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- S ---17. Add # of a pound, 7. of a crown, and 9 of a shilling

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Sum required 1 O 53. the answer.

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4. 19. Add + of a pound to # of a shilling. Sum 16s. 10d. o

5 20. Add 12 of a guinea, # of a pound, and # of a shilling together. Sum 12s. 5d.;. 3 21. Add lo of an English ell to # of a yard. Sum lyd. 1gr.

22. Add # cwt. and + lb. together. Sum 34r. 14b. 1202. 12; dr. 23. Add + mile and # furlong together. Sum 2fur. 16p. 24. Add + of a square mile, i. of an acre, and # of a rood

together. Sum 161a. 19p.

25. Add # barrel, . gallon, and # quart of beer together. Sum 8gal. 24t, #pt.

191. When the fractions are such as will not reduce to known quantities without remainder. Rule. Reduce the given fractions to fractions of the highest denomination mentioned, (Art. 183.) then reduce these to a common denominator, (Art. 180.) add the numerators together, as in Art. 187, and reduce the sum to its proper quantity, (by Art. 186.) which will be the answer".

26. Add # of a pound, # shilling, and } penny together.

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I first reduce +hill. and -*.d. to fractions of a pound, which is the 9

- - - - - - - I highest denomination in the question. I have then + ; and 270° all frac- d

* This rule will be readily understood; for it is plain, from what has been shewn in the preceding notes, that in order to add fractions together, they must be reduced first to parts of the same whole, and then to parts of the same denomination; after which the sum is evidently found (as before) by adding all the new numerators together, placing the common denominator under the sum, and reducing this fraction to its equivalent value in known denominations.

tions of a pound, these I reduce to a common denominator, and add as in Art.

180; the sum o: is next reduced to its lowest terms, and lastly to its pro

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SUBTRACTION OF VULGAR FRACTIONS.
192. When the given fractions are both simple.

RULE I. Reduce the fractions to a common denominator, beginning with the numerator of the greater fraction.

II. Subtract the lower new numerator from the upper, and under the remainder place the common denominator; this fraction being reduced to its lowest terms will be the answer".

* As fractions of different denominations cannot be added, so neither can they be subtracted; we must first reduce them to a common denominator, and then it is plain that their difference is found by taking the difference of the new numerators, and placing it over the common denominator. Thus in Ex. 1. ExAMPLEs. 8 5 1. From — take —. 9 7 OPERATIon. Erplanation, - Beginning with the numeraThus, : x % – o: 7lew mum. tor 8 of the greater fraction, 1 rex 9 = *. duce the fractions to a common 11 difference. denominator; I then subtract - 45 from 56, and place the re9 X 7 = 63 common den. mainder ll over the common

11 - - denominator 63, which fraction Answer 63 the difference required. being in its lowest terms, is the

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193. When there are mired numbers, compound or compler fractions. RULE I. Reduce mixed numbers to improper fractions, compound and complex fractions to simple ones, reduce these to a common denominator, and proceed as before.

8 and -: reduced become ; and #. respectively, and the difference of

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these is evidently *:::: , or 63? as in the example.

Nothing can be plainer than this rule; for if one fraction be subtracted from another of the same denomination, the remainder is evidently a fraction of the same denomination with both; thus, if two fifths be taken from three fifths, the remainder will be one fifth; and the same of other fractions.

II. If the answer be an improper fraction, reduce it to its equivalent whole or mixed number".

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First, I reduce the mixed number to an improper fraction *. Secondly,

the compound fraction to a simple one # Thirdly, I reduce these two to a 2

so common denominator, and subtract, which gives the fraction #. Fourthly,

I reduce this fraction to its lowest terms #, and this to a mixed number.

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Erplanation. 16

The two complex fractions are first reduced to the simple ones o and 33”

these are next reduced to a common denominator; and all the rest as before.

* This rule is sufficiently plain from what is shewn in the note on the similar rule in Addition of Fractions, (Art. 189.)

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