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DIVISION OF VULGAR FRACTIONS.
the rules of reduction, and invert the divisor, then proceed as in Multiplication.
1. Divide by 5x9-15 nun. 3x20=60 den. 3. 2. Divide by
.Facit . 3. Divide 672 by 13
.Facit 48. 4. Divide 7935 liy 18
.Facit 4307. 5. Divide še by off of
Facit jo 6. Divide of io by of
.Facit 19 7. Divided of by j of
.Facit = 8. Divide 9 ii by of
..Fucit 2 9. Divide x bg 4
Fucit s. 10. Divide 16 bv 24....
.Facit . 11. Divide 5205 by of 91
.Facit 711. -12. Divide 34 by 9.1.
THE SINGLE RULE OF THREE DIRECT, IN
VULGAR FRACTIONS. RULE. Reduce the numbers as before directed in Reduc
tion. State the question as in the Rule of Three in whole numbers, and invert the first term of the proportion, then multiply the three termis continually together, and the product will be the answer.
1. If $ of a yard cost of a £. what will jo of a yard come to at that rate?
Ans. 158. yard : £. - : foyd. : £. for 4x5X I=180) num. and 3X8 X 10=240 den.
or X= 2. If; of a yard cost } £. what will }} of a yard.cost?.
Ans. I 4s. 8d. 3. If of a yard of lawn cost 7s. 3d. what will 10 yards
关 cost ?
Ans. £t...19...104. 4. If } lb. cost ds. how many pounds will of 1s. buy ?
Åns. 1 lb. iis a. Ifell of Holland cost } £. what will 1% ells cost at .that rate ?
Ans. £7...0...84 7. 6. If 12 yards of cloth cost 155. 9d. what will 487 cost at the same rate ?
Ans. S...0...91 7. If 4 of an cwt. cost 2845. , what will 7 cwt. į cost at the same rate ?
Ans. £118...6...8. 8. If 3 yards of broad cloth crat £3..., what will 10 yards ; cost?
9. If of a yard cost of a £. what will of an ell English come to at the same rate?
ARs. £2. 10. If 1 lb. of cochineal cost £1...5, what will 36 lb. Yo come to ?
Ans. £45...17...6. 11. If I yard of broad cloth cost 15s.}, what will 4 pieces cost, each containing 27 yards ; ?
Ans, £ij...14...37% 12. Bought 3 pieces of silk, each containing 24 ells, at 65....Of. per ell, I desire to know what the whole quantity cost ?
- Ans. £25...17...21 SINGLE RULE OF THREE INVERSE, IN
IF F 48 men can build a wall in 21 days , how many men can do the same in 192 days ?
Ans. 6 unen 177 2. If 25s. will pay for the carriage of 1 cwt. 145 miles }, how far may o cwt. į be carried for the same money ?
Ans. 22 miles ir 3. If 31 yards of cloth, that is 1} yard wide, be sufficient to make a cloak, how much must I have of that sort which is ; yard wide, to make another of the same bigness? Ans. 4; yards.
1. If 3 men can do a piece of work in 4 hours , in how many hours will 10 men do the same work ?
Ans, 1 hour to. 5. If a penny white loaf weigh 7 0%. when a bushel of wheat cost 58. 6d. what is the bushel worth when a penny white loaf weighs but 2} 0%. ?
Ans. 15s. 4d: . 6. What quantity of shalloon that is yard wide will line 7 yards of cloth that is 14 yard' wide ?
Ans, 15 yds,
DOUBLE RULE OF THREE IN VULGAR
la carrier receives £2for the carriage of 3 cut: 150 miles,
how much ouglit he to receive for the carriage of 7 cwt. 3 qrs. $50 roiles ?
Ans. £ 1... 16...9. 9. If £100 in 12 months gain £6 interest, what principal will: gain £3 in 9 months ?
Ans. £75. 3. If 9 students spend £107 in 18 days, how much will 20 students spend in 30 days ?'
Ans. £39...18...4,360 4. A man and his wife having laboured one day, earned 4s. , how much must they have for 10 days \, when their two sons helped them?
Ans. £t.. 17...11. 5. If £50 in 5 months gain £24, what time will £11 f require to gain £15?
Ans. 10 15 months. 6. If the carriage of 60 cwt. 20 miles cost £141, what weight san I hare carried 30 miles for £5 ja ?
Ans 15 cwt.
(T. S.) Promiscuous Questions in Vulgar Fractions. In reducing a compound fraction to single one, the work may frequently be considerably shortened by cancelling the fractions ; that is by dividing the numerator and denominator of any two terms by the same number. 1. Reduce and to a common denominator.
35. to its lowest terms. 3
25 to an improper fraction. 4
i to its proper terms.
off off to a single fraction. 6.
of of of one pound to its real value. 7.
of a penny to the fraction of a pound. 8.
4020 of a pound to the fraction of a penny. 9.
to a fraction of the same value, whose numerator
shall be 75. 10.
to a fraction of the same value, whose denominator
shall be 100.
to a simple fraction. , 27
to a simple fraction. 25
of a pound sterling to its proper quantity. 14. 42d to the fraction of a shilling. 15. Add and í together 16.
f and of a pound sterling together. 17.
of a pound to i of a shilling. 18. From á take of 19. - 641 take of 20.
of a pound take of a shilling. 21.
3 of of 4 of a pound take off of a crown. 22. Multiply by of 23.
367 by 37 24.
by 은 25.
9 by 910 26. Divide £ by } 27.
3 by 94 28. ff of a yard cost of a pound, what will be a yard cost ? 29. 1864 be 194, what will 194 be ? 30. An old gentleman spent half of his fortune, and left the re
mainder to A. who spent half of it, and left the remainder to B, who spent one tifth of what he received, and left C of the old gentleman's property, what sum had each person
at the first if a had 1000 ? 31. A gentleman had nine sons and one daughter, to whom ho
left of his property, which was £50, and fof what he received with his wife, whose fortune was $ of £4750. Now the eldest son was to have four times as much as the the youngest, and the da'ghter and the youngest but one were to have each half as much as each of the other six brothers, and each of the six received to of the gentle. mau's fortune, what did each receive ?
32 Reduce and to a common denominator. 33 Add
and i together. 3+.
and ã of a pound together. 35. Reduce to its lowest terms, to which add f. 36.
5005 to an improper fraction. 37.
to its proper terins. 38.
454 to its proper terms. 39.
off of to'a single fraction. 40.
of off to a single fraction. 41.
of a penny to the fraction of a pound.
Too of a pound to the fraction of a penny. 43.
to a fraction of the same value whose numerator
shall be 15. 4+.
ito a fraction of the same value whose denominator
shall be 20.
to a simple fraction. 54
to a simple fraction.
f of a pound to its proper quantity. 48. 401 } to the fraction of a shilling. 49. Add and together. 50.
of a penny to of a pound 51. From
take de 52.
of a shilling take ž. 53. Multiply } by š. 64.
21 by 2 ; viz. 2s. 60. by 2s. 6d. 65. Divide 2} by it.
2} by 24. 57. If } of a yard costs of a pound, what will of a yard cost ? 68.' I 3 yards of lace cost £15, what will 104 yards cost ? 59. If of a yard cost 15s. what will 31 yards cost? 60. Divide 940 pounds, and four times the half of 30 pounds, in
such a inanner that A may receive of }, and.B may have of To of what remained, and D to have what
was left. 01 Divide 7 by twice. 62. Place four 3's in such a manner that they will make just 31. 63. Divide 19 hy 9} multiplied by 13 + }, 64. Add * to yo 65. If I lend my friend £34 for of a year, how much ought he
to lend me for of a year, in order that I may neither
gain nor lose in the use of cash ? 66. Reduce 5s. to the decimal, and also to the fraction of
a pound. 67.
2s. 60. to the decimal, and also to the fraction
of a pound. 08.
10s. to half its value in decimals, and also in
fractions. 69. Divide 9.00 by io.
DECIMAL FRACTIONS. IN ,
one yard, one gallon, &c. is supposed to be divided into ten equal parts, and those parts into tenths, and so on without end.
So that the denominator of a decimal being always known to consist of an unit, with as many cyphers as the numerator has places, therefore is never set down, the parts being only distinguished from the whole numbers by a comma prefixed : thus ,5 which stands for
But the different value of figures appears plainer by the following table :
Whole numbers. Decimal parts.
7 6 5 4 3 2 1 2 3 4 5 6 7
io, ,25 for 25
,123 for 123
Parts of Hundreds,
Parts of X Thousands.
Parts of Millions.
From which it plainly appears, that as whole numbers increase in a ten-fold proportion to the left hand, decimal parts decrease in a ten-fold proportion to the right hand : so that cy: phers placed before decimal parts decrease their value, by removing them farther from the comma, or unit's place; thus ,5 is 6 parts of ten, or jó; ,05 is 5 parts of 100, or i. ; ,005 is 5 parts of 1000, or 1000 ; 0005 is 5 parts of 10000, or 7600 But cyphers, after decimal parts, do not alter their value. For, ,5, ,50, ,500, &c. are each but is of the unit.
A FINITE DECIMAL is that which ends at a certain number of places; but an INFINITE is that which no where ends.
A RECURRING DECIMAL is that wherein one or more figures are continually repeated, as 2,75222.
And 52,275275275 is called a coMPOUND RECURRING DE
Note, a finite decimal may be considered as infinite, by making cyphers to recur ; for they do not alter the valué of the decimal.
In all operations, if the result consists of several nines, reject them, and make the next superior place an unit more: thus for 26,25999 write 96,26.
In all circulating numbers, dash the last figure, us in 86,54666.