Types of fractions

Common Fraction. A common fraction is a number that has the numerator 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 to 1 or larger than the denominator, the fraction is called an improper fraction. The value of improper fraction is equal to or larger than 1. 5/3, 3/2, 8/ 8 are improper fractions.

Mixed numbers. A number which consists of a whole number and a fraction is called a mixed number. 2 1/9, 5 1/4, 9 2/5 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 terms, divide the numerator and the denominator by the largest number that will divide into both of them evenly. This process is called the reduction of a fraction to its lowest terms. The 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:

is equal to - равен

to reduce a fraction - сократить дробь

Exercises:

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

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

2. Give all possible derivatives of the following words:

value, convenience, to represent, to explain, to divide.

3. Suggest the English for:

значение неправильной дроби, наименьший показатель, сокращение дроби, наибольший общий делитель, выражены в простейшей форме, разделить их поровну, равно или больше чем, число расположено под дробной линией, этот процесс называется сокращением.

4. Express agreement or disagreement with the following:

1. The value of a proper fraction is always less than 1.

2. A mixed number is a number which contains only a fraction.

3. We can't express a fraction in its simplest form.

4. In a common fraction the numbers are placed above and below the horizontal line.

5. A greatest common divisor is the smallest common divisor of two or more quantities.

5. Fill in the blanks with prepositions if necessary:

1. ... convenience and clarity a fraction must be always expressed ... its simplest ... form.

2. A number which ... consists ... a whole number and a fraction is called ... a mixed number.

3. The value ... improper fraction is equal ... or ... larger than 1.

4. This process is called ... the reduction ... a fraction ... its lowest term.

6. Answer the following questions:

I. 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 1/2?

4. What do we call mixed numbers?

5. How do you reduce a fraction to its lower terms?

7. Translate into Russian:

Fraction indicates division, the numerator being a dividend, the denominator is a divisor, and the value of the fraction is the quotient.

A fraction can be reduced to lower term 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 term, therefore, it is seen at once that the greatest common divisor must be used.