3. Reduce

7. Reduce

8. Reduce

9. Reduce

of a pound to the fraction of a shilling.
of a shilling to the fraction of a pound.

of an eagle to the fraction of a mill. of a mill to the fraction of an eagle. 10. Reduce 105 of a guinea to the fraction of a farthing. 11. Reduce of a farthing to the fraction of a guinea. 12. Reduce of a pound to the fraction of a guinea. 13. Reduce of a guinea to the fraction of a pound. 14. Reduce of a day to the fraction of a minute. 15. Reduce 1440 of a minute to the fraction of a day. 16. Reduce of a bushel to the fraction of a quart. 17. Reduce 19 of a quart to the fraction of a bushel. 18. Suppose one man has of a pound, another of a shilling, and another of a penny; what fraction of a dollar has each.

1441

160 171

A. $. 19. Reduce of a pound to the fraction of a crown at 6s. 8d. each A. 801 crown

20. What fraction of a pound is of 3 of a hundred weight?

A. 300lb.

21. Suppose you owe of a guinea, (28s.) and pay what part of a pound do you still owe?

100

=

3 pounds. of the debt, A. £3.

30

22. If A buys of 5 hogsheads of molasses, and sells B. of it, what fraction of a gallon does B buy? A. 63 of a gallon. 23. Suppose of of a pound is the numerator of a fraction, and of £2 the denominator; what fraction of an eagle will express the same value? A. of an eagle.

CASE XV.

20

To find the integer from having a fractional part given.

RULE.

1. Multiply the integer by the denominator, and divide the product by the numerator. LII. 10.

2. Find that number

3. What number is that

of which is 205.

of which is 20,000 ?

A. 888. A. 55,000.

4. Suppose a merchant sells exactly 11hhd. 49gal. 3qt. 1pt. 3gi. of molasses, it being of all he has on hand; what quantity had he at first? A. 78hhd. 39gal. 1pt.

1920

Q. How is 960 (=) of a farthing reduced to the fraction of a pound? 8,9 CASE XV. Q. 40 is of what number? If 12 be of a certain number. what is that number? What is the rule? 1. When a man pays 8 dollars for of a barrel of flour, what is a barrel worth at that rate?

5. Find that sum

of which is £3. 5s. 6d. 6. The postage of a letter for 400 miles is

A. £5. 17s. 11 d.

of a dollar; how far,

at that rate, can a letter be carried for one dollar? A. 2,133 miles. 7. 503 is of 5 of what number? A. 1475

8. It is estimated that nearly 25,000,000 persons die annually being of the population of the earth; what, according to that esti mate, must be the whole population of the globe? A. 800,000,000

ADDITION OF FRACTIONS.

GENERAL RULE.

LXIII. 1. Reduce complex and compound fractions to single ones, and all to a common or least common denominator; over which write the sum of the numerators. LV. 1, 2.

2. This sum may often be reduced either to lower terms, or to a whole or mixed number.

3. Add together £3, £ £} and £}.

A. £=£2.
A. 18.

835 941

4. Add together 11, 347, 417, and 11. 5. To add mixed numbers.—Find the sum of the fractional parts first, and if it contain a whole number, add it to the sum of the other whole numbers.

6. Or, reduce the mixed numbers first to improper fractions, then add them by the general rule.

7. Add together $1,20317, $9,40613, and $8,9061.

9. Find the sum of 67533, 89133, and 91533.
10. Suppose that one pile of wood contains 136

A. 19,517.

A. 2,48317. cords, another

95653 cords, and another 45231 cords; how many cords are there in all the piles?

3

A. 1,545 cords.

11. Add together, 2, 1, and . Reduce them first to their least common denominator.

12. Find the sum of 463, 893 and 40 7.

A. 2.

A. 177 40
A. $50.

A.

years, an 2,1403

8

13. Add together $182, $51, $715%, $83, and $97. 14. What is the sum of 7894 years, 8173 years, 316 216 years? 15. Find the sum of 2, 3 of %, and 3 of 51. Reduce the fractions to single ones first.

3 2

8

A. 419.

LXIII. Q. What is the general rule for adding fractions? 1. What may oftentimes be done with the result? 2. What is the sum of 9,,, and? What is the sum of 84, 92, and 101? What is the rule for the last example? 5,6 What is the sum of and? See 11.

16. What is the sum of 8193 barrels, of § barrels, 4093 barrels, and of 5 barrels ? A. 1,232 barrels.

6

17. Add together, and Reduce them first to single 3' *&

fractions, then proceed as before.

15

A 15 18. Add together the complex fractions that may be formed by dividing 2 by 3, 2 by 4, 3 by 3, and 21 by 3. A. 5. 19. To add fractions of different denominations.-First find the alue of each in compound numbers, then add them as in Compound Addition.

20. Or, first reduce the fractions of different denominations to those of the same, then add them by the general rule. 21. Add together of a pound and of a shilling. £}=3s. 4d.— s. 8d. Then 3s. 4d. +8d. =4s. A. 4s.

22. Add together £3 and of a shilling. 23. Find the sum of of a ton,

pound.

A. 8s. 10d. 12qr.

of a hundred weight, and of a 11cwt. 2qr. 13lb. 3oz. 634dr.

A. 24. Find the sum of 3 of a league, A. 1m.

of a yard, and of a foot. 6fur. 16rd. 2ft. lin. 1b.c. 25. Add together of an ounce and of an ounce. A. 14 dr. 26. A man labored 103 hours in one day, 9 hours in another, and 11 hours in anotner; how many hours did he labor in all? A. 31h. 35m. 13 sec

SUBTRACTION OF FRACTIONS

GENERAL RULE.

LXIV. 1. Reduce complex and compound fractions to single ones, and all to a common or least common denominator, over which write the difference of the numerators. LV. 1, 2.

2. From of a dollar take of a dollar.

3. From take 2759.

9539

9539 3795 9328.

4. From 1531 take 31

9328

A. $

A. 5808 9539.

A. 3736

9328

5. From take 1 Reduce them first to their least common denominator.

A. 23.

A.

24 14 53

8. A bought of a load of hay, and B. of a load; how much did one buy more than the other?

Q. How are fractions of different denominations added? 19, 20. What is the sum of £2 and of a shilling? What is the sum of 3 of a mile and 3 of a furlong? LXIV. Q. From take 3. From take. What is the rule? 1. From of of a dollar take of a dollar.

1

9. From of 5 take

10. From 4 take of 3.

A. 7=211
A. 2.

11. A. having bought a quantity of sugar, sold of it to B, who of what he bought to C; what part had B left?

sold

A. 15.

13. To subtract a mixed number from a whole number.-Write the difference between the numerator and denominator over the denominator, and carry 1 to the whole number.

14. For, since the denominator expresses all the parts of 1 unit, the process is the same in pinciple, as borrowing and carrying in simple numbers.

Say, 5 from 16=11, that is, and carry 1. For from 18 (=1 unit borrowed from 815) leaves and 1 to carry as before.

A. £2,5381 A. 227 years. A. league. A. 1000. A. 3.

16. From £5,075 take £2,53615.
17. From 487 years take 259 years.
18. From 1 league take 25 of a league.
19. How much less than unity is 3999?
20. From 1 take the sum of 3 and 4.
21. From 1 take the sum of and.
22. What fraction added to the sum of and will make a unit?

4000

1

A. 18

A. .

7

23. Suppose a pole standing so that of it is in the mud, 3 in the water, and the rest above water; what part is above water? A. 17. 24. From 1 take the sum of 25. A gentleman spent of his America, and the rest in France. in the latter country?

and 3.
A.
life at school, in England, in
What part of his life did he spend
A. 13.

26. To subtract one mixed number from another.-Having reduced the fractions to a common denominator, subtract as at first, but if the lower numerator exceed the upper one, subtract it from the common denominator and add the difference to the upper numerator, carrying one as before.

Say, 5 from 11=6, that is,, or from ==3. 16

27 From £96
Take £18 18

5

29. A merchant owing $405, paid $293; how many dollars re main unpaid?

A. 112.

Q. How is a mixed number subtracted from a whole number? 13. Why is the numerator to be subtracted from the denominator? 14. From 4 gallons take 23 gallons. From £1 take £3. How much does unity exceed

10

7 2 217

How is one mixed number subtracted from another? 26. A man having 4 yards of broadcloth, sold 2 yards; how many yards had he left? From take 15.

32. From 4 take 3. Reduce the fractional parts to the least

common denominator first.

13

A. . A. $59.

33. From the sum of $453 and $62% take $49. 34. A merchant purchased 21 barrels of flour of one man, and barrels of another; how much will he have left after he has sold 303 barrels ? A. 3 barrels. 35. To subtract fractions of different integers.-First find their separate values, then subtract as in compound numbers. 36. From of a day take 3 of an hour. 37. From £3 take of a shilling.

A. 18h. 27m. A. 8s. 4d. qr.

16

38. When a man has traveled 4 of the distance from New York to Philadelphia, it being 90 miles, how far has he still to travel?

A. 38m. 4fur. 22rd. 4yd. 2ft. lin. 24b.c

MULTIPLICATION OF FRACTIONS.

LXV. 1. To multiply a fraction by a whole number.—Multiply the numerator, or rather divide the denominator when it can be done without a remainder. LVII. 17.

2. If you pay of a dollar for a yard of ribbon, what will 2 yards cost?-4 yards cost?-8 yards cost?

A. $1; 81; $1. A. 240 120.

3

3

18.

6

A. 17

3

14

107.

5. All fractional answers should be expressed in their lowest terms.

14

49

14

A. 495; 185 495

A. 3; 2; 1

6. Multiply by 4;-by 12 ;-by 14. 7. Multiply by 8;-by 6;-by 4. 8. If one horse consume of a ton of hay in a month, how much will 7 horses consume in the same time?

21

A. 1 ton.

9. To multiply a whole number by a fraction.-Multiply by the numerator and divide by the denominator, or divide first when it can be done without a remainder.

10. This rule proceeds on the same general principle as that for whole numbers, viz.

11. That as many times as the multiplier is made smaller, so many times the product is made smaller.

Q. How are fractions of different integers subtracted? 35. From

take

of a minute. From 4 dollars take of a dollar. From of take of 1qr.

of a day

of lewt

LXV. Q. How is a fraction multiplied by a whole number? 1. Multiply 3 by 5;-4 by 5;-16 by 320. How is a whole number multiplied by a fraction? 9. On what principle is the rule based? 11.