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OF THE SINGLE RULE OF THREE DIRECT, IN

VULGAR FRACTIONS. How

OW is the Rule of Three in Fractions performed? A. The operation of the Rule of Three in Fractions, both Single and Double, Vulgar and Decimal, are exactly agreeable to the principles laid down in the same rules in Whole Numbers.

Q. How are the following examples proved ?
A. By changing the order of them.

EXAMPLES 1. If 14lb. of sugar cost of a shilling, what cost ** Ib? Answer, ens.=4d. 3qrs. 1875:

2. If ell cost žl. what cost 12 ell? Ans. 158 80
3. If ell costil. what cost i ell ? Auş. 18s 100zl.

4. If 2 oz. silver cost 158 5d. what cost oz. Answer, 6s id 3qrs.

5. If 6 yards {cost 18s. what cost 9 yards 1? Ans. Il. 58. 7d. Iqr.

6. If i dollar be worth 56 d. what are 500 dols. worth? Answer, 1171 18s 4d.

7. If lyd cost 98. what cost 16 yds 1 ? Ans. 5l 17s. 8. If ! pistole be 175. }, what are 100 pistoles ? A. 861. 9. If oz. cost !!. what cost i oz? Ans. 11 58 8d.

10. If an ingot of silver weighs 16 oz. it, what is it worth at 5s 6d. per oz. ? Answer, 41 12s od Iqrig.

11. If faC. cost 141. 4s. what will 70. { cost ? Ans. 1181. 6s. 8d.

12. If of an ell cost i of 19s. what cost 7 ells ? Answer, 71 7s 9d Iqr.

13. If 8lb of tobacco cost 48 9d }, what cost 1lb? Answer, 7d .

14. If lyd. broad cloth cost 158, what will 4 pieces each containing 27 yards cost? Ans. 851 108 1104.

15. A mercer bought 3 pieces of silk, each containing 24 yards at 68 od per yard-I demand the value of the 3 pieces at that rate? Answer, 25l 148 6d2qr ia

16. If {lb. less by cost 13d }, what cost 14 lb. less by of 2 lbs

Answer, 4298 Ods 17. A merchant had 5C, sugar, at 6d per lb. which he would barter for tea, at 8s per lb. T demand how much tea must be given for the sugar? Ans. 431h zia:

18. Bought 120 lb. of tea at 88 per lb. and sold it for 701 wbat was the gain per eent? zos. 35l 58 3d 3qrs gifs

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OF THE SINGLE RULE OF THREE IN VERSE,

IN VULGAR FRACTIONS. 1

IF 34 yards of cloth, that is iş yard wide, be sufficient to make a cloke; how much must I have of that sort which is of a yard wide, to make a cloke of the same bigness? Answer, 4 yards.

2. If 16 men finish a piece of work in 28į days, how long will 12 men require to do the same work? Answer, 37 days.

3. If yard in breadth require 201 yards long to make a garment; what length will i of a yard wide require to make the same? Answer, 3441

4. How many pieces of merchandize, at 20s. s. per pieee, are to be given for 240 pieces 4, at 12s.) per piece? Answer, 1492254 pieces.

5. How many yards of canvas that is 1 yard 1 wide, will be sufficient to line 20 yards of Say, that is of a yard wide ? Answer, 12 yards of canvas.

1

300 1158

OF THE DOUBLE RULE OF THREE IN VULGAR

FRACTIONS.
IF
F 9 students spend 101 in 18 days; how much will

3
20 students spend in 30 days ? Ans. 391 188 4d

2. Three men having worked 19 days i, received 81. Tó, how much must 20 men have for 100 days 1. Answer, 3051 Os 8d 1%.

3. A man and his wife having laboured 1 day, earned 45. 1; I demand low much they must have for 10 days į when their two sons helped them? Ans. 41. 175. izd.

4. A man with his family, which in all were 5 persons, did usually drink 7 gallons of beer in a week; how much will be drank in 22 weeks , when 3 persons more come into their family? Answer, 280 40 gallons.

5. Seven men with their wives, upon examining into their expences for 20 weeks past, found that they laid out 401 ; ; I demand in what time 201} may be spent by 46 men in like proportion; Answer, 3 weeks

6. Three sailors having been aboard 9 months, received 401 ; I demand how much 100 sailors must receive for 28 months service ? Answer 41181 65 od iqrs 17

65688

1 303 T1855

THE

SCHOOLMASTER'S ASSISTANT.

PART III.

OF DECIMAL FRACTIONS.

4 What do you understand by Decimals in general?

A. Any thing which is called one; as one frot, cne pound, oue shilling, one year, &c. is conceived in imagination to be divided into ten equal parts, and every one of those parts into ten other equal parts, and so on, by a Decimal Division without end.

Q. What is a decimal Fraction ?

A. Any number having a point placed before it, thus, .641 is a decimal.

Q. How do you distinguish a whole number from a Decimal Fraction?

A. Any number. having a point placed after it, thus, 641, is a whole number.

Q. What is a mixt number?

A. Any quantity of figures having a point placed some where between them, thus, 6.4), or thus, 64.1, is a mixt number.

Note. The Decimal points musi never be omitteil; because without it, a Decimal cannot be distinguished from a whole or mixt number. But when a whole number alone is given, it is as cominon to omit it as to insert it, as appears by several Examples fulluwing:

OF NOTATION OF DECIMALS.

Q. How do Decimal places increase?

A. In the same manner as whole wumhers do: that is by tens'; for every place towards the left land is ten • times grenter than that which is next it towards the right hand, as appears by the following tahle.

M

TABLE.

OC. Thousands
w X Thousands
* Thousands
co Hundreds
ou Tenth Parts
c: Hundreth Parts
+ Thousand Parts
m X. Thou. Parts
oC. Thou. Parts
-Units
a Tens

Q. May not Cyphers sometimes be annexed to Decimals ?

A. They may, but they, alter not their value: Thus,.44 and 4100 are the same.

Q. May not Cyphers sometimes be prefixed to Decimal Parts?

A. Yes; and then they decrease their Value by removing them farther from the point: thus .0041 is less than .41.

OF ADDITION AND SUBTRACTION OF DECIMALS.

2. How

OW are Decimals added or subtracted? A Place the numbers according to their value, and work as in addition or Subtraction of whole numbers.

Q. How are the operations proved ?
A. As in whole numbers.

EXAMPLES IN ADDITION.

Shillings. 14.47 1

1.191 1.8126 3.6126 7,1281 18.8 126

Yds.
47.4
19.71
461.721
400.004

7.1004
707

Gallons.
7004. 16
712.712
19.0174

7.3126
70.1851
3.108

L. 71.001 120.07 31.1291

13.4101 76.04 7.3

Miles. 41.8101 140.037 18.10

7.8141 16.4612 7.81

16. .16.18104

3.14 1.181 7.7121 8.19817 13.071

Acres. .61271 .8712 2012 .87 .04

Ounces. 48.9108 1.8191 3.1080

.7012 ..0012 *0018

EXAMPLES IN SUBTRACTION.
Years.
Duys.

Weeks.
From 1081.761 712.10009

127.19 Take 10.00012 7.121

121.

Hours. 12.

.12

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Q. How are Decimals multiplied ?

A. As whole numbers are.

Note 1. Wien numbers are Multiplied, make as many decimal parts in the product as there are in two Factors taken together.

2. If Decinal places are wanted in the product, supply them with cyphers to the decimal point. 3. Observe the saine Nole here, which is given in Multiplication of Vulgar Fractions.

Q. How are the following examples proved ?
A. By inverting the Factors.

EXAMPLES.

1 Multiply .612 by 4. 12
2 Multiply 48. by :48
3 Multiply 37.9 by 46.5
4. Multiply .121 by 17.2
5 Multiply 1.81 by 71
6 Multiply 4.1 by 1.42
7. Multiply.00071 by .21

8 Multiply .00041 by .0007 9 Multiply .0027 by 4.1. 10 Multiply 410. by .0012 11 Multiply .07

by .07 12 Multiply 1.007 by .04! 13 Multiply 4.001 ly .004 14 Multiply 004 by .204

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