Page images
PDF
EPUB

ought to be greater than the second term, I mark the less extreme for a divisor; I multiply the two unmarked terms together, and divide the product by the marked term, the quotient 13.54166 &c. reduced to its proper terms is the answer.

7
8

2. If 2yds. 3qrs. of cloth yard wide will make a coat, how

much shalloon half yard wide will be required to line it throughout?

[blocks in formation]

3. Sold a barrel of ale for 3l. 7s. 6d.; what sum will pay for 35.264 barrels ? Ans. 1191. Os. 3d. .36.

4. If 50l. will pay for 16cwt. 1qr. 16lb. of raisins, what is the price per cwt.? Ans. 31. 1s. .00218.

5. Bought

purchase.

4

5

3

8

of a levant trader for 3571. 5s. what sum will

of the remainder ? Ans. 4761. 6s. 8d.

6. Paid 9.871. for 6.54 cwt. of stock-fish; what quantity can be had for 32.17. at that rate? Ans. 21cwt. 1qr. 2lb. .2297856.

7. If a lump of ore, weighing 15.253 lb., be valued at 3s. 9d. what is the cargo of a ship, carrying 180 tons of the same, worth? Ans. 4956l. Ss. Od. 4.939.

8. A piece of cloth was cut into two parts, one of which measured 5 English ells, and the other 8 Flemish ells; what is the value of the whole, at 8s. 4d. per yard?

239. COMPOUND PROPORTION IN DECIMALS.

RULE. Prepare the numbers (if they require it) as in the preceding rule, and work as in Compound Proportion in whole numbers".

EXAMPLES.

1. If 7 men earn 97. 10s. 6d. in 10 days, what sum will 28 men earn in 314 days.

[blocks in formation]

2. If 301. in 20 months gain 10l. 5s. what ́sum will 201. gain in 10 months?

[blocks in formation]

3. If 3yd. 2qr. 1n. of cloth that is yard wide cost 9s. 6d., what cost 4yd. 3qr. 2n. of yard wide, and of equal goodness? Ans. 19s. 6d.

4. Paid 31. 7s. 4d. for the carriage of 5cwt. 3qrs. 150 miles; what sum will pay for the carriage of 7cwt. 2qr. 25lb. 64 miles at the same rate? Ans. 11. 18s. 7d..0525.

b This rule depends on the same principles with Compound Proportion in whole numbers.

CIRCULATING DECIMALS.

240. Circulating, repeating, or recurring decimals are those in which one or more of the figures continually recur, and may be carried on indefinitely; the figures that recur are called repetends.

241. A pure repetend is a decimal in which all the figures recur; as .222 &c. .012012 &c. .153153 &c.

242. A mixed repetend is a decimal in which some of the figures do, and some do not, recur; as .5333 &c. .341212 &c. 419375375 &c.

243. A single repetend is that in which only one figure repeats, as .333 &c. and is denoted by a point placed over the circulating figure, as .3.

244. A compound repetend is that in which the same figures repeat alternately, as .1212 &c. .345345 &c. and is expressed by a point over the first and last repeating figure, as 12....345 &c.

245. Similar repetends are those which begin at equal distances from the decimal mark; thus .2357, .471, and .493857, are similar.

246. Dissimilar repetends are those which do not begin at equal distances from the decimal mark; thus .23123 and .4531 are dissimilar.

247. Conterminous repetends are such as end at equal distances from the decimal mark; thus 232323 and .315315 conterminous, as are .34517 and 82413.

are

248. Similar and conterminous repetends are such as begin. at the same distance from the decimal mark, and end at the same distance; thus .785343434 and .000789789 are similar and conterminous, as are .12345 and .54321.

REDUCTION OF CIRCULATING DECIMALS.

249. To reduce a pure repetend to its equivalent vulgar

fraction.

RULE I. Under the given repetend as a numerator write as many nines as the repetend has figures for a denominator. II. Reduce this fraction to its lowest terms, which will be the fraction required'.

EXAMPLES.

1. Required the values of .3 and .36 in vulgar fractions ?

Thus .3= = Ans. and .36=

3 1
9 3

36 4

Ans.

99 11

2. Reduce .234 and 341231 to equal vulgar fractions.

[blocks in formation]

2

3. Reduce .6 and .45 to vulgar fractions. Ans. and

5

3

11

4. Reduce 213 and 7286 to equal vulgar fractions. Answer

[blocks in formation]

5. Reduce .135 and 769230 to fractions. Ans. and

5

370

37

481

i If unity, with ciphers subjoined, be divided by 9, in infinitum, the quotient

will be 1 continually; thus

[blocks in formation]
[merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small]

1; wherefore every single repetend is equal to a vulgar frac

tion, the numerator of which is the repeating figure, and the denominator 9.

[blocks in formation]

003; and the same holds true universally.

Wherefore every pure repetend is equal to a vulgar fraction, the numerator of which consists of the repeating figures, and its denominator of as many nines as there are repeating figures; which was to be shewn,

250. When any part of the repetend is a whole number. RULE. Subjoin as many ciphers to the numerator as the highest place of the repetend is distant from the decimal mark".

6. Reduce i.oi and 12.78 to fractions.

[blocks in formation]

7. Reduce 2.46, is.24, and 1234.8 to vulgar fractions. An

[blocks in formation]
[ocr errors]

8. Reduce 1.3, 21.7, and 312.4 to equal vulgar fractions.

[blocks in formation]

251. To reduce a mixed repetend to its equivalent vulgar

fraction.

RULE I. Prefix as many nines as there are places in the repetend, to as many ciphers as there are places in the finite part, for a denominator.

II. From the given mixed repetend subtract the finite part for a numerator, and reduce the fraction to its lowest terms for the answer.

101

999

k This rule may be explained by example 6; where if we suppose ioi to be wholly a decimal, its equivalent vulgar fraction will be by the preceding rule; but i.oi is ten times ini, whence the foregoing fraction multiplied by will be the value of 1.0i. Again, if 1278

10, (thus

101 999

× 10,) or

1010
999

be considered as a decimal, its equivalent vulgar fraction will be

[blocks in formation]

i2.78 is 100 times .1278; wherefore the vulgar fraction, equal to the former,

will be 100 times as great as that equal to the latter, that is, 12 which is the rule,

[ocr errors][merged small]

12.78 =

9999

« PreviousContinue »