FRACTIONS.

ARTICLE 91. When a melon is divided into two equal parts, each of the parts is called one half; when it is divided into three equal parts, each of the parts is called one third; when it is divided into four equal parts, one of the parts is called one fourth; two of the parts are called two fourths; three of the parts, three fourths, etc.

ART. 92. When a number or thing is divided into five equal parts, one of the parts is called one fifth; two of the parts are called two fifths; three of the parts are called three fifths, and

so on.

ART. 93. The value of one of the equal parts will depend upon the number of parts into which the number or thing is divided. The greater the number of parts, the less will be each part. Thus, one half of a thing is greater than a third of it, and a third is greater than a fourth.

ART. 94. When a number or thing is divided into equal parts, these equal parts are called FRACTIONS.* Hence,

A FRACTION is an expression representing a part or parts of a unit, or whole. Thus, one sixth represents a part of a unit; four sixths represent parts of a unit.

ART. 95. FRACTIONS are divided into two classes-COMMON and DECIMAL.

COMMON FRACTIONS.

ART. 96. A common fraction is expressed by two numbers-one placed above the other, with a line between them.

* Fraction, from the Latin word, fractus, signifying broken, because the number is, as it were, broken into equal parts or pieces.

The number below the line is called the DENOMINATOR; the number above the line is called the NUMERATOR.

ART. 97. The DENOMINATOR* shows into how many equal parts the number or thing is divided. In the fraction the unit is supposed to be divided into four equal parts; in }, it is divided into eight parts.

The NUMERATOR† shows how many of the equal parts are used. Thus, in the fraction, four parts are used; in §, five parts are used.

ART. 98. The numerator and the denominator taken together are called the TERMS of the fraction. Thus, is a fraction— 5 and 7 are its terms; 7 is the denominator, and shows that the unit is divided into seven equal parts, making each part one seventh; 5 is the numerator, and shows that five of the equal parts are used. It is read five-sevenths.

ART. 99. When we tell the names of the parts of a frac tion and explain their meaning, we are said to analyze the fraction.

Ex. 1. Analyze the fraction §.

Analysis. 5 and 8 are the terms; 8 is the denominator, and

*Denominator, from the Latin word, denomino, signifying to name, because it gives name or denomination to the fraction.

† Numerator, from the Latin, numero, signifying to number, becausc it numbers the parts, or tells how many there are.

shows that the unit is divided into eight equal parts, making each part one-eighth; 5 is the numerator, and shows that five of the equal parts are used. It is read five-eighths.

Let the pupil analyze the following fractions, viz. :

ART. 100. The value of a fraction is the quotient of the numerator divided by the denominator. The value of is 2; 융 of 12 is 3; of 20 is 5. From these examples we see that every fraction indicates division; the numerator being the dividend, the denominator being the divisor, and the value of the fraction being the quotient. All the rules of division are therefore applicable to fractions.

When the numerator is equal to the denominator, the value of the fraction is a unit, as 4, 7, 8, etc.

When the numerator is less than the denominator, the value of the fraction is less than a unit, as, J, etc.

When the numerator is greater than the denominator, the value of the fraction is greater than a unit, as 4, 7, etc.

ART. 101. A PROPER fraction is one whose numerator is less than its denominator, as 3, 4, etc.

An IMPROPER fraction is one whose numerator is equal to or greater than its denominator, as §,, etc.

A MIXED NUMBER consists of a whole number and a frac tion, as 2, 4, 5, etc

ART. 102. Any whole number may be expressed as a frac tion by writing 1 below it for a denominator; thus 4 may be written; 6 may be written f.

ART. 103. A COMPOUND fraction is a fraction of a fraction as of ; # of 4.

A COMPLEX fraction is one which has a fraction either in its numerator or in its denominator, or in both; as

21;

5

QUESTIONS TO ILLUSTRATE FRACTIONS.

Ex. 1. How many halves in 2?

Analysis. In 1 unit there are 2 halves, and in 2 units there are 2 times as many halves, which will be 4 halves; or, expressed thus,

2. How many thirds in 3?

Ans.

Analysis. In 1 unit there are 3 thirds, and in 3 units there are 3 times as many thirds, which will be 9 thirds; or, ex pressed thus,

3. How many fourths in 3?

Ans. .

Ans. 12.

Analysis. In 1 unit there are 3 thirds, and in 4 units there are 4 times as many thirds, which make 12 thirds, and 2 more thirds make 14 thirds; or, expressed thus, . 12. How many fourths in 53?

Ans. 1.

Analysis. In 1 unit there are 4 fourths, and in 5 units there are 5 times as many fourths, which make 20 fourths, and 3 more fourths make 23 fourths; or, written thus, 23.

13. How many halves in 7?

14. How many thirds in 5?

Ans. 23.

Ans. 5.

Ans.

Ans

20. How many tenths in 35?

21. If of a number is 9, what is the number?

Analysis. If one third of the number is 9, then three thirds f the number, or the entire number, will be 3 times 9, which will be 27.

Ans. 27. 22. If of a pound of candy cost 8 cents, what would be the cost of a whole pound?

Analysis. If one fourth of a pound cost 8 cents, then four fourths, or a whole pound, would cost 4 times 8 cents, which will be 32 cents.

23. Mary has a piece of ribbon, and inches; how long is the whole piece?

24. If half an ounce of mace cost 10 whole ounce cost?

Ans. 32 cents.

of it measures 6 Ans. 18 inches. cents, what would a

Ans.

25. A man paid 9 dollars for of an acre of land; what was the price of a whole acre?

Ans.

26. One sixth of a man's life is 12 years; how old is he?

Ans.

27. Jane has a basket of roses, and of the number of roses is 6; how many has she?

Ans.

28. One ninth of the number of acres in a field is 15; how many acres in the field?

Ans.

29. William has a bag of chestnuts, and of the number is

13; how many chestnuts has he?

Ans.

30. If of a firkin of butter contain 8 pounds, how many

pounds in the whole firkin ?

Ans.

31. A man paid 18 dollars for one fifth of a bale of cotton; what was a whole bale worth?