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4. From take

Result to 3 X 5 = 152

new numerators. 2 X 7 14

5 *7 = 35 com, denom.

12

9

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99

9

35
5. From 1 take 1:

Result
6. From 11 take :

Result
7. From take :
go

Result š. 8. From 1 take go

Resultat Note 2.-When mixed numbers are given, reduce them to improper fractions, and reduce these to fractions which have a common denomingtor ; then subtract as before. 9. From 8 take it

Result 194 10. From 9 take 4.

Result 40 11. From 77 take 34.

Result 4 Note 3.—When compound fractions are given, reduce them to single ones, and these again to a common denominator; then subtract as before. 12. From 1 of 1o take of 를

Result 61

186 13. From of 1 take 1 of

Result 133 14. From take off.

Result 14 Note 4. When a fraction or a mixed number is given to be subtracted from a whole number, subtract the numerator of the fraction from its denominator, and under the remainder set the genominator ; then carry 1 to be subtracted from the integer8. 15. From 6 take .

Result 5
16. From 3 take a
17. From 100 take 99166

Note 5.-When the given fractions are of different deno. minations, reduce them to their proper values, or quantities, and subtract as in the following example. 18. From 7 of a pound, take to of a shilling. of a L. = 158. 6d.

d. d. jo of a s. = 3d.

- = ਤ

Result 21%
Result. Ito

13 17

a

158. 31 Result.

N

19. From of a L. take of a shilling. Result 14s. 3d. 20. From of a lb. troy, take of an ounce.

Result 8 oz. 16 dwt. 16 grs. 21. From of a yard take of an inch. Result 5 in.. 22. From of a L. take of of a shilling.

Result 10s. 7d. Iqr.

MULTIPLICATION OF VULGAR FRACTIONS.

GENERAL RULE.

Reduce compound fractions to single ones, and mixed numbers to improper fractions; then multiply the numerators together for a new numerator, and the denominators for a new denominator.

1

1

144

EXAMPLES. 1. Multiply s by.

Resultat

Result 2. Multiply to by . 3. Multiply by 18.

Result 2

Result 96 4. Multiply 12 by 7.

123= 43 and 7į = *}; then 3 x2 = '40 = 963. 5. Multiply 77 by 84

Result 614 6. Multiply 41 by .

Result is 7. Multiply by 1316

Result 128

Result 750 8. Multiply of by to of it.

Result 2 9. Muluply 4 by jof 10. Multiply į of 7 by 를

Result 13 11. Multiply 21 by 11, and multiply the product by of of .

Result ş.

9

45

DIVISION OF VULGAR FRACTIONS.

GENERAL RULE. Prepare the given fractions, if necessary, then invert the divisor, and proceed as in Multipli ation.

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Prepare the given terms, if necessary, and state them as in whole numbers ; multiply the second and third terms together, and divide the product by the first. Or,

Invert the dividing term, and multiply the three term's together, as in Multiplication.

EXAMPLES 1. If ļof a yard cost of a shilling, what will of a yard come to?

Ans. 2s. 4d. yd. yd. yd.yd. If : :: 3 :

= 25. 4d. Inverted 1 x x }

= 26. 4d. 2. If of a yard cost 1 of a pound, what will of a yard come to ?

Ans. 3s. 4d:

56 24

1657

.

3. If is of a lb. of sugar, costs of a shilling, what cost * of a 16.

Ans. 4d. 3qrs. 1634. If of a yard of lawn cost 75. 3de what will 104 yards cost?.

Ans. 4L: 19s. 10d. 2qrs. . 5. If 11 yard cost 95. what is the value of 164 yards?

Ans. 5 L. 17s. 6. What is the value of 100 yards of cloth, at l} shillings per yard?

Ans. 6L: 7. If 1 ounce of silver cost 5fs. what is the value of 164 oz.?

Ans. 4L. +2s. 1 qrs. 8. How much will 4€ lb. of cheese come to, at 12 cents

Ans. 553. cents. 9. If i bushels of apples cost 39 cents, what is the value of 3 bushels ?

Ans. $1.0135 10. What will of a lb. come to, if of a lb. cost of a shilling?

Ans. 475. 11. If yo ewt. cost 147, L. what will 71 cwt. amount to?

Ans. 118L. 6s. 8d. 12. If 8 lb. of sugar cost 45.990. how much is it per lb.?

per lb.

Ans. 7 d.

13. If I yard of cloth cost 15ks. whať will 4 pieces, each containing 27 yards cost?

Ans. 85 L. 10s 11 d. 14. What will licwt. of pepper come to, if 151 lb. cost 123s. ?

Ans. 6L. 163. 347d. 15. A person having of a sloop, sells { of his share for 391 L. what is the value of the whole vessel, at that rate?

Ans. 598 L. 2s. 6d.16. A merchant had 5. cwt. of sugar, at 6d. per lb. which he bartered for tea, at 8-s. per Ib. How much tea did he receive for the sugar?

Ans. 4375lb.

INVERSE PROPORTION.

RULE. Prepare the terms as in Direct Proportion, then multiply the first and second terms together, and divide the product by the third. Or,

Invert the third term, and multiply the three terms together as in Multiplication.

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EXAMPLES. How much shalloon, of a yard wide, will line 44 yards of cloth, 14 yard wide?

Ans. 9 yards. yd. yd.yd.yd.

Or thus : 41 ly

As j ::::9 ix}x}= 100 = 9. 2. What quantity of shalloon, yard wide, will line 7 yards of cloth, 11 yards wide ?

Ans. 15 yards. 3. If 16 men finish a piece of work in 28 days, how long will 12 men require to do the same work?

Ans. 37 days. 4. If 3 men can do a piece of work in 41 hours, in how many hours will 10 men do the same in?

Ans. 5. If 254 dollars will pay for the carriage of 1 cwt. 1454 miles, how far may 62 cwt. be carried for the same money?

Ans. 22 miles. 6. How many pieces of cloth, at 20 dollars per piece, are equal in value to 2404 pieces, at 12 dollars per piece ?

Ans., 149 172 pieces. 7. A merchant bartered 59 cwt. of sugar at 6 d. per

lb. för tea at 8 s. per lb. How much tea did he receive?

Ans. 43-516.

THE DOUBLE RULE OF THREE

IN VULGAR FRACTIONS.

RULE.

Prepare the given terms when necessary, by reduction, then proceed as directed in whole numbers. Or,

Invert the dividing terms, and multiply the upper figures continually for the numerator, and those below for the denominator of the fractional answer.

EXAMPLES 1. If yard of cloth, 3 yard wide, cost L. what is the value of yard, 11 yard wide, of the same quality ? .

X ji .

Xix=1= 16 * = }} = 318 = {L. = 139.-4d. Answer.

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Syd.
7 yd.

70

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