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2. Reduce the integral part to the same term, for a denominator.

NOTE 1. If there be a fraction given with the said quantity, add it to the numerator of the fraction required. NOTE 2. This case and Case XI. prove each other.

EXAMPLES. 1. Reduce 135. 4d. to the fraction of a pound (money.)

1 3

12 160

1 2 20

12 370

Ans. 140= 2. Reduce 52's pence, to. che fraction of a shilling.

4}

4 3

213

1

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Ans. $18=41. 3. Reduce 9 ounces Troy, to the traction of a pound.

Ans. =* 4. Reduce 15.cwt. to the fraction of a ton. Ans. 5. Reduce £4 13 54 to the fraction of £5.9. 4. 1354

5 9 20

20

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Ans. 1848

=

7848
9156

= 6. Reduce 1 yard to the fraction of an Ell English.

Ans. f 7. Reduce 1 hogshead, 49.gallons, to the fraction of a ton.

Ans. 8. Reduce 12 h. 55 m. 23-sec. I's to the fraction of a natural day

Ans. 1 .9. Reduce 8oz. 14drs. , to the fraction of a pound, Avoirdupois.

Ans. 10. Reduce 4 fu. 22 po. 4 yds. % f. 1 in. 2 bc. to the fraction of a mile.

Ans.

1 T)

11. Reduce 31į gallons of beer to the fraction of a barrel.

Ans. s. 12. Reduce 131 bushels of coals to the fraction of a chaldron.

Ans. 13. Reduce 8C. 17r. 25lb. loz. 71 dr. to the fraction. of 10C. Iqr. 121b.

Ans. Á 14. Reduce 3 qrs. 2 na. of cloth, to the fraction of a yard.

Ans. š. 15. Reduce 12 gallons of beer to the fraction of a hogshead?

Ans: . 16. Reduce 6 gallons of ale to the fraction of a

3 barrel.

17. Reduce 1 rood, 30 rods of land, to the fraction of an acre.

Ans. 1o. 18. Reduce 9 ounces Troy, to the fraction of a pound.

Ans.

를 19. Reduce 60 cents to the fraction of a dollar.

Ans. You = = . 20. Reduce 140 dollars to the fraction of 180 dollars.

H= .

Ans. 16

12

108 148

Ans. 140

180

ADDITION OF VULGAR FRACTIONS.

Reduce the fractions (given to be added together) to their lowest terms by Case I.

If they are of different denominations, reduce them to a common denominator by Case II.

Add all the numerators together, for a new numerator, under which write the common denominator.

Note. This rule may be proved by subtraction, when only two fractions are given to be added.

EXAMPLES 1. Add 1 and together.

1

7 8

2

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2. Add to 1, and %, together.

Ans. 21886. 3. Add 19,7, and į off together. Ans. 20% or 26. 4. Add Iof and of together. Ans. 106 5. Add of 95 and 3 of 14 together.

Ans. 598 6. Add and 17 together.

Ans. 18. 7. Add together 12, 3, and 44 Ans. 2012 8. Add 6 of for of , and 7 together.

Ans. 143384 Nore. In the following questions the given fractions must be reduced to their proper quantities by Case XI. in Reduction of Vulgar Fractions, and then added as in Compound Addition. 9. Add of a pound to of a shilling.

1
1

17s. 6d.
20

12

+9

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9

17 6
10. Add of a penny to ģ of a pound.

Ans. 2s. 31d.. 11. Add g a pound Troy to te of an ounce.

Ans. 6 oz. 11 dwt. 16 gr. 12. Add of a ton to io of an cwt.

Ans. 12 cwt. I qr. 8 lb. 12 oz. 12 dr. sc. 13. Add of a mile to 'o of a furlong.

Ans. 6 fu. 28 po. 14. Add a yard to i of a foot. Ans. 2ft. 2in. 15. Add of a chaldron of coals to g of a bushel.

Ans. 16 bush. 34 pecks.

SUBTRACTION OF VULGAR FRACTIONS.

When a vulgar fraction is given to be subtracted from another giyen one.

1. If they are of different denominations, 'or in high terms, reduce them as directed in Addition of Vulgar Fractions.

2. Subtract the lesser numerator from the greater, and under the remainder place the common denominator.

Note 1. When whole numbers are given with fractions, the lower numerator will sometimes be the greatest, in which case subtract it from the denominator, and to the remainder add the upper numerator, and carry one to the unit's place of the lower whole number. Nare 2. This rule is proved by addition.

EXAMPLES. 1. From 113 take . 111

3

112
4
112

4

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Ans. 379

TOO

7

21
9671
1477

8131 Ans. 3. From 141 take of 19.

Ans.l's 4. From 100 take 5. From 96 take .

Ans. 95. 6. From of 76, take of 21.

Ans. 7. From 11%, take jol, of

2640=70 8. From 715 take is.

Ans. 7035. Note. In the following examples the given fraction must be reduced to their proper quantities, and then su tracted as in Compound Subtraction.

7

Ans. 1936

163

9. From t of a pound (money) take Å of a shilling

1
1

10s. Od.
20 12

9

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8

9d. 10. From { a shilling take of a penny.

Ans. 51d. 11. Fromn of an ounce Troy take ; of a penny weight.

Ans. 11dwt. 3gr. 12. From j cwt: take 1 of a pound.

Ans. I' qr 27 lb. 6oz. 10 dr. i7. 13. From of a league' take to of a mile.

Ans. Im. 2fu. 16po. *14. From 1 Ell English, take to of a yard.

Ans. 2 qr. O na. 15. From io of a hogshead of beer take 1 gallon.

Ans. 124 gallons 16. From of a chaldron of coals take of a bushek.

Ans. 17 bu, lj peck.

8

MULTIPLICATION AND

DIVISION
VULGAR FRACTIONS.

OF

1. Prepare the given fraction by reduction (if necessary) by reducing them to their lowest terms, if mixed fractions, reduce to single ones.

2. Multiply the numerators together for a new numerator.

3. Multiply the denominators together for a new deminator.

NOTE. When any number, either whole, fractional, or mised, is multiplied by a fraction, the product will be less than the multiplicand, in the same proportion as the multiplying fraction is less than 1, or an unit.

In Division of Vulgar Fractions prepare the given fractions (if necessary) as for multiplication ; then invert

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