Урок 3. Fractions. Exercises

Упражнение 5. Найдите с тексте английские эквиваленты следующих слов и выражений.

дробь - fraction,

дробный - fractional,

числитель - numerator,

знаменатель - denominator,

правильная и неправильная дробь proper and improper fraction,

смешанное число - mixed number,

простая и десятичная дробь - common and decimal fraction,

величина - value,

делимый - divisible,

кратное – denominator,

указывать - indicate,

отличать – differ

 

Упражнение 6. Найдите в тексте антонимы следующих слов.

whole – fractional

vertical – horizontal

numerator – denominator

proper – improper

fraction – integer

indivisible – divisible

unequal – equal

greater than – smaller than

smaller – greater

improper fraction – proper fraction.

 

Упражнение 7. Переведите следующие предложения на русский язык.

1. Having arrived a day before the opening of the conference we had enough time to go sightseeing.

Прибыв за день до открытия конференции, мы имели достаточно времени для осмотра достопримечательностей.

 

2. The child sat on the floor packing his toys.

Ребенок сидел на полу, упаковывая свои игрушки.

 

3. Having ordered his dinner he began looking through a newspaper.

Заказав обед, он начал просматривать газету.

 

4. While talking to the man she remembered that she had seen him before.

Разговаривая с мужчиной, она вспомнила, что видела его прежде.

 

5. Having found out why some students were absent the chairman opened the meeting.

Выяснив, почему некоторые студенты отсутствовали, председатель начал собрание.

 

6. Being asked what he was going to do next the pilot said that he wanted to repeat the flight.

Когда пилота спросили, что он собирается делать дальше, он сказал, что он хочет повторить полет.

 

7. Having been written the letter was sent to the manager.

Когда письмо было написано, он было отправлено менеджеру.

 

8. We spent much time lying in the sun and swimming during our leave.

Мы провели много времени, лежа на солнце и купаясь, во время нашего отпуска.

 

9. We know of millions of workers in capitalist countries being out of work.

Мы знаем о миллионах безработных рабочих в капиталистических странах.

 

10. Having settled down the travelers decided to prepare dinner.

Обустроившись, путешественники решили приготовить обед.

 

Упражнение 8. Выберите правильный ответ.

1. In what case ca a fraction be reduced to lower terms?	1. If the numerator and denominator of a fraction have no common divisors. 2. If the numerator and the denominator of a fraction are divisible by a single number. 3. If the numerator and the denominator of a fraction are divisible by their greatest common divisor.
2. What do we call a proper fraction?	1. A fraction whose numerator is less than the denominator. 2. A fraction whose numerator is equal to or larger than the denominator. 3. A fraction whose denominator is any power of 10.
3. What does the numerator of a fraction indicate?	1. It indicates the operation of division. 2. It indicates the number of fractional units contained in the fraction.
4. What happens to the quotient if the divisor of a fraction increases some times?	1. The quotient increases the same number of times. 2. The quotient decreases the same number of times. 3. The quotient remains the same.

 

Упражнение 9. Выберите правильный ответ.

1. Which of the following fractions is a proper one?

25/8, 1 3/7, 1/5.

 

2. Which of the following fractions is written in its lowest terms?

25/35, 1/7, 6/28.

 

3. Which of the following expressions is greater?

¾ of 60, 5/8 of 80, 5/7 of 49.

 

4. What number if 6 times as big as 2/3?

5/6, 4, 1½.

 

5. Which of the following numbers is greater (less)?

3/7, 10/7, 19/7.

Greater: 19/7

Less: 3/7.

 

Упражнение 10. Выберите правильный вопрос

1. A fraction is one or the sum of several fractional units.	1. What are the general principles of fractions? 2. What do you mean by a fraction? 3. What term of a fraction names its fractional units?
2. The denominator names the fractional unit.	1. Is the denominator one of the terms of a fraction? 2. What does the denominator of a fraction indicate? 3. What fractional unit can the denominator name?
3. A number which is expressed by a whole number and a fraction is called a mixed number.	1. What are the parts making a mixed number? 2. Can any whole number be expressed as a fraction? 3. What fraction can be expressed as a mixed number?
4. In general a fraction can be reduced to lower terms if numerator and denominator are divisible by a single number, that is, if they have a common devisor.	1. What do we call a common devisor of the numerator and denominator of a fraction? 2. What do we mean by reducing a fraction to its lower terms? 3. When can a fraction be reduced to the lower terms?

 

 

Упражнение 11. Прочтите следующие утверждения. Скажите, правильные они, неправильные или не включены в текст.

 

1. Since a fraction indicates a division the value of an improper fraction will not be greater than 1, because the numerator is greater than the denominator. (F, can be greater than 1)

 

2. In general, the least common denominator of two or more fractions is the least common multiple of their several denominators. (T)

 

3. When fractions with the same denominator are added or subtracted, the result is a fraction with the same denominator. (T)

 

4. The process of working out 1 1/2 : ¼ is equivalent to finding how many quarters there are in 1 ½. (T)

 

5. In general when the denominators are the same, fractions having larger numerators have larger values. (T)

 

6. We know that fractions indicate division where the numerator is a divisor, the denominator is a dividend and the value of the fraction is the quotient. (F, the numerator is a dividend, the denominator is a divisor)

 

7. If we interchange the numerator and the denominator of a fraction than the fraction so obtained is called the reciprocal of the given one. (no information)

 

8. Adding zero to any fraction changes the number. (F)

 

9. Subtracting zero from any number (fraction) leaves the number unchanged. (T)

 

10. The quotient resulting from the division of zero by zero is always zero. (F, you cannot divide by zero)

 

 

Упражнение 12. Расположите следующие предложения в логической последовательности.

 

I.

1. This is written in symbol ¼.
2. Thus, if the unit is divided into four equal parts, each fractional unit is called one fourth.
3. If a single unit, as 1 foot, 1 pound, 1 object of any kind, is divided into equal parts each of the parts is called a fractional unit and is named according to the number of equal parts.
4. Similarly, each of ten equal parts is called one tenth, 1/10; etc.

 

Ответ: 3, 2, 1, 4.

 

II.

1. In a fraction such as ¼, 1/6, 2/3, 7/11, etc, the horizontal line separating the two numbers in each fraction is called the fraction line.
2. The denominator names the fractional unit and the numerator indicates the number of those units contained in the fraction.
3. A fraction is one or the sum of several fractional units.
4. The numerator and denominator taken together are sometimes called the terms of the fraction.
5. The number above the fractional line is the numerator and that below is the denominator of the fraction.

 

Ответ: 3, 1, 5, 2, 4.

 

III.

1. In general, a fraction can be reduced to lower terms if numerator and denominator are divisible by a single number, that is, if they have a common divisor.
2. Similarly, if the numerator and denominator of 8/12 are separately divided by 4, the fraction 8/12 is reduced to the equivalent fraction.
3. On examination it is seen that in order to reduce 3/12 to ¼ the numerator and denominator are each separately divided by 3.
4. In order to reduce a fraction to its lowest terms, therefore, it is seen at once that the greatest common divisor must be used.
5. Thus, we have the following rule: to reduce a fraction to its lowest terms, divide its numerator and its denominator by their greatest common divisor.

 

Ответ: 1, 3, 2, 4, 5

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