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SUBTRACTION OF VULGAR FRACTIONS.

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RULE.* PREPARE the fractions as in Addition, and the ference of the numerators written above the common nominator, will give the difference of the fraction requir

EXAMPLES.
1. From take of
of =*='s Then i and 1=1 ir

Therefore 9--7= the Ans. 2. From 25 take

Answers.
S. From 11 take
4. From 14 take
5. What is the difference of u and it?
6. What differs from ?
7. From 141 take 4 of 19
8. From take

O remains, 9. From of a pound, take of a shilling., of orthof. Then iiom 14. takeofo. ns. ito. Note. In fractions of money, weight, &c. you may, you please, find the value of the given tractions (by Cas VIII. in Reduction) and then subtract them in their pro per terms.

10. From 16. take 3 shilling. Ans. 5s. 64. 2grs. 11. From of an oz. take of a pwt.

Ans. 11pwt. 3gr. 12. From 1 of a cwt. take of a Ib..

Ans. Igr. 27lb. 6oz. 10-8 dr. 13. From 3 weeks, take of a day, and fofofo an hour.

Ans. Sw. 4da. 12lo. 19min. 171sec

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*In subtracting mixed numbers, when the lower fraction i: greater than the upper one, you may, without reducing then to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference add the upper numerator, carrying one to the unit's place o the lower whole number.

Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number.

MULTIPLICATION OF VULGAR FRACTIONS.

E RULE. REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.

EXAMPLES.
1. Multiply by m y

Answers
2. Multiply by tas
3. Multiply 51 by
4. Multiply of 7 by :
5. Slultiply is by
6. Multiply of 8 by of 5
7. Multiply by 91

:: 693 1, 8. Multiply of s by of S

9. What is the continued product of of 5, 7, 53 and of ?

i " Ans. 45

hemos

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DIVISION OF VULGAR FRACTIONS.

RULE PREPARE the fractions as before; then, invert the divisor and proceed exactly as in multiplication :--The products will be the quotient required. i

EXAMPLES.'

4 X 5 1. Divide by Thus,

Ans. ?

3 X 7
2. Divide 17 by :
3. Divide of by :
4. What is the quotient of 17 by ?
5. Divide 5 by yo
6. Divide } of of } by 1 of
7. Divide 4 by of 4
8. Divide 71 by 127
9. Divide 52051 by of 98.

Answer

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RULE OF THREE DIRECT IN VULGAR

FRACTIONS,

RULE. PREPARE the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion; then multiply all the three terms continually together, and the product will be the answer, in the same name with the second or middle term.

EXAMPLES. 1. If of a yard cost of a pound, what will is of an Ell English cost?

byd.= of of = or 1 Ell English. El. G. EIL.

s. d. grs.' As::: And xx * £:=10 3 1 Ans.

2. If of a yard cost of a pound, what will 40% yds. come to?

. Ans. £,59 8s. 644. 3. If 50 bushels of wheat cost 1731. what is it per bush

Ans. 75. Od. izgrs. * 4. If a pistareen be worth 14 pence, what are 100 pistareers worth?

Ans. £ 6 5. A merchant sold 54 pieces of cloth, each containing 241 yds. at ssd per yard; what did the whole amount to

Ans. £,60 10s. Od. 3 grs. 6. A person baring of a vessel, sells of his share for 312l. ; when the whole vessel worth ? Ans. £780

7. If orchin be worth of her cargo, valued at 88001. what is the whole ship and cargo worth?

Sins. £10031 14s. 112 d.

INVERSE PROPORTION.

RULE.

PREPARE the fractions and state the question as before, then invert the third term, and multiply all the three Toomas together, the product will be the answer.

EXAMPLES.

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1. How much shalloon that is yard wide, will line 51 yards of cloth which is 14 yard wide ?

Yds. yds. yds. .
As 18:51::3 And ;x!!

X 399=16Ans. 2. If a man perform a journey in 3 days, when the day is 12 hours long; in how many days will he do it when the day is but 9 hours. Ans. 4 ans days.

3. If 13 men in 11 days, mow 21} acres, in how many days will 8 men do the same. Ans. 1825. days.

4. How much in length that is a inches broadl, will make a square foot ?

Ans. 20 inches. 5. If 25 s. will pay for the carriage of an cwt. 1454 miles; how far may 6 cwt be carried for the same money ?

Ans. 2200 miles. 6. How many yards of baize which is 14 yards wide, will line 183 yards of camblet yd. wide ?

ins. 11yds. 1gr. -1} na. I

RULE OF THREE DIRECT IN DECIMALS.

RULE. REDUCE your fractions to decimals, and state your question as in whole numbers ; multiply the second and third together; divide by the first, and the quotient will be the answer, &c.;

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SIMPLE INTEREST BY DECIMALS.

A TABLE OF RATIOS. linte per cent, 1 Rutio. Rate per cent. I Ratio.

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,06
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7 Ratio is the simple interest of 11. for one year; or in federal money, of $1 for one year, at the rate per cent. agreed on.

RULE. Multiply the Principal, Ratio and time continually together, and the last product will be the interest required.

EXAMPLES. 1. Required the interest of 211 dols. 45 cts. for 5 years, at 5 per cent. per annum?

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