Here I have a mind to shew how several questions, usually solved by the Rule called Position, may more easily and intelligibly be solved. In order thereto it is only necessary to consider the contrast, already taken notice of between Addition and Subtraction; between Multiplication and Division, viz. that whatever is effected by the one is unravelled by the other.

One being asked how old he was answered, if my age be doubled, the and of my age added to it, more 1 year, I should be 100 years old. What is his age? Ausw. 36 years.

Here from the last number 100 given I easily discover the number sought: for being doubled, i. e. multiplied by 2; the and added, that is multiplied likewise by

and

the sum of the products more 1, makes 100; consequently the sum of the products is 100 less 1. viz 99. Then since the number sought multiplied by 2, by ; by 4, respectively, the sum of the products is 99; if it be multiplied by, the sum of these multipliers, the product will be likewise 99. Therefore we have given the product 99 and the multiplier 23 to find the multiplicand.

From

100

THRE

CHAP. VII.

THE RULE OF THREE IN FRACTIONS.,

HE Rule of Three in Fractions, is analogous to the Rule of Three in whole Numbers, both in the Stating and Operation, For

The

The first and third number or fraction must be of the same name or kind, and reduced to fractions of the same name or denominator.

Multiply the second and third terms together and divide the product by the first; the quotient is the fourth term required; due regard being had to the rules laid down for multiplying, dividing and reducing fractions.

Note. When the first term is 1, the fourth is found by multiplying the second and third; and when the second or third is 1, the fourth is found by dividing the other by the first.

Examples.

1. If of sugar costs. what cost 7?

tb

8.

2. If of a yard cost 5. what will yard cost?

Ansrv. 10s.

3. What will

92

Answ. 49 d.

b. cost, ifs. buy 7th.?

4. If 19b cost. what quantitity can I have for §s. › Answ. b.

5. What will

Cwt. come to if 63 Cwt. cost 21 31?

Answ. 11. 12s. 2 d.

6. How many b of pot-ashes can I have for 124 if 1b cost 1 d. Answ 7b.

7. If for 10's. I buy one hundred of oranges; how many hundred can I have then for 1051s.?

Answ. 104 hundred.

8. If 1 of any thing cost 548 what will come to? Answ. 48. 7 d.

9. Ilow much will Cut, come to, at the rate of 153s. the Cut. Answ. 3s. 11 d.

Although the method before laid down be universally applicable, as by the foregoing examples appeareth, yet there are other methods more ready and accommodate in practice in some particular cases.

Rule

Rule I.

If the first and third terms be fractions, and the second pot, reduce the said first and third to one common denominator; then rejecting the denominators, I make the numerator of the first, the first term, and the numerator of the third, the third term, and work as in whole numbers, &c.

Application.

10. If yard of linen cost 2s. what cost yard at that rate?

11. If of a pound of tea cost 18 9d. what cost 1b.?

Answ. 4s. 44d.

12. If 3 yard cost 9s. 44d. what cost yard?

Answ. 16s. 8d.

43

13. If of a pound Troy cost 19s. 6d. what cost 11 Answ. 21. 138. 71d.

Rule II.

If of the first and third terms one be 1, and the other a fraction, put the denominator of the fraction instead of 1, and the numerator in the place of the fraction, and work the question as in whole numbers as before.

Application.

14. If 1 ton of tallow cost 351. what cost of a ton?

15: If 1 ounce of silver cost 5s. how much cost of an ounce?

Answ. 38. 1d.

16. At 25s. ' Cwt. how much will 3 of a C. cost?

Answ. 188. 9d.

17. If the freight of a ship be 2477. 16s. 8d. what must AB receive for his thereof? Answ. 771. 8s. 111⁄2d. 18. What will 1 yard come to, if yard cost 18d.?

Answ. 2s.

19. If half a quarter of Flanders lace cost 3s. what is that a yard? Answ. 11. 4$.

Rule III.

Of the first and third, if one be a whole number and the other a fraction, multiply the whole number by the denominator of the fraction and work as before. Or if one be a whole number and the other a mixed number, bring the mixed number to an improper fraction and put the numerator in the place of the fraction or mixed number, and multiply the whole number by the denomina tor of the fraction and place the product in the room of the said whole number,

Application.

20. If a piece of cambric 15 yards long cost 31. 15s. what cost yard?

21. If a piece of linen containing 40 yards cost 30s. what is the price of 44 yards?

Answ. 38. 7 d.

22. If 63 C. of goods cost 2131. what cost 1 ton?

Answ. 641. 8s. 10 d.

23. Bought a bag of wool, wt, neat 53 C. at 9s. 6d. H stone; what doth it amount to? Answ. 191. 2s. 44d.

Rule.

Rule IV.

If the second term be a fraction likewise, the first and third being brought to one denomination, multiply the first by the denominator of the second for a divisor, and the third by the numerator of the second for a dividend, divide the last by the first and the quotient is the answer.

Answ. 24s. or 2s. 4d.

25. At 1.

Answ, 351.

yard, how much will 42 yards cost?

26. How much will 650. come to, at 33s. b. ? Answ. 121. 178. 6d.

27. If of an ounce, Avoirdupois, cost 101d. what cost alb? Answ. 8s. 9d.

28. What will 14 C. of pepper come to, if 1541. cost 1238.? Ansiv, 61. 16s. 357d.

part is 176 of 368 ?

ནཱ་

3. By how much must I multiply 133 that the product

may be 49!? Answ. 33.

4. What differs 72d. from 318.?

Answ. 2s. 81d.

5. What number is that which when added to,' and together will make

?

Answ.

6. What number is that, to which, it of of 4} be added, the total may be 1?

Answ. 33.

7. A father dying left his son a fortune, of which he ran out in 6 months; of the remainder held him a twelvemonth

M 2