12. How many pounds in 5640 farthings? A. 5£ 17 s. 6 d. 13. Multiply 3600 by 25. A. 90600.

14 What will 1 ton of clover-seed cost, at 5 mills an ounce ? A $179,20.

15. At 2 cents an inch, what will 1 yard of cloth cost? A 72 cents.

16. Reduce 1 tun to gills. A. 8064 gills.

17. Reduce 20 bushels to pints. A. 1280 pints.

18. Reduce 4 tons to drams. A. 2293760.

19. How many barley corns will reach across the Atlantin Ocean, allowing it to be 3000 miles. A. 570240000.

20. How many times will a watch click in 20 years, if it click at the usual rate of 60 times in a minute? A. 631152000.

21. A father left legacies to his children as follows: to Thomas 75£ 14 s. 6 d., to William 3 times as much as Thomas, to his daughter Mary as much as Themas, and to Susan, his youngest child, as much as all the rest, lacking 20£ 13 s. 8 d.: how much did each receive? A. William 227£ 3 s. 6 d., Mary 12£ 12 s. 5 d., Susan 294£ 16 s. 9 d.

¶ XXXIV.

FRACTIONS.

1. If one third (3) of an apple cost 2 cents, what will a whole apple cost?

2. If one third cost 3 cents, what will a whole one cost? If one third cost 4 cents, what will one whole apple cost? If one third cost 6 cents? 8 cents? 9 cents? 20 cents? 50 cents?

100 cents?

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

4. If you pay 2 dollars for one eighth (3) of a ticket, what 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 equal 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 1 part called?
Q. Into 5 parts, what is 1 part called?
Q. Into 8 parts, what is 1 part called?
Q. Into 8 parts, what are 2 parts called?
Q. 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 called?'

A. Fractions.

Q. Why called fractions?

A. Because fraction signifies broken.

Q. You have seen, that, when any whole thing is divided into 3 parts, these parts are called thirds; into 4 parts, called fourths: what, then, does the fraction take its name or denomination from ?

A. From the number of parts into which any thing is divided.

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

giving. &•

Q. What is the 6 (in ) called?

A. The denominator.

Q. Why so called?

A. Because it gives the name or denomination to the parts.

Q What is the 5 (in ) called?

A. 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.

Q. Which is the denominator?

A. The number below the line.
Q. 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.

9

Q. In the expressions, 16, 12, 6, 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 do 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?

A. They are broken parts of a whole number. 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 reprcsented in like manner; what, then, may justly be considered 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 divisor.

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?
A.

Q. What is the quotient of 7 divided by 8?

A..

Q. How, then, are fractions represented?
A. By the sign of division.
Q. What does express?

A. The quotient, of which {

2 is the dividend.
3 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 be 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, , Ans. If 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; how 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. .

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

6. What part of 1 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

AN IMPROPER FRACTION.

Q. When the numerator is as large,

or larger than the denominator, as,f,, 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 denomi

nator.

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, §, 2, 8§, 18, 73, 5o ?

¶ 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 2? In ? In 24? In $8? In 288?

2. How many weeks in 4 of a week? In 28? In 42? In 5? In

?

3. How many pints in gills? In 32 gills? In 4 gills? In 120 gills?

4. How much is § of a dollar? A. $1. Is ? A. 1 and 1. Is? Is 16? Is 7? Is 24? Is 25?

Q. What is the finding how many whole things are contained in ar 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 18 make 1 dol lar, it is plain, that as many times as 16 is contained in 33, so many dollars it is; 16 is contained 2 times and I over; that is, 2 dollars.

RULE. Q. What, then, is the rule for reducing an improper fraction to a whole or mixed number?

A. Divide the numerator by the denominator.