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16

2. It is required to take 910 from 10.

10

3. It is required to take 12 from 103.

Ans. 8

CASE VI.

To subtract when the fractions are of different denominations; such as parts of cwt. qr. lb. &c.

-

RULE. Find the value of the fraction (by case 10th in Reduction,) then subtract as in compound subtraction. If fractions happen in finding the val ue of the parts, reduce them to common denominators and subtract as in case third.

Examples.

1. It is required to take of a cwt. from
of a cwt. from of

10

a ton.

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3 3

Ans.

*18

2

2. Required to take of a cwt. from 12
Ans. 12 cwt. O qrs. 18 lb. 10 oz. 10 dr.

12
18

6100

cwt.

MULTIPLICATION OF VULGAR FRACTIONS.

CASE I.

RULE. Reduce compound fractions to simple ones; mixed numbers to improper fractions; then multiply the numerators all together for a new numerator, and the denominators for a new denomi

nator.

YOU

en

100

Examples.

4. It is required to multiply by of of

2

5.

1.

10 3

30

of of 3072

Ans.

16

384

5.

-512

2. It is required to multiply 23 by of.

66

Ans. 64

5

3. It is required to multiply by

F

4. It is required to multiply ¦ by

1

2

Examples.

1. It is required to divide

5

2. It is required to divide by

1

9

To

DIVISION OF VULGAR FRACTIONS. RULE. Reduce compound fractions to simple ones; mixed numbers to improper fractions; then invert the divisor (that is put the numerator for the denominator) and multiply the numerators together for a new numerator, and the denominators together for a new denominator; and the fraction thus found is the quotient required.

3. It is required to divide 10 by of.

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45

Ans. 120

10°

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Ans.

by g.

inverted is x Ans.

3

4. It is required to divide 10 by 7

7

64

Ans. 33

Ans. 77

Ans. 1

3

8

249

5-1-1

Miscellaneous Questions in Vulgar Fractions.

1. A schoolmaster being asked one day how ma ny scholars he had, made answer that one fifth of them sat on one seat, one tenth on another, two fifths on another, two tenths on another, and 6 on another; I demand the number his school consisted of.

1

540

54 +

1 1 2 2 9)

10

6

+-+-+-=-10--9 =1=2 of 2 of

S 10 5: 10 10

1

10 1

6= 60 Ans.

2. A man, having returned from a journey, was asked
by a friend, what his expenses were; the answer was,
that he spent in Boston of his money; between Boston
and New York; in New York; beyond New York
; and he brought home $40; I demand the sum he
carried, and also what he spent.

Ans. carried $160, and spent $120..
RULE OF THREE IN VULGÁR FRACTIONS

RULE-State the question as in the Rule of Three Direct, invert the divisor, and multiply the numerators together, and the denominators together, and the frac tion thus found is the fourth term or answer; compound fractions must be reluced to simple ones, and mixed numbers to improper fractions.

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=

400

10

3. If of of a ship is worth how much is of of her worth?

I s

Ans.

2. If 10 bushels of potatoes cost $3; how many may be had for $124 ?

Dols.

1

1- Ans.

8

4100

104

104

of 16000 dollars;

Ans. $4571-42-8384

44

39

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SIMPLE INTEREST.

DEFINITION. Interest is a premium paid to the lender, by the borrower, for the use of money lent. Simple Interest is reckoned at 6 per cent. that is, at the rate of 6 dolls. for the use of 100 dolls. one year; and so in proportion for a longer, or shorter time, or for a smaller, or larger sum.

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Principal is the money lent.

Rate per cent. is the price agreed on.

The amount is the principal and interest together,

CASE 1.

The principal and rate given, to find the interest
for one year, or more, &c.

SW

RULE,-Multiply the principal by the rate per cent. and that product by the number of years; the last product pointed, according to the rule of decimals, will be the answer for that time, in dollars and parts of dollars,

Examples.

1

# 1, What is the interest of $22-16 cents for one year, at 6 per cent. per annum?

dols. cts.

22.16 principal.

06 rate per cent.

1.3296

1 time

$1.3296 $1.32.9 Answer.

NOTE. Six per cent. must be written 06 and seven per cent. should be written '07, &c. this being observed, the rule of dec imal fractions exactly applies.

2. What is the interest of $223.14 cts. for 5 years, at per cent. per annum ?

$223·14×06

yrs. D. cts. m. 13.38 84×566·94.2† Ans.

3. What is the interest of 123 dols. 10 cts. 1 mill, for

7

years, at 9 per cent. per annum ?

Ans $77.55-31

CASE II.

When the amount is required.

RULE. Find the interest as in case first, and to it add. the principal, the sum is the amount.

Examples.

1. What will $10.15 cts. amount to in 12 years, at 6. per cent. per annum?

$10.15
'06

•6090
12

7.3080 interest.

10.15

years mo.

6

Ans.

17.4580 amount.

2. What is the amount of $1.12 cts. for 12 years, at 12 Ans. $2.73.21. per cent. per annum ?

3. What is the amount of $242.17 cts. for 3 years, at annum ? 9 per cent. per Ans. $307-55-5)

CASE III.

principal added.

When there are years, months and days in the time.

RULE 1st. Reduce the days and months to the deci mal of a year, then multiply the principal, rate, and time together, the product pointed for decimals according to rule will be the answer.

RULE 2d. Find the interest for the years by case first; for the months, divide a year's interest by the aliquot parts of a year; and for the days, divide a month's interest by the aliquot parts of a month; the several quotients added with the interest for the years will be the

answer.

Examples.

1. What is the interest of $6.22 cts. for 2 years, months, 10 days, at 6 per cent. per annum ?

D. cts.

cts. m.

days years

10 2·527 × 6·22 × 0694.3.† Ans.

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