EXAMPLES.

1. Reduce of a pound to its proper value.

2. Reduce of a pound to its proper value.

Result 6s. 8d.

3. Reduce of a shilling to its proper value.

1

Result 5d..

4. Reduce & of 5L. 9s. to its proper value.

Result 4L. 13s. 5d. .

5. Reduce of a dollar to its proper value.

Result 60 cents.

6. Reduce of a lb. troy to its proper quantity. Result 9oz. 7. Reduce of a lb. avoirdupois to its proper quantity. Result 8oz. 14dr.. 8. Reduce of a ton to its proper quantity.

Result 3cwt. 8lb. 9oz. 13dr..

9. Reduce of a mile to its proper quantity.

Result 4fur. 125yds. 2ft. lin. . 10. Reduce of a yard to its proper quantity. Result 2ft. 8in.

11. Reduce of an acre to its proper quantity.

Result 1 rood, 30 perches. 12. Reduce of a tun of wine to its proper quantity. Result 1hhd. 49gal.

13. Reduce of a yard of cloth to its proper quan

Result 3qrs. 2 nails.

tity.
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 13s. 4d. to the fraction of a pound.

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

Result

L.

3. Reduce 41⁄2d. to the fraction of a shilling. Result is. 4. Reduce 5d. to the fraction of a shilling.

Result 1s. 5. Reduce 9oz. troy, to the fraction of a lb. Result lb. 6. Reduce 9oz. 2dr. 4, avoirdupois, to the fraction of a pound. Result.

1

7. Reduce 3cwt. 8lb. 9oz. 13dr. 15, to the fraction of a ton.

Result 1 ton.

8. Reduce 3qr. 2na. to the fraction of a yard.

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

mile.

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

an acre.

ADDITION OF VULGAR FRACTIONS.

GENERAL RULE.

Reduce the given fractions, if necessary, to single ones, and to a common denominator; then add all the numerators together, and place the sum over the com mon 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 denominator, add their numerators together and place the sum over the common denominator.

1. Add,, and together.

Result .

sum of the numerators.

common denominator.

Result .

Result.

Result 1.

Result 24.

3. Add 17, 17, and 17 together.

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.

Note 3.-When mixed 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.

Note 4.-When compound fractions are given,

reduce them to single fractions, and proceed as be

fore.

16. Add of o, and of together. Result 18.

60

17. Add of and of together. Result 37

18. Add 13, of, and 92% together. Result 11

19. Add 1, 6, of, and 71⁄2 together.

Result 16

120

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

Result 15s. 10,d.

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.

Note 1---When the given fractions have not a common denominator, reduce them to such as have,

and then subtract as before.

Note 2.-When mixed numbers are given, reduce them to improper fractions, and reduce these im

proper fractions to such as have a common denoті

nator; then subtract as before.

Note 3. When compound fractions are given,

reduce them to single ones, and reduce these single

fractions to such as have a common denominator,

then subtract as before.