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7. What is the difference of L. and of 4 £.? Anf. 158. 10.

8. Required the difference between £. and guinea?

9. From of 5% £. take

Anf. 10s. 6d.

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10. From of an oz. take of a dwt. 13

11. From of a yard take

Anf. 11 dwts. 3 grs.

of an inch.

12. From 7 weeks take 97 days.`

Anf. 2 ft. 2 ins.

Anf. 5 ws. 4 ds. 7 hs. 12 ms.

13. From of a hhd. of beer take 3

Anf.

of a gn. 23 gns. of q.

MULTIPLICATION of VULGAR

FRACTIONS.

RU L E.

Let the fractions be prepared as before. Then, multiply all the numerators for a new numerator; and all the denominators for a new denominator. Reduce this last fraction as before directed for the answer.

EXAMPLE S.

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2. Required the product of, and

3. What is the product of and of?

Anf. 2
Anf.

4. Multiply 4, of and 184 continually together.

5. I demand the product of 33 and 414?

Anf. 948
Anf. 14134.
Anf. 301.

6. Find the product of 7 of 4 and 81.
7. Multiply of a pound by 4 of a fhilling..

Anf. 24 d.

8. Required the product of of 341. and 4 of a guinea?

Anf. Is. 2d.

9. Multiply of a ton and g of a cwt. together.

Anf. 3 cwts.

14

10. Find the product of of a yard and of an ell English. Anf. In. 11. Required the product of 4ft. 10ins. by of of a yard? Anf. 8 ins. 12. Multiply of a week by of 4 days. Anf. id. 8hs.

DIVISION of VULGAR FRACTIONS.

RULE.

Having prepared the fractions properly, multiply the aumerator of the dividend by the denominator of the divifor for a new numerator; and the other two fractions for a new denominator. Or, invert the divifor, and

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2. Divide by of.

Anf. 24.
Anf. 3.

Anf. 1

Anf. 275.

6. Divide of of 4 by of

of of 8.

Anf. 1585.
Anf. Is. of d.

3. Divide 7 by 95

4. What is the quotient of 35 by 21?

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5. What is the quotient of 4 by 5 of 4?

7. Divide of 31. by of 158.
8. What is the quotient of 2 ft. 5 ins. by

10 ins. Anf. 2, ft.

9. Divide of 9 feet by 3 of 2 ft. 9 ins.

10. What is the quotient of

Anf. 5 ft.

of 41 gs. by 37 qts.?
Anf. 4gs. 13 pt.

The

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The RULE of THREE in VULGAR

FRACTIONS.

RULE.

State the questions as in whole numbers, having first prepared the fractions as they may require Then, multiply the denominator of the firft term into the numerators of the fecond and third terms for a new numerator, and the numerator of the first term into the denominators of the fecond and third terms for a new denominator. Let this new fraction be reduced to its proper quantity for the anfwer.

EXAMPLE S.

1. If 194 bufhels of oats be worth 11. 18s. 6d.; what are 61 bushels of the fame worth?

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2. If worth?

:: 40

4X77X247=76076

77X40X 4=12320

ell Flemish coft 33s.; what are 4 yards

Anf. l. os. 3d. 3. If of of a lb. of tea be worth of of 13s. ; what are 31 lbs. worth? Anf. 21. 58. 6d. 4. If 34 acres be worth 371.; what are 15%as. worth? Anf. 151. 158. 6. 5. If of a fhip be worth 731. 18. 3d.; what part of her may I buy for 2501.?

Anf. 4. 6. How many pieces of cloth at 201s. per piece, are to be given for 240 pieces, at 12s. per piece? Anf. 149.

At 1L per cwt., what do 3lbs. come to?

8. If when the days are 13 performs his journey in 35

I 77

Anf. 10 d. hours long, a traveller days; in how many days

will he perform the fame journey when the days are hours long?

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by

Anf. 40

9. If lb. lefs by coft 133d.; what coft 14lbs. lefs of 2lbs.?

Anf. 41. 10s. 8d.

10. What must be paid for 53 ozs. at the rate of 54s. per lb. troy? Anf. 28. 6d. 11. If 13 men in 11 days mow 21 acres of grass; in how many days will 8 men do the fame ?

Anf. 18

days. 12. How much shalloon, of a yard broad, will line a coat, containing 3 yds. of cloth of a yd. broad?

13. If 8 cwts. of fugar coft loaf of it come to weighing 17

Anf. 4 yds. 25 l.; what does a

lbs.?

68

Anf. 9s. 5ord.

R E M A RK.

By obferving the rules already given, and the rules given in common Arithmetic, you may perform the rule of five, intereft, discount, barter, lofs and gain, fellowfhip, or exchange, by vulgar fractions. Examples of cach of thefe would only fwell the book, and may easily be fupplied from the former part of the work.

DECIMAL

FRACTIONS.

A Decimal fraction is a fraction whofe denominator is an unit, with one or more ciphers annexed to it. Decimal fractions are expreffed without any denominators, by writing down the numerator, and putting a point before it, at the top of the figure; thus, is written 5, and 100 55.

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Ciphers put on the right hand of a decimal fraction do not alter its value; but when they are put on the left hand of a fignificant figure, every cipher decreases its value in a tenfold proportion.

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The firft figure on the right hand of a decimal point is called tenths, or the tenth part of an unit; the fecond, hundredths; the third, thousandths; the fourth, tens of thousandths, &c.; as, 74, is read, 7 and 4 tenths; 6.35, is read, 6 and 3 tenths 5 hundredths, or 6 and 35 hundredth parts; and 215, is read, 2 tenths 1 hundredth and 5 thoufandths, or 215 thousandth parts.

A finite or terminate decimal ends at fome certain number of places; an infinite decimal has no end.

A repeating or recurring decimal is a decimal wherein the fame figure is repeated as often as you chufe; as, 4444, &c.; the first figure of which ought to have a dot over it, or a dash through it.

A circulating decimal is when more than one figure is repeated; as, 638463846384, &c.; here both the first and last figures of the repetend fhould have dots over them.

REMARK.

Some accountants mark off decimals with a comma; thus, 4,5—6,08 3,72; others with a period at the bottom of the figure; thus, 7.2,-8.07, 9.28; and others in the way before directed. I have given the preference to the last method, because, by it, the distinction is fo clear between the decimal points and the flops, that they cannot be mistaken for one another.

ADDITION of DECIMALS.

R U L

E.

Write the numbers under each other, fo that the decimal points may ftand in one column. Draw a line under them, and add them as whole numbers. Then, point off as many places, for decimals, as are equal to the greateft number of decimal places in any line of the queftion.

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