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Let the following fractions be reduced to other fractions equivalent thereto, each set having one common denominator.

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- * ... Let the following fractions be reduced to other fractions equivalent thereto, having the least common denominator.

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Case 7th.—To find the value of a fraction in the inferior denominations of the integer of which it is a part

Multiply the numerator by the number of parts in the next inferior denomination, and divide the product by the denominator, as before directed in Simple Division, in that part of the rule which referred to the treatment of the remainder, the quotient or , several quotients thus found will be the value required. -

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Here it is evident that to find the value of + of se is no more than to divide 51 by 8, or to find the value of or of an cwt. to divide 5 cwt. by 16, and the same may be applied to any fraction of any integer. - -

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Case 8th.--To bring any compound quantity to the fraction of the integer of which it is a part.

Bring the compound quantity (by multiplying by the parts of its inferior denominations) to the lowest name mentioned in it, which make the numerator of the fraction to be found, and the integer expressed in parts of the same name or value, will be the denominator.

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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, lar 141b to the fraction of an cwt. 3. 8s 3d to the fraction of a £ 4, 5s 93d to the fraction of a £: . 12s 93d to the fraction of a £ 6, 34r 171b to the fraction of an cwt . 5d 8grto the fraction of afbtroy 8, 4oz7dwt 15grs the frac of aib T . 5oz 7dr to the fraction offb avois 10, 17%gal to the fraction of an hlid ll. 15st to the fraction of a b.wheat 12, 12ct2gr 15lb to fraction of aton 13. 4qr 3}n to the fraction of an E.E. 14, 3f 15p to the fraction of a mile 15, 24r2gn to the fraction of a yard, 16, 5f 17póyd to the frac of an I mile 17.37d 15h 17m to the frac. of year 18, 5s 9{d 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, 213 feet to the frac of ton timber 23. list 121b to the fraction of boats 24, 3s 93d 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. 33rampleg. Let or of a shilling be re- . . Reduce or of a se to the duced to the fraction of a £ str fraction of a penny. w +or X*w-row +'s-X 49 X # = ***= *d. or 16d, Let the following fractions be reduced, viz. I, #d to the fraction of a shilling, 2, #s to the fraction of a £ sterl 3, # of a £ to the fraction of penny 4, #d to the fraction of a £ 5, # yard to the fraction of a nail, 6, 3 of an oz troy to the frac of a sh 7, is to the fraction of a guinea, 8, row £ to the fraction of a penny 9, #dwt to the fraction of a btroy, 10, ris cwt to the fraction of a b, 11, 3 dram to the fraction of an cwt 12, rorth to the fraction of an cwt, 13, #yd to the fraction of a perch E. 14, 3 gal to the fraction of an hlid, 15, 3 hr to the fraction of a week, 16, 5 gal to the fraction of a tun, 17, dwt to the fraction of a btroy 18, # cwt to the fraction of a fo,

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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.

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Case 2d.--To add fractions which have not a common denominator. Reduce them to a common denominator and add as before.

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