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To reduce the fraction of a higher, to the fraction of a
lower denomination, retaining the same value. Rule.-Multiply the numerator of the given fraction, into the denominators of the compound ones between itself and the denomination to which you would reduce it, for a new numerator; which being placed over the given denominator, will form the fraction required.
RULE 2.-Invert the denominations between the given denomination, and the one to which you would reduce it; then multiply all the numerators together for a new numerator, and the denominators, for a new denominator.
Examples. 1. Reduce 10000 of a dollar, to the fraction of a mill.
2. Reduce 1767 of a year to the fraction of a day.
of į sós inverted is so of į of *** and idco x 305
To express the value of a fraction in the several de
nominations of the Integer: Rule.-Multiply the numerator of the fraction into the known denominations of the Integer, and divide the product by the denominator, the quotient is the value of the fraction; in the denominations of the Integer.
1. What is the value of a dollar.
1 Dol.100X9=900:10:90 cts. Ans.
2. What is the value of of an cwt. avoirdupois.
Ans. 2 qr. 18 lb. 10 oz. 107 dr. 3. What is the value of of a cord of wood ?
Ans. 96 solid feet.
4. What is the value of 7 of a yard ?
3. Ans. 3 qr. 27na.
To reduce parts of an Integer which are expressed in several denominations, to the fraction of a
greater of the same kind. RULE.Reduce the several denominations to the lowest denomination mentioned, for a numerator ; and reduce the integer to the same denomination for a denominator.
Examples 1. It is required to reduce 1 dime, 6 cts. and 9 mills, to the fraction of an Eagle. 1 dime 6 cts. 9 m.
169 1 Eagle 2. Reduce 2 rods, 12 feet to the fraction of a mile, and to its lowest terms.
Ans. The 1. Reduce 10 feet 100 inches to the fraction of a
17380 cord, wood measure.
ADDITION OF VULGAR FRACTIONS.
RULE.-Add the numerators all together, divide the sum by the common denominator, the quotient is the answer
Examples. 9 10 6
5 11 12 14 Add 15' 15' 15' 15' 15' 15' 15
together. the numerators 9+10+6+5+11+12+1467
CASE II. To add fractions having different denominators.
Rule.--Find a common denominator by case 5th (in Reduction,) use it as a dividend; use each given denominator as a divisor; divide, and multiply the quotients by the several numerators, and the sum of all the products is the numerator to the common denominator, and is the fraction required.
840; 53168 X 3=504
2. It is required to add
6 8 10 3. It is required to add
qog' li' 12
together. Ans. 4
2772 CASE III. To add mixed numbers whose fractions have common
whole num. 104 +111 +96+80 = 391 num. of frac. 2+16+14+16=48:20 = 276
2. Required to add 14, 15, 18, 7 together.
CASE IV. To add mixed numbers whose fractions have differ
.ent denominators. Rulez-Add the fractions as in case second, and the whole numbers as-in simple addition ; then add the sum of the fractions, to the sum of the whole numbers, and it is done.
Sum of the fractions. 31%
Ans. 8372 2. Add 2116, 67, 1275, and 141214 together.
of cwts. ; parts of qrs.; parts of lbs. &C.
Eramples. 1. Add a cwt. of a qr. and of a lb. together.
of a lb. is O 00 13.5
22 15 2. What is the difference between
? 41 41
96 3. What is the difference between,
74 and ? 212 212