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Let the following compound quantities be reduced to the several fractions of the respective integers of which they are parts. 1. 9s 4d to the fraction of a £ 2, 1qr 141b to the fraction of an cwt 3. 8s 3d to the fraction of a £ 4, 5s 94d to the fraction of a £ 5. 12s 94d to the fraction of a £ 6, 3qr 171b to the fraction of an cwt 7. 5d 8gr to the fraction of a tb troy 8, 4oz 7dwt 15grs the frac of a tb T 9. 5oz 7dr to the fraction of ib avois 10, 174gal to the fraction of an hhd 11. 15st to the fraction of a b.wheat 12, 12ct 2qr 15lb to fraction of a tōn 13. 4qr 34n to the fraction of an E.E 14, 3f 15p to the fraction of a mile 15. 2qr 24n to the fraction of a yard, 16, 5f 17p6yd to the frac of an Imile 17. 37d 15h 17m to the frac. of year 18, 5s 94d to the fraction of a guin. 19. 2ft 3in to the fraction of 1 yard, 20, 2r 27p to the fraction of an acre 21. 135d 5h to the fraction of a year 22, 214 feet to the frac of ton timber 23. 11st 12lb to the fraction of b.oats 24, 3s 94d to the fraction of a sovr.

CASE 9th. To reduce a fraction of one denomination to that of another denomination, still retaining the same value. If the reduction be to a less denomination, multiply the numerator of the given fraction, by the parts of the next lower denomination, but if to a higher, multiply the denominator of the given fraction, by the parts of the higher denominations.

Examples.

Let of a shilling be re- Reduce of a to the duced to the fraction of a £ str fraction of a penny. TX?XY==d. or 16d.

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Let the following fractions be reduced, viz.

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11,

13,

15,

16,

17,

dram to the fraction of an cwt 12, Tr th to the fraction of an cwt,

yd to the fraction of a perch E. 14,
hr to the fraction of a week,

dwt to the fraction of a b troy 18,

gal to the fraction of an hhd,

gal to the fraction of a tun,

cwt to the fraction of a lb,

CASE 10th.-To reduce à complex fraction to a simple fraction.

Multiply each term by the denominator of the fraction in the numerator or denominator of the given complex fraction, and the products will express the terms of the simple fraction required, provided but one term has a fraction in it; but if there is a fraction in both, first multiply each term, by the denominator of the fraction in the numerator, and multiply the products by the denominator of the fraction, if there is any in the denominator thus produced, which latter products will give the terms of the fraction required, which if not in its least terms, reduce it thereto.

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From the observations made concerning the nature of fractions, it is evident, that in any complex fraction the numerator may be considered as a dividend, and the denominator as a divisor; therefore, by dividing the numerator by the denominator, the above reduction would be effected, but the rule in that form, would more properly belong to Division of Fractions.

ADDITION OF FRACTIONS.

CASE 1st. To add simple fractions which have a common denominator.

Add all the numerators together, and place their sum over the common denominator, which if greater than it, reduce to its equivalent whole or mixed numbers, as the case may require.

Add #, §, and together.

Examples.

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Reduce them to a common denominator and add as before.

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CASE 3d.-To add mixed numbers.

Add the fractional parts as before, and if their sum be an improper fraction, reduce it to its equivalent whole or mixed number, and add the integral part with the whole numbers of the given mixed numbers.

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12.

13.

14.

15.

oz and gib Troy.

2. 5, 64, and + of 4 of 5 4., of and of 23

6.

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1, 94 & 4 of of 45 8. † of 2, 4 of 5, ÷ of 3,&\ of 4 10. cwt, 5b and of a ton.

foot, yard, of a perch Irish, and five furlongs cwt,b of a b and 111⁄2 oz.

yard, ell English, and of an ell Flemish.

of 121, 441, of of a £, and g of a Shilling.

* When fractions are of different kinds, it will be necessary to reduce them to one name, before they can be added or subtracted,

SUBTRACTION OF FRACTIONS.

CASE 1st. To subtract a simple fraction from a simple fraction, having a common denominator.

Subtract the less numerator from the greater, under the difference place the denominator, and the fraction thus formed will be the difference required.

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CASE 2d. To subtract simple fractions from simple fractions, not having a common denominator.

Reduce both fractions to a common denominator, and proceed as before.

Gramples.

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When the given fractions are compound or complex, they must be reduced to simple fractions, with which proceed as

before.

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