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EXAMPLES FOR PRACTICE. 2. Reduce rado of a pound to the fraction of a farthing.

Ans.

Ans. 3. What part of a penny is 45 of a shilling? 4. What part of a grain is goio of a pound Troy?

Ans.

Ans. 124 5. What part of an ounce is 1727 of a cwt. ? 6. Reduce 1320 of a furlong to the fraction of a foot.

Ans. t. 7. What part of a square foot is 58080 of an acre ?

Ans. 1. 8. What part of a second is getoo of a day?

Ans.

Ans. q. 9. What part of a peck is it of a bushel ?

Ans. 10. What part of a pound is ado of a cwt. ?

ART. 168. To reduce a fraction of a lower denomination to a fraction of a higher. Ex. 1. Reduce of a farthing to the fraction of a pound.

Ans. Ibo

OPERATION.

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OPERATION BY CANCELLATION.

4

1

Since 4qr. make a penny,

-£. 9 X 4 X 12 x 20 2160 there will be as many

pence as farthings; there. fore we divide the fqr. by 4, and obtain d. And, since 12d. make a shilling, there will be fi as many shillings as pence; hence we divide d. by 12, and obtain tas. Again, since 20s. make a pound, there will be zo as many pounds as shillings; therefore we divide tes, by 20, and obtain = 16 £. for the answer.

Rule. Divide the given fraction by the numbers that would be employed in reduction of whole numbers to reduce the denomination of the fraction to the higher denomination required.

EXAMPLES FOR PRACTICE. 2. Reduce # of a grain Troy to the fraction of a pound.

Ans. Todoo

Questions. - Art. 168. Do you multiply or divide to reduce a fraction of a lower denomination to the fraction of a higher ? What is the rule ?

Ans. 36o

Ans. st. 3. What part of an ounce is ir of a scruple?

Ans. To 4. What part of a ton is of an ounce ?

: 5. What part of a mile is g of a rod ? 6. What part of an acre is of a square

foot ?

Ans. 51 7. What part of a day is the of a second ?

Ans. godoo: 8. What part of 3 acres is of a square

foot ?

Ans. Jg4030 9. What part of 3hhd. is 4 of a quart?

Ans. 1323 10. What part of Ğ of a solid foot is į of a yard solid ?

Ans.

Art. 169. To find the value of a fraction in whole numbers of a lower denomination. Ex. 1. What is the value of 18 of 1£. ?

Ans. 7s. 9d. 1}qr.

OPERATION.
7
20

18

18) 140 (7.

126
14

12
18) 168 (90.
162

6

4
18) 24 (1fqr.

18
fs=1

The reason of this operation will be seen, if we analyze the question according

7 x 20 to Art. 167. Thus, 73 £.= = - 14es.

14 x 12 =714s.; and 1 s. = 168d. = 9,6d.; and fd.= is ={$r.= 1.jqr.

Ans. 7s. 9d. 14qr.

18 6 X4

RULE. - Multiply the numerator of the given fraction by the number required of the next lower denomination to make one of the denomination of the given fraction, and divide the product by the denominator. Then, if there is a remainder, proceed to multiply and divide in this manner, until it is reduced to the denomination required; and the several quotients will be the answer.

QUESTION. - Art. 169. What is the rule for finding the value of a fraction in whole numbers of a lower denomination ?

EXAMPLES FOR PRACTICE.

2. What is the value of 7 of a cwt. ?

Ans. 3qr. 3lb. loz. 12fdr. 3. What is the value of } of a yard ? Ans. 3qr. Ofna. 4. What is the value off of an acre ?

Ans. IR. 28p. 155ft. 824in. 5. What is the value of şof a mile?

Ans. lfur. 31rd. lft. 10in. 6. What is the value of 11 of an ell English ?

Ans. Iqr. 1 fna. 7. What is the value of 4 of a hogshead of wine ?

Ans. 18gal. Oqt. Opt. 8. What is the value of 11 of a year ?

Ans. 232da. 10h. 21m. 4914 sec.

OPERATION.

Art. 170. To reduce a simple or compound number to the fractional part of any other simple or compound number of the same kind. Ex. 1. What part of 1£. is 3s. 6d. 2fqr. ?

Ans. 8. £.

In performing this operation, we 3s. 6d. 23qr. = 512

reduce the 3s. 6d. 23qr. to thirds

15. of qr., the lowest denomination 1£. = 2880

in the question, for the numerator of the required fraction, and i£. to the same denomination for the denominator. We then reduce this fraction to its lowest terms, and obtain £. for the answer.

Rule. - Reduce the given numbers to the lowest denomination mentioned in either of them; then write the number which is to become the fractional part for the numerator, and the other number for the denominator of the required fraction.

EXAMPLES FOR PRACTICE. 2. Reduce 4s. 8d. to the fraction of 1£. ?

Ans. 3. What part of a ton is 4cwt. 3qr. 121b. ? 4. What part of 2m. 3fur. 20rd. is 2fur. 30rd. ? Ans. 75. 5. What part of 2A. 2R. 32p. is 3R. 24p. ? 6. What part of a hogshead of wine is 18gal. 2qt. ?

s .

Ans. 17.

Ans. .

Ans. 37

Question. - Art. 170. What is the rule for reducing a simple or compound number to the fractional part of any other simple or compound number of the same kind ?

7. What part of 30 days are 8 days 17h. 20m. ?

Ans. 8. From a piece of cloth containing 13yd. Oqr. 2na. there were taken byd. 2qr. 2na. What part of the whole piece was taken? 9. What part of 3 yards square are 3 square yards ?

Ans. 1.

Ans. 4.

ADDITION OF FRACTIONS OF COMPOUND NUMBERS.

FIRST OPERATION.

8.

d.

qr.

1 24

SECOND OPERATION.

7

Art. 171. To add fractions of compound numbers.
Ex. 1. Add of a pound to [ of a shilling.

Ans. 175. 11d. 0A9r.

We find the value of each Value of $£.=17

fraction separately, and add the Value of js.

9 1}

two values together according to

the rule, for adding compound 17 11 0:41 numbers. (Art. 101.)

We first reduce [ of a shilling Eğ

x 20

I fo£.

the fraction of a

shilling to the frac $£. +1.£.=+*£.=17s. 11d. 0,4qr. tion of a pound, then add the two fractions together, and find the value of their sum. (Art. 169.)

EXAMPLES FOR PRACTICE. 2. Add Af of a pound to $ of a shilling.

Ans. 7s. 11d. 339qr. 3. Add together ii of a ton, ş of a ton, and # of a cwt.

Ans. IT. 14cwt. lqr. 633lb. 4. Add together of a yard, g of a yard, t of a quarter.

Ans. lyd. 2qr. 2na. 033in. 5. Add together t of a mile, $ of a mile, į of a furlong, and 1 of a yard.

Ans. 6fur. 29rd. 3yd. ift. Offin. 6. Add together it of an acre, f of a rood, and of a square rod.

Ans. 1A. OR. 3p. 169ft. 1024 in. 7. Sold 4 house-lots, the first of an acre, the second 7 of an acre, the third și of an acre, and the fourth of an acre, what was the quantity of land in the four lots ?

Ans. 3R. 38p. 45,933ft.

Questions. - Art. 171. What is the first method of adding fractions of com. pound numbers ?

What is the second ?

SUBTRACTION OF FRACTIONS OF COMPOUND NUMBERS.

Art. 172. To subtract fractional parts of compound numbers. Ex. 1. From of a pound take it of a pound.

Ans. 9s. 10d. 149qr.

We find the value of each Value of $£.

fraction separately, and sub1 24

tract one from the other, acValue of £. = 7 3 111

cording to the rule for sub9 10 11

tracting compound numbers. (Art. 102.)

FIRST OPERATION,

d.

qr.

= 17

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$£. £. * £.

We first subtract the less fraction from the greater, and then find the value of their difference. (Art. 169.)

9s. 10d. 1549r.

EXAMPLES FOR PRACTICE.

2. From # of a ton take it of a cwt.

Ans. llcwt. Oqr. 81,1b. 3. From } of a mile take is of a furlong.

Ans. 5fur. 33rd. 5ft. 6in. 4. From 11 of an acre take of a rood.

Ans. 3R. 16p. 154ft. 5. From a hogshead of molasses containing 100 gallons, i of it leaked out; of the remainder I kept for my family ; what quantity remained for sale ? Ans. 24gal. Oqt. 13 pt.

6. The distance from Boston to Worcester is about 41 miles. A sets out from Worcester and travels of this distance towards Boston ; B then starts from Boston to meet A, and having travelled 4 of the remaining distance, it is required to find the distance between A and B.

Ans. 12m. 6fur. Ord. 5ft. 9 in. 7. A agrees to labor for B 365 days, but he was absent on account of sickness + part of the time ; he was also obliged to be employed in his own business i of the remaining time ; required the time lost. Ans. 137da. 11h. 13m. 149 sec.

QUESTIONS.-- Art. 172. What is the first method of subtracting fractions of compound numbers? The second ?

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