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CASE III. To reduce an improper fraction to its equivalent whole or

mited number. RULE.—Divide the numerator by the denominator, and the quotient will be the whole or mixed number required.

EXAMPLES.

1. Reduce to its equivalent whole or mixed number.

16)981(617

96

21
16

5 or 981=981-16=6136 the answer. 2. Reduce 449 to its equivalent whole or mixed number.

Ans. 121 3. Reduce 426 to its equivalent whole or mixed number.

Aps. 25. 4. Reduce se to its equivalent whole or mixed number.

Ans. 7. 5. Reduce 621613 to its proper terms. Ans. 1209317

CASE IV. To reduce a whole number to an equivalent fraction, hav

ing a given denominator. RULE.—Multiply the whole number by the given denominator, and place the product over the said denominator, and it will form the fraction required.

EXAMPLES. 1. Reduce 7 to a fraction, whose denominator shall be 9.

7x9=63, and 63 Answer.

And 62=63:9=7 Proof. 2. Reduce 13 to a fraction, whose denominator shall be 12.

Ans. 15 3. Reduce 746 to a fraction, whose denominator shall

Ans. 44760.

be 60.

CASE V. To reduce a compound fraction to an equivalent single one.

Rule.-Multiply all the numerators together for the numerator, and all the denominators together for the denominator, and they will form the fraction required.

If part of the compound fraction be a whole or mixed number, it must be reduced to an improper fraction by one of the former cases.

When it can be done, divide any two terms of the fraction by the same number, and use the quotients instead thereof.

1

EXAMPLES 1. Reduce şof of 4 of li to a single fraction. 2x3 x4x8

-=:=ts the answer.-Or, by expunging 3x4x5X11 equal numerators and equal denominators, the answer will be as before,=15. 2. Reduce şof of to a single fraction. Ans. 1. 3. Reduce 1 of 15 of is of 10 to a single fraction.

Ans. 440 4. Reduce } of g of to a single fraction. Ans. 81

711

CASE VI. To reduce fractions of different denominators to equiva

lent fractions, having a common denominator. Rule.-Multiply each numerator into all the denominators except its own, for a new numerator; and all the denominators continually for the common denominator; first reducing the fractions to their lowest terms, &c.

Note.-By Note 9, in case 1, it will be seen, that several fractions of different denominators may be readily reduced to a common denominator. Thus į may be reduced to the same denominator as f by multiplying its terms by 3, by which it becomes g. Also j, i, and a may be reduced to a common denominator, by multiplying the terms of the first fraction by 6, of the second by 3, and dividing those of the last by 5. And so of others.

do.

EXAMPLES. 1. Reduce 1, }, and to equivalent fractions, having a common denominator.

1x5x7=35 the new numerator for J.
3x2x7=42

do. do.
4x2x5=40 do.

2x5x7=70 the common denominator. Therefore the equivalent fractions are 78, 43, and 48 the answer.

2. Reduce , $,$, and to equivalent fractions, having a common denominator. Ans. 338, 336, 137, and 1448.

3. Reduce }, is of 4, 5, and if to a common denominator.

Ans. 148, 343, 34386, 37 4. Reduce 13, 4 of 14, i and $ to a common denominator.

Ans. 12:17, 18816, 13114, 11:18

60

3135 570

3 5 5

CASE VII.

To find the value of a fraction in any known parts of

the integer. RULE.-Multiply the numerator by the parts in the next inferiour denomination, and divide the product by the denominator ; and if any thing remain, multiply it by the next inferiour denominator, and divide by the denominator as before ; and so on, as far as necessary; and the quotients placed after one another, in their order, will be the answer required.

EXAMPLES.

1. What is the value of of a shilling? Ans. 41d.

3

12

8)36(4d.

32

4 4

8)16(2qrs.

2. What is the value of its of a dollar ?

Ans. 41cts. 6 mills. 3. What is the value of 4 of a mile?

Ans. 4fur. 22 pol. 4yds. 24feet. 4. What is the value of of a month ?

Ans. 3w. 1d. 9h. 36m. 5. What is the value of It of an acre ?

Ans. Irood, 30poles. 6. What is the value of of of of $49,95cts. ?

Ans. $5,55cts.

CASE VIII. To reduce a fraction of one denomination to that of

another, retaining the same value. Rule.

Make a compound fraction of it, and reduce it to a single one.

EXAMPLES.

1. Reduce of a penny to the fraction of a pound.

of it of zbido=ads the answer.

And ato of 20 of ==&d. the proof. 2. Reduce of a farthing to the fraction of a pound

Ans. 1920 3. Reduce t of a mill to the fraction of a dollar.

Ans. 50 4. Reduce 15€ to the fraction of a penny.

Ans. 40=131d. 5. Reduce of a pound Avoirdupois to the fraction of

Ans. 7545382 6. Reduce is of a month to the fraction of a day.

Ans. 1956, 7. Reduce 7s. 3d. to the fraction of a pound.

8. d.
ny 3

20 in a £
12

12

an cwt.

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8.7

87 numerator. 240 denominator.

7=28 Ans. 8. Reduce 6 furlongs, 16 poles to the fraction of a mile.

Aps.

ADDITION OF VULGAR FRACTIONS.

Rule.-Reduce compound fractions to single ones; mixed numbers to improper fractions; fractions of different integers to those of the same ; and all of them to a common denominator ; then the sum of the numerators, written over the common denominator, will be the sum of the fractions required.

Note 1.-In adding mixed numbers that are not compounded with other fractions, find first the sum of the fractions, to which add the whole numbers of the given mixed number.

Note 2.— When adding fractions of money,weight,&c. reduce fractions of different integers to those of the same integer. Or, find the value of each fraction by Case 7, in Reduction, and then add them in their proper terms.

EXAMPLES.

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1. Add 33, , of į and 7 together.

First, 3 =2, of f=8=70, 7=7.

Then the fractions are 2, }, jy and 7.
29x8x10x 1=2320
7x8x10x 1= 560
7x8x 8x 1= 448
7X8 X 8x10=4480

7808

=12128=121 Ans. 8x8x10x1=640 2. Add $, 74, and of together.

Ans. 83 3. What is the sum of j of 95 and } of 14 ?

Ans. 4311 4. Add 19, 7, and 1 of together.

Ans. 261. 5. Add and 174 together.

Ans. 184 6. What is the sum of £4, s. and of a penny

? Ans. 113gs. or 3s. Id. 14iqrs. 7. Add 4 of 15£. £34, f of of of a pound and of 4 of a shilling together. Ans. £7 17s. 54d.

8. Add f of a yard, of a foot and of a mile together.

Ans. 660yds. 2ft. Sin. 9. Add of a week, 7 of a day and of an hour together.

Åns. 2days, 144hours. 0

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