remainder changed if one and the
same number is added to the subtrahend and minuend?
1. The
result of the operation of subtraction is the same, one and the same number
being added to the subtrahend and the minuend.
2. Using the fundamental property of the
difference we may add one and the same number to the subtrahend and minuend.
3. Any changes in the subtrahend yield the
changing of the remainder.
3. What is required to find in dividing the
number 8 by the number 2?
1. It is required to find such a number which
is 2 units greater than the number 8.
2. It is required to
find out how many times the number 2 is contained in the number 8.
3. It is required to find the number which
being added to the number 2 gives the number 8.
Упражнение 12.
Выберите правильный вопрос
1. The equality sign shows that any indicated
operation or combination of numbers written before it (on the left) produces
the result or number written after it.
1. What
sign is placed between the two results if the first gives the second?
2. What relation should be between the
dividend and the divisor for the operation of division to be exact?
3. What fundamental operations in arithmetic
do you know?
2. The signs most used in arithmetic to
indicate operations with numbers are the plus, minus, multiplication, and
division signs.
1. How many operations are there in
arithmetic?
2. What
signs indicating the arithmetical operations do you know?
3. What does the sign + placed between any
two numbers indicate?
3.
In finding the product of any two numbers which do not contain the same
number of figures, the one with the lesser number of figures should be taken
as the multiplier.
1. What operations should be performed over
any two numbers if their product is to be found?
2. What rule do you
follow to multiply two numbers having different number of digits?
3. What happens to the product, the
multiplier decreasing several times?
4. The numbers to be added are called the
addends.
1. What operation is performed over the
numbers called the addends?
2. What do we call
the numbers, if their combined amount is spoken of as the sum?
3. Is the sum changed if one of the addends
increases?
Упражнение 13
Прочтите следующие утверждения,
скажите, правильные они, неправильные или не включены в текст.
1. If a certain number is the product of two or
more other numbers each of those other numbers is called a factor of that
number. (T)
2.
A
divisor of any number is another number which is contained in that one a whole
number of times, that is, exactly and without a remainder. (F, may be with a remainder)
3. The number 5 is a factor of the number 12. (F, we can’t divide 12 into 5, see 1)
4. We shall call number 2 and 3 and 4 and 6
proper factors of 12. (T)
5.
A
number which has the number 3 as a factor is called an even number. (F, not always, f.e. 9)
6. The integer "m” is a factor of the integer "n”
if mg=n, where q is an integer. (T)
7.
In
general if "m” and "n” are positive integers and if "m” is a factor of "n”, we
say that m divides n, or n is divisible by m. (T)
8. We shall say that 0 is divisible by every
integer, but 0 does not divide any number. (T)
9. If any even number is divisible by 3 it is
divisible by 8. (T)
10. If the number consisting of the last two
figures of any given number is divisible by 4 or by 25, the entire number is
divisible by 4 or 25, respectively. (T)
