3. If you pay 3 cents for one fifth (1) of an orange, what will a whole orange cost?

4. If you pay 2 dollars for one eighth (§) of a ticket, wha will a whole ticket cost?

Q. How many halves to an apple, or any thing?

Q. How many thirds? Fifths? Eighths? Sixteenths?

Q. When an apple, or any thing, is divided into two equa parts, would you call one of these parts a half or a third Into 3 equal parts, what is one part called?

Q. Into 4 parts, what is one part called?
Q. Into 5 parts, what is one part called?
Q. Into 8 parts, what is 1 part called?
Q. Into 8 parts, what are 2 parts called?
Into 8 parts, what are 5 parts called?

Q. When an apple, or any thing, is divided into two equal parts, how would you express one part, on the slate, in figures? A. I set the 1 down, and draw a line under it; then write the 2 under the line.

Let me see you write down, in this manner, on the slate one half. One third. One fourth. One fifth. One sixth. Two sixths. Three sixths. Three eighths. Eight twelfths.

Q. What are such expressions as these called? A. Fractions. Q. When, then, any whole thing, as an apple, a unit, &c. is broken or divided into equal parts, what are these parts call ed? A. Fractions.

Q. Why called fractions? broken.

A. Because fraction signifies

Q. You have seen, that, when any whole thing is divided in to 3 parts, these parts are called thirds; into 4 parts, callea Fourths: what, then, does the fraction take its name or denomi nation from? 9. From the number of parts into which any thing is divided.

Q. When an apple is divided into 6 parts, and you are de sirous of giving away 5 parts, how would you express these parts? A. t.

Q. What is the 6 (in ) called? A. The denominator.

Q. Why so called? A. Because it gives the name or donomination to the parts.

Q. What is the 5 (in ) called? 9. Numerator.

Q. Why so called? A. Because it numerates or numbers the parts.

Q. Which is the numerator, then? A. The number above the line.

Which is the denominator? A. The number below the line.
What, then, does the denominator show? A. The number

of parts a unit, or any thing, is divided into.

Q. What does the numerator show? A. How many parts are taken, or used.

Q. In the expressions 3, 16, 12, 30, which are the numerators, and which are the denominators?

Q. If you own & of a vessel, how many parts is the vessel supposed to be divided into? and how many parts dɔ you own? A. 40 parts, and I own 28 parts.

Q. Is of an apple more than } of it?

Q. What fraction, then, is greater than? Than‡? Than Than? Than? What fraction is less than? Than Than Than &?

Q. From these remarks, what appears to be a correct definition of fractions? 9. They are broken parts of a whole num

ber.

Q How are they represented? A. By one number' placed above another, with a line drawn between them.

Q. In Simple Division, you recollect, that the remainder was represented in like manner; what, then, may justly be consid ered the origin of fractions? A. Division.

Q. What may the numerator be considered? A. The dividend.

Q. What may the denominator be considered? A. The di

visor.

Q. What, then, is the value of a fraction? A. The quotient of the numerator divided by the denominator.

Q. What is the quotient of 1 dollar divided among 2 men? 4. .

Q. What is the quotient of divided by 8? Q. How, then, are fractions represented? of division.

Q. What does express?

A.

.

A.

By the sign

2 is the dividend.

The quotient, of which is the divisor.

1. If 3 apples be divided equally among 8 boys, what part of one apple will each boy receive? 1 apple among 8 boys would ne of an apple apiece, and 3 apples would be 3 times as much; that is, of an apple apiece

Ans. .

2. If 4 oranges be divided equally among 8 boys, what part of an orange is each boy's part? 1 orange among 8 boys

, and 4 oranges are 4 times as much; that is, §, Ins. li 2 oranges among 7 boys? A. . 9 oranges among 13 boys? 20 oranges among 37 boys?

3. One orange among 2 boys is of an orange apiece; ho

much is 1 divided by 2, then? Ans. . How much is 1 divided by 3? A. . The quotient of 5 divided by 6? A. §. Of 3 by 5? Of 7 by 9? Of 8 by 13? Of 11 by 15?

4. What part of one apple is a third part of 2 apples? A third part of one apple is, and a third part of 2 apples must be twice as much; that is, of 1 apple. A. 3.

5. What part of 1 apple is one fourth (4) part of 3 apples? of 3 apples is 3 times as much as 4 of l'apple; that is, & of 1 apple. A. 1.

6. What part of one apple is of 3 apples? A. . What part of 1 apple is of 4 apples? A. of 4 apples is what part of 1 apple? Ans. .

A PROPER FRACTION. Q. We have seen that the denominator shows how` many parts it takes to make a whole or unit ; when, then, the numerator is less than the denominator, is the fraction greater, or less, than a whole thing or unit? A. It must be less.

Q. What is such a fraction called? A. A Proper Fraction. Q. How may it always be known? A. The numerator is less than the denominator.

Q. What kind of fractions are,, }, &c.?

AN IMPROPER FRACTION. Q. When the numerator is as large, or larger than the denominator, as, §, H,, it is plain, that the fraction expresses 1 whole, or more than 1 whole, what is such a fraction called? A. An Improper Fraction.

Q. How may it be known? A. The numerator is greater than the denominator.

Q. What kind of fractions are, 42, §, &c

A MIXED NUMBER. Q. What is a mixed number? A. A fraction joined with a whole number.

Q. What kind of fractions are 15, 167, &c.

Q. What kind of fractions are each of the following expressions, viz. 15, 8, 21, 8, 18, 71, 50?

1 XXXV. To change an Improper Fraction to a Whole or Mixed Number.

1. How many whole apples are there in 6 thirds (§) of an apple? In 8 quarters ()? In ? In 16? In 2? In ? In 488 ?

2 How many weeks in 40? In 4?

of a week? In 2? In 47 ? In

3. How many pints in gills? In 22 gills In 4 gills

In 120 gills'

4. How much is of a dollar? A. $1. Is ? A. 1 and 1. Is? Is 46? Is 7? Is 24? Is 25?

Q. What is the finding how many whole things are contain ed in an improper fraction called? A. Reducing an improper fraction to a whole or mixed number.

1. James, by saving of a dollar a day, would save in 33 days; how many dollars would that be?

OPERATION.

16)33

Ans. 2 dollars.

In this example, as & make 1 dollar, it is plain, that as many times as 16 is contained in 33, so many dollars it is, 16 is contained 2 times and 1 over; that is, 21 dollars.

RULE I. What, then, is the rule for reducing an improper fraction to a whole or mixed number? A. Divide the numerafor by the denominator.

More Exercises for the Slate.

2. A regiment of soldiers, consuming of a barrel of pork a day, would consume in 28 days 28 of a barrel; how many barrels would that be? A. 53 barrels.

3. A man, saving of a dollar a day, would save in 365 days 365; how many dollars would that be? A. $73.

4. Reduce 101 to a mixed number. 4. 20.

5. Reduce,

6. Reduce

to a mixed number. A. 7219.

to a mixed number. A. 4. 7. Reduce 134 to a mixed number. A. 12.

8. Reduce 167 to a mixed number. A. 131.

12

9. Reduce to a mixed number. A. 23148.

272

10. Reduce 172 to a whole number. A. 144.

! XXXVI. To reduce a Whole or Mixed Number to an Improper Fraction.

1. How many halves will 2 whole apples make? Will 3/ Will 4? Will 6? Will 20? Will 100?

2. How many thirds in 2 whole oranges? In 24? In 23 In 3 In 3? In 8? In 12?

3. A father, dividing one whole apple among his children, gave them of an apple apiece; how many children were there?

4. James, by saving of a dollar a day, found, after several days, that he had saved 13 of a dollar; how many 8ths did he save? and how many days was he in saving them?

5. How many 7ths in 2 whole oranges? In 24? In 29? In 34?

This rule, it will be perceived, is exactly the reverse of the last, and proves the operations of it.

RULE I. What, then, is the rule for reducing a mixed or whole number to an improper fraction? A. Multiply the whole number by the denominator of the fraction.

II. What do you add to the product? A. The numerator. III. What is to be written under this result? A The denominator.

More Exercises for the Slate.

2. What improper fraction is equal to 20? 3. What improper fraction is equal to 7219? 4. What improper fraction is equal to 4? 5. What improper fraction is equal to 12?

A. 1201

A. 874.

A. 38.

A. 38.

A. 197.

= 18..

6. What improper fraction is equal to 16? 7. What improper fraction is equal to 17? A. 189. 8. What improper fraction is equal to 144? A. 1729. 9. Reduce 30 pounds to 20ths. As zo of a pound 28., the question is the same as if it had been stated thus · in 30£ 5 s. how many shillings? A. 605605 shillings. 10. In 144 weeks, how many 7ths? A. 191101 days. 11. In 268 pecks, how many 8ths? A. 21211 quarts.

=