FRACTIONS.

116. 1. When anything is divided into two equal parts, what is each part called? Into three equal parts? Into seven equal parts? Into eight equal parts? Into nine equal parts? Into fifteen equal parts?

How

2. How many halves are there in anything? How many thirds? How many fifths? How many tenths? many fifteenths? How many twentieths?

3. What part of an apple will each boy receive when it

is divided equally among 7 boys? Among 8 boys?

4. How much is one fifth of 10 cents? Of 15 cents? Of 30 cents?

5. How much is one sixth of 12 cents? Of 18 cents? Of 24 cents?

6. How much is one seventh of 14 oranges? Of 21 ? Of 28 oranges? oranges

7. In 6 hours James earned 36 cents. How much did he earn per hour?

8. A school has 4 classes of the same size, and the whole number of pupils in the classes is 40. How many are there in each class?

117. One or more of the equal parts of anything is called a Fraction.

Two numbers, written one above the other with a line between them, are used to express a fraction.

118. The number which shows into how many parts a thing has been divided is called the Denominator.

It is written below the line.

Thus, in the fraction, 9 is the denominator. It shows that something has been divided into 9 equal parts.

119. The number which shows how many parts form the fraction is called the Numerator.

It is written above the line.

Thus, in the fraction, 7 is the numerator. It shows that the fraction contains 7 of the 9 equal parts.

120. The numerator and denominator together are called the Terms of the Fraction.

121. A fraction whose numerator is less than its denominator is called a Proper Fraction.

Thus,,, and 15 are proper fractions.

The value of a proper fraction is, therefore, less than 1.

122. A fraction whose numerator equals or exceeds its denominator is called an Improper Fraction.

Thus, 4, 5, and are improper fractions.

The value of an improper fraction is, therefore, 1 or more than 1.

123. A number expressed by an integer and a fraction. is called a Mixed Number.

Thus, 3, 83, and 1413 are mixed numbers.

124. The unit which is divided into equal parts is called the Unit of the Fraction.

A fraction whose unit has been divided into any number of equal parts is called a Common Fraction.

A fraction whose unit has been divided into tenths, hundredths, thousandths, etc., is called a Decimal Fraction.

125. One of the equal parts into which a unit has been divided is called a Fractional Unit.

126. A fraction also expresses unexecuted division.

Thus, 10 is equal to 10 ÷ 5; 1o is equal to 19 ÷ 4.

127. Fractions are read by naming first the number of fractional units, and then the kind of them.

1. Seven ninths. Eight elevenths. Four fifteenths.

2. Six nineteenths. Nine fourteenths. Five seventeenths. 3. Three twentieths. Six forty-fifths. Nine eighteenths. 4. Seventeen twentieths. Thirteen forty-sevenths.

5. Twelve thirtieths. Fifty-five eighty-fifths.

6. Seventeen fifty-fifths. Thirty-four ninety-eighths.

129. 1. Interpret the expression .

EXPLANATION. - represents 7 of 9 equal parts of a thing. It also represents one ninth of 7, and 7 divided by 9. It is read seven ninths.

REDUCTION.

130. To reduce fractions to higher terms.

1. In yard, how many fourths are there? How many eighths?

2. In of a foot, how many sixths are there? How many ninths?

3. Since is equal to 4, how may the terms of the fraction be obtained from ? from ? from ? & from ?

4. Since the terms of the fraction may be obtained from by multiplying them by 4, how may the terms of the fraction be obtained from ?

5. What changes, then, may be made in the terms of a fraction without changing its value?

131. The process of changing the forms of fractions without changing their values is called Reduction of Fractions.

132. A fraction is expressed in higher terms, when its numerator and denominator are expressed by larger numbers.

133. PRINCIPLE. - Multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction.

WRITTEN EXERCISES.

134. 1. Change to 48ths.

EXPLANATION.- Since there are 48 forty-eighths in there are

1, in

of, or; and in

7 times, or 21.

Or,

there are

16 x 348

Since the denominator of the fraction is to be 48, both terms of the fraction must be multiplied by 3.

RULE. Multiply the terms of the fraction by such a number as will change the given denominator to the required denominator.