1. Reduce

EXAMPLES.

of a pound to the fraction of a penny. -
= d. Result.
1440

5 X 20 X 12 = 1200

2. Reduce

120

of a pound to the fraction of a penny.

Result 4d.

Result qr.

3. Reduce of a shilling to the fraction of a farthing.

4. Reduce of a dollar to the fraction of a cent.

Result ct.

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

3

Result oz.

6. Reduce of a cwt, to the fraction of a lb. avoirdup.

Result lb.

7. Reduce of a hhd. to the fraction of a pint.

Result pt.

8. Reduce of a day to the fraction of a minute.

CASE 8.

Result

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. Reduce of a pound to its proper value.

Result 6s. 88.

3. Reduce 13 of a shilling to its proper value.

Result 5d.

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

Result 4L. 13s. 5d. 4.

Reduce of a dollar to its proper value.

Result 60 cents.

6. Reduce of a lb. troy to its proper quantity.

Result 9 oz. 7. Reduce of a lb. avoirdupois to its proper quantity. Result 8 oz. 14 dr. 3.

8. Reduce of a ton to its proper quantity.

Result 3cwt. 8 lb. 9oz. 13dr.4.

9. Reduce of a mile to its proper quantity.

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

Result 2 ft. 8 in..

10. Reduce
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 1 hhd. 49 gal.

Result 3 qrs, 2 nails.

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

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 nume rator 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 44d. to the fraction of a shilling. Results. 4. Reduce 5d. to the fraction of a shilling. Result 18s. 5. Reduce 9 oz. troy, to the fraction of a lb. Result lb. 6. Reduce 9 oz. 2 dr. 4, avoirdup. to the fraction of a lb. Result

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

a ton.

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

Result 7 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

acre.

Result

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 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.

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 8-When mixed numbers are given, add the frac·tions 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 53, 67, and 41 together.

Fractions.

3 +3 +1=2

Result 17

Integers 6

4

Sum of fractions 224

1724

Note 4.- When compound fractions are given, reduce them to single fractions, and proceed as before.

16. Add of, and of together.

Result 1.

Result 137.

17. Add 2 of 3 and 4 of 10 together.
18. Add 13, off, and 93 together.
19. Add 1, 67, of and 7 together.

Result 11.

Result 16,730.

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. 10d.

24. Add of a mile, to of a furlong.

Result 6 fur. 28 poles.

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