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CASE IX.

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.

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3

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

1460

1095

2460 Ans.

CASE X.

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.

Examples.

1. What is the value of a dollar.

1 Dol.100X9=900:10:90 cts. Ans.

F the

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.

1

4. What is the value of 7 of a yard ?

3. Ans. 3 qr. 27na.

CASE XI.

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.

10000 Ans.

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.

Ans. 221184

.

ADDITION OF VULGAR FRACTIONS.

CASE I.
To add fractions having common denominators.

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

67-15-47Ans.

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.

Examples.
1. Add P12 14 together.

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nume.

denom.
Com. Den. 840* 2—4201420

840; 53168 X 3=504
840; 6—140 X 4560
840; 8-105 X 6630
840+10= 84% 8=672
840--125 70x10=700
840-145 60X12720
numerator 4206 zoo Ans.
6 12
together.

AAS. 2167
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2. It is required to add

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6 8 10 3. It is required to add

qog' li' 12

together. Ans. 4

1842

2772 CASE III. To add mixed numbers whose fractions have common

denominators.
RULE.-Add the fractions as in case 1st, and the
whole numbers as in Simple Addition; then add
the sum of the fractions to the whole number.

Examples.
1. Required to add 104 111 964 80

whole num. 104 +111 +96+80 = 391 num. of frac. 2+16+14+16=48:20 = 276

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2. Required to add 14, 15, 18, 7 together.

Ans. 56

13

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.

Examples.
1. Add 12, 163, 179, 1617, and 19together.
Whole num. 12 + 16 + 17 + 16 +19=80.

Sum of the fractions. 31%

Ans. 8372 2. Add 2116, 67, 1275, and 141214 together.

Ans. 14277110

CASE V.
To add fractions of several denominations, such as parte

of cwts. ; parts of qrs.; parts of lbs. &C.
Rule.--Find the value of each separate fraction
by, case tenth in reduction, and add the several
sums together as in compound addition..

Eramples. 1. Add a cwt. of a qr. and of a lb. together.

gr.

oz. dr.
of a cwt. is = 2
$ of a qr. is =0 21 O 0

of a lb. is O 00 13.5

lb.

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CASEI.
To subtract simple fractions having common denar-

inators.
RULE.-Subtract the least numerator from the
largest, and the remainder placed over the common
denominator will be the difference required.

Examples
1. What is the difference between and 12

19
largest numerator 12
smallest numerator 10

12

2 =

. 19

22 15 2. What is the difference between

? 41 41

7 Ans.

41

96 3. What is the difference between,

74 and ? 212 212

22 Ans.

212.

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