6. What is the sum of, and ?

Ans. 21. 7. A merchant purchased a lot of cotton yarn, and sold of it to one man, and of to another: what part of the lot did he sell?*

Ans.

5 3

8. A man sells of a lot of iron to one man, and of to another: what part does he sell?

Ans. The whole. 9. If one gentleman own of a common pasture: a 2d, and a third,, what part of the pasture is owned by the 3?

Ans. 998

10. What part of a day is the sum of and of an hour?

3

1015

of a day Ans. 1.

137

0

Explanation.-- of an hour equal of a day.

4

11. What part of a pound is the sum of pound, and of a shilling?

Ans.

of a

12. What part of a ton is the sum of 3 of a cwt. and & of a qr.?

Ans.

13. What part of an inch is the sum of 3 3 of a mile?

rod and

6

6 1

Ans.

of a

14. What part of a pint is the sum of of a quart of a gal. ?

and

Ans. 43.

15. A merchant has 4 casks of rum which contain No. 1, 972 gal.; No. 2, 100; No. 3, 1103; and No. 4, 115. How many gallons in the 4 casks?

1260)2773(2 number of whole gal. contained in the fractions.

2520

New num. 253

The compound fraction must be reduced to a simple one, and the simple fraction used instead of the compound one.

Explanation. In the first place, we reduce the fractions to a common denominator. Each fraction reduced, expresses the same part of a gallon which it did before. (See Illustration, page 156.) Each mixed number in the right hand column, represents the same quantity as the number standing against it in the left. Next we add all the numerators of the fractions in the right hand column, and find their sum to be 2773. It requires 1260 of the fractional units to equal one gal., therefore, as many times as 1260 can be taken from 2773, so many whole gallons are expressed by the fractions, which we find to be two, and these two gal. we add to the unit column..

In adding other mixed numbers, one must be added to the whole number for each time the common denominator can be taken from the sum of the numerators, for the common denominator will always show how many parts, like those expressed by the fractions, are required to equal an unit or 1, in a whole number.

16. A man owes 3 debts, viz.: one of $753; one of $283; and one of $43. What is the sum of the 3 debts? Ans. $14771. 17. A, B and C, performed a journey in company with equal sums of money to defray the expenses of the same. A spent of his money, B, of his, and C of his; what part of the money possessed by the 3, was expended?

18. Add together 6,, 9, 53, and 4.

Ans. 3.

Sum, 26.

MULTIPLICATION OF VULGAR FRACTIONS.

RULE.

Multiply the numerator of the multiplicand by the numerator of the multiplier, and the denominator of

the multiplicand by the denominator of the multiplier, the former product written over the latter, will constitute the answer. If either or both of the given fractions be compounded, the continued product of the numerators and the continued product of the denominators will form the answer required.

unit.

Remark. The product will be as much less than the multiplicand as the multiplier is less than an If the multiplier be more than an unit, the product will be as much greater than the multiplicand as the multiplier is greater than an unit.

Most of the questions belonging to this rule are similar to the first 30 questions in reduction of compound fractions, and are operated in a similar manner and for the same reasons. The student should re-examine the illustration on page 145, and the several explanations under the first part of that rule, for he should pass over no questions without endeavouring to understand the principles on which their operations are founded.

1. What is the product of multiplied by &?

Explanation. The multiplier, being less than an unit, we can only take such a part of, the multiplicand, as is of an unit, and this we shall do by multiplying one fraction by the other, since the product of the denominators will be greater than that of the numerators. The question is the same as if it had been-what is of .

2. Multiply

X= the answer.

by

3. What is the product of 13, multiplied by of?

4. What is the product of 13 into?

13

Ans. 12

Ans., or 13.

Note 5.-When a mixed number is given, it is most convenient to change it to an improper fraction, then the improper fraction may be used instead of the mixed number, the same as the improper fraction in the last question.

Own

5. If a man own of 962 acres of land, how many does he ? Ans. 387, or 197 6. At 3 dollars per cwt., what will of a cwt. of

acres

logwood come to?

Ans. $117. 7. If a pipe of brandy be worth $96, what is of a pipe worth? Ans. $349. 8. What is the freight of a quantity of goods which cost $26737, if the freight equal of of the first Ans $243 9. At 5 dollars per cwt. what will 123 cwt. of

cost?

iron cost?

Explanation.-Reduce both numbers to improper Ans. $6615.

fractions.

10. If a barrel of mackerel cost $41, what will 3 bar. cost at the same rate?

Ans. $17

11. What is the product of 1201, multiplied by 100? Ans. 12122• 12. A man labours for 12 dollars per month, what will be his wages for 8 months?

Ans. $106. 13. At of a dollar per yard, what will 4 yards of riband come to ?

Explanation. If one yard cost 1 fifth of a dollar, 4 yards must cost 4 fifths; and this we shall obtain by multiplying the numerator of by 4 the number of yards. Ans of a dollar. The numerator of any simple fraction always denotes how many parts of an unit, or single quantity, are expressed by the fraction, therefore by multiplying the numerator by a whole number, we place in the numerator of the product, the number of parts, or fractional units, contained in the given numerator, as many times as there are units in the whole number. In multiplying the numerator of a fraction by a whole number, we increase the real value of the fraction, because the denominator not being altered, the parts of a quantity express

ed by the numerator of the product, are just as large as the parts contained in the numerator of the multiplicand, and we have more of them.

14. What is the product of, multiplied by 2?

Ans. 13, or 15.

15. What number is equal to 5 times ??

Ans. 2. 16. At of a shilling per pound, what will 7 lb. of copperas come to? Ans. 1 s. 17. If a man work for 1 of a dollar per day, what will he receive for 101 days' work? Ans. 795. 18. If a horse eat of a bushel of oats in one day, how many bushels will he eat in 30 days?

Ans. 81 19. What will a hog, weighing 371 lb. come to at of a dollar per pound? Ans. $163. 20. The toll of a certain bridge is $825 a year, and is divided into 60 shares. A gentleman owning 7 shares, wishes to know what his part of the toll will be for one year.

Explanation. He owns of the whole. If we divide 825 by 60, the quotient will be the value of one share, and multiplying the value of one share by 7, will give the value of 7 shares. But if we multiply 825 by 7, and divide the product by 60, the dividend, 5775 is 7 times 825, consequently the quotient must be 7 times as large as when we divided 825 by 60. Ans. $961. From this explanation it appears, that we shall obtain the same result whether we multiply a whole number by the numerator of a fraction, and divide by the denominator, or divide the whole number by the denominator and multiply the quotient by the numerator.

21. What is the product of 1091, multiplied by 7? Ans. 8485. 22. A and B bought a lot of cotton in company for 1150 dollars, of which A paid 635 dollars, and В the