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1200

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EXAMPLES. 1. Reduce Ting of a pound to the fraction of a penny: 5 X 20 X 12 =

d. Result. 2. Reduce Taco of a pound to the fraction of a penny.

Result d. 3. Reduce o't of a shilling to the fraction of a farthing.

Result qr. 4. Reduce no of a dollar to the fraction of a cent.

Result cc. 5. Reduce iz of a lb. troy, to the fraction of an oz.

Result soz. 6. Reduce a of a cwt. to the fraction of a lb. avoirdup.

Result lb. 7. Reduce is of a hhd. to the fraction of a pint.

Result pt. 8. Reduce 7th of a day to the fraction of a minute.

Result ti CASE 8. To find the value of a fraction in the known parts of an integer

RULE. Multiply the numerator by the known parts of the integer, and divide by the denominator..

EXAMPLES. 1. Reduce of a pound to its proper value. 2 thirds of a pound 20

Or thus :

of 20 =4 = 13s. 4d. 3)40 thirds of a shilling.

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138.-)

12

3)12 thirds of a penny.
4d.

Result 13s. 4d.
2. Reduce of a pound to its proper value.

Result 65.gd

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3. Reduce 15 of a shilling to its proper value.

Result 5d. 4. Reduce of 5L. Is. to its proper value.

Result 4L. 13s. 5d.. 5. Reduce of a dollar to its proper value.

Result 60 cents. 8. Reduce 1 of a lb. troy to its proper quantity,

Result 9 oz. 7. Reduce of a lb. avoirdupois to its proper quantity. en

Result 8 oz. 14 dr.. 8. Reduce the of a ton to its proper quantity. Result 3cwt. 8 lb. 9 oz. 13dr

.. 9. Reduce of a mile to its proper quantity.

Result 4 fur. 125 yds. 2 ft. 1 in.. jo. Reduce o of a yard to its proper quantity

Result 2 st. 8 in. 11. Reduce 1 of an acre to its proper quantity.

Result 1 rood, 30 perches. 12. Reduce of a tun of wine to its proper quantity.

Result 1 hhd. 49 gal. 13. Reduce of a yard of cloth to its proper quantity.

Result 3 qrs, 2 nails. 14. Reduce of a year to its proper quantity,

Result 328 days, 12 hours.

CASE 9. To reduce any given value, or quantity, to a fraction of any greater denomination of the same kind.

RULE. Reduce the given quantity to the lowest denomination mentioned for a numerator, and the integer into the same denomination for a denominator.

Note. If a fraction be given, multiply both parts by the denominator thereof, and to the numerator add the numerator of the given fraction.

EXAMPLES.
1. Reduce 135. 4d. to the fraction of a pound.
13s. 4d. 160d.

L.
IL,

= 20s. = 240d.

43

2. Reduce 10s. 6d. to the fraction of a pound.

Result . 3. Reduce 4 d. to the fraction of a shilling. Result js. 4. Reduce 5.-d. to the fraction of a shilling. Result is. 5. Reduce 9 02. troy, to the fraction of a lb. Result 3lb. 6. Reduce 9 oz. 2 dr. {, avoirdup. to the fraction of a lb.

Result 7. Reduce 3 cwt. 8 lb. 9 oz. 13 dr. is, to the fraction of a ton.

Result i ton. 8. Reduce 3 qr. 2'na. to the fraction of a yard.

Result yd. 9. Reduce 6 furlongs, 16 poles, to the fraction of a mile.

Result 10. Reduce 2 roods, 20 perches, to the fraction of an

Result

acre.

ADDITION OF VULGAR FRACTIONS:

GENERAL RULE. Reduce the given fractions, if necessary, to single onts, and to a common denominator; then add all the numerators together, and place the sum over the common denominator.

If fractions be of different denominations, find their value separately, and add as in compound addition.

EXAMPLES. Note 1.-When the given fractions have a common deno. minator, add their numerators together, and place the sum over the common denominator. 1. Add 4, 4, and together.

Results sum of the numerators. *x4x=

common denominator. 2. Add ş, , and } together.

Resultat 3. Add 1 and 1 together.

Result in 4. Add 1sis, and together. 151

Result 1. 5. Add , , , , and together.

Result 27

3

2

5

4

99

20

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Note 2.-When the given fractions have not a common denominator, reduce them to such as have, by rule in Case 2 of Reduction ; then add, as in the foregoing examples. 6. Add 1 and together.

Result 17 1 X 5

17
numerators.
3 X 4

4 X 5 = 20 com. denom. 17 sum. 7. Add , , and together. Result yout='225 8. Add and together.

Result let 9. Add o 1, and together.

2

14,
11

Result 2136 Note 3-When uničed numbers are given, add the fractions as under note 1 or 2 ; then, if their sum be an improper fraction, reduce it to a mixed number, and add its integers to the given integers ; but if it be not an improper fraction, annex it to the sum of the given integers.

10.--Add 5, 63, and 41 together. Result 1720

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967

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Integers 6

Fractions.
+*+1=22

4

Sum of fractions 224

36

110

C

172a 11. Add 21 and 3 together.

Result 6412. Add 7 and 5 together.

Result 126 13. Add 171 and together.,

Result 184 14. Add 4, 6, 9, ., and together.

Result 2016 15. Add 5, 71, ş, and 11 together. Result 13,59

Note 4.-When compound fractions are given, reduce them to single fractions, and proceed as before. 16. Add gof , and of together.

Result 125. of 18 = 1

28 + Flags iz of

Result 133 17. Add off and of 2; together. 18. Add 1%, of , and 9% together.

Result 1lt 19. Add 116, 67, of i and 71 together. Result 16726

10

45 60

28

48

73

17

Note 5.- When the given fractions are of several deño. minations, reduce them to their proper values or quantities, and add as in the following example. 20. Add ; of a pound, to x of a shilling:

Result 15s. 1043d.

d. Z of a L. = 15 6

. .
d. d. d.
.

15 6
+ = 1

0 3 so of a s. 0 33

IS

8. d.

8.

13

12

15 1013 21. Add of a pound, to of a shilling. Result 185. 3d. 22. Add i of a penny, to } of a pound.

Result 25. 3d. Iqr. . 23. Add į lb. troy, to iż of an ounce.

Result 6 oz. 11dwt. 16grs. 24. Add of a mile, to jy of a furlong.

Result 6 fur. 28 poles. 25. Add į of a yard, to şof a foot. Result 2 ft. 2 in. 26. Add ļof a day, to į of an hour. Result 8h. 30 min.

27. Add ij of a week, of a day, and į of an hour toge. ther.

Result 2 days, 14 hours, 30 min.

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SUBTRACTION OF VULGAR FRACTIONS.

GENERAL RULE. Prepare the given fractions as in addition, then subtract the less numerator from the greater, and place the difference over the common denominator.

EXAMPLES. 1. From take

Results 2. From 1 take i.

Result 1 3. From Yo take fo.

Resuit Note 1.-When the given fractions have not a coniimon denominator, reduce them to such as have, and then subtract as before

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