FRACTIONS AND THEIR MEANING

A fraction represents a part of one whole thing. A fraction indicates that something has been cut or divided into a number of equal parts. For example, a pie has been divided into four equal parts. If you eat one piece of the pie, you have taken one part out of four parts. This part of the pie can be represented by the fraction 1/4. The remaining portion of the pie, which consists of¹ three of the four equal parts of the pie, is represented by the fraction² 3/4.

In a fraction the upper and lower numbers are called the terms of the fraction. The horizontal line separating the two numbers in each fraction is called the fraction line. The top term of a fraction or the term above the fraction line is called numerator; the bottom term or the term below the fraction line is called the denominator.

A fraction may stand for³ part of a group. There is a group 5 apples. Each is 1/5 (one fifth) of the group. If we take away 2 apples, we say that we are removing 2/5 of the number of apples present. If we take away 3 apples, we are removing 3/5 of the apples present. In this instance, a fraction is being used to stand for a part of a group.

A fraction also indicates division. For example: one apple was divided into eight parts and the man has eaten one part. Therefore he has eaten 1/8 of the apple. How much of the apple is left? How many eighths are in the whole apple?

Principle to Remember. If in any fraction the numerator and denominator are equal, the fraction is equal to 1.

Notes:

¹ consists of —складється з

² is represented by the fraction — представлена дробом

³ may stand for- може означати

EXERCISES

I. Read the following words paying attention to the pronunciation:

sign, piece, upper, numerator, denominator, number, fraction.

II. Make up sentences of your own using the words and expressions given below:

remaining portion, equal, to apply, to consist of, represented by, may stand for, is being used, to indicate.

III. Answer the following questions:

1. What does a fraction represent? 2. What do we call "the terms of fractions"? 3. What is the numerator? (denominator?) 4. What does a fraction indicate? 5. When is the fraction equal to 1?

IV. Translate into Ukrainian:

The horizontal line separating the two numbers in each fraction is called the fraction line. The number above the fraction line is the numerator and that below is the denominator of the fraction. The denominator names the fractional unit and the numerator indicates the number of those units contained in the fraction.

V. Translate into English:

Дріб являє собою частину цілого. Число, яке стоїть над лінією, називається чисельником дробу. Число, яке стоїть під лінією, називається знаменником дробу. Чисельник і знаменник називаються членами дробу.

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TYPES OF FRACTIONS

Common Fraction. A common fraction is a number that has the numerator and the denominator represented by numbers placed the one above and the other below a horizontal line. 3/7 is a common fraction.

Proper Fraction. If the numerator of a fraction is less than denominator the fraction is called a proper fraction. The value of a proper fraction is always less than 1. 6/7, 1/5 and 9/10 are proper fractions.

Improper Fraction. If the numerator of a fraction is equal to¹ or larger than the denominator, the fraction is called a improper fraction. The value of an improper fraction is equal to or larger than 1. 5/3, 3/2, 8/8 are improper fractions.

Mixed number. A number which consists of a whole number and a fraction is called a mixed number. 2¼, 5¾, 9¼ are mixed numbers.

Reducing a Fraction to Lower Terms. For convenience and clarity a fraction must always be expressed in its simplest form. That is, it must be reduced to its lowest terms. To reduce a fraction to its lowest terms², divide the numerator and the denominator by the largest number that will divide into both of them evenly.

The process of crossing all common factors out of numerator and denominator is called the redaction of a fraction to its lowest terms. The greatest (largest) quantity which is a common divisor of two or more quantities is called a greatest common divisor of these quantities. It is written G.C.D.

Notes:

1 is equal to – є рівним

2 to reduce a fraction to its lowest terms — (тут) для того, щоб скоротити дріб

EXERCISES

I. Read the following words paying attention to the pronunciation:

reduce, value, both, other, mixed, proper, improper.

II. Give all possible derivatives of the following words:

value, convenience, to represent, to express, to divide.

III. Make up sentences of your own using the words and expressions given below:

evenly, to reduce to, for the convenience, expressed in, is equal to.

IV. Answer the following questions:

1. What is a common fraction called? 2. What is a proper fraction called? 3. Is the value of a proper fraction more or less than 1? 4. What do we call mixed numbers? 5. How do you reduce a fraction to its lower terms?

V. Put 6 questions to the text.

VI. Translate into Ukrainian:

Fractions indicate division, the numerator being a dividend, the denominator a divisor, and the value of the fraction the quotient.

A fraction can be reduced to lower terms if the numerator and the denominator are divisible by a single number, that is if they have a common divisor. In order to reduce a fraction to its lowest terms, therefore, it is seen at once that the greatest common divisor must be used.

VII. Translate Into English:

Дріб, у якого чисельник менше знаменника, називається правильним дробом. Правильний дріб менше одиниці.

Дріб, у якого чисельник дорівнює знаменнику або більший за нього, називається неправильним дробом. Таким чином, неправильний дріб або дорівнює одиниці, або більший за неї.

Числа, які складаються із цілого числа і дробу, називаються змішаними числами.

Скороченням дробу називається заміна його іншим, рівним йому дробом з меншими членами шляхом ділення чисельника і знаменника на одне й те ж саме число. Це число називається найбільшим спільним дільником.

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