Ex. (7) A person spends of his money, and then

the remainder; what fraction of the whole has he left? and if the money left amounts to 4s., what was his original sum?

(4) Find the sum of 33, 21, 5, 710, 122.

(5) Express £13 18s. 5d. as the fraction of £17 25. 8d.

(6) Simplify? of 21 of 3 of 4}.

(7) A has £4 98. 3 d., and B £2 198. 7d.; how much has A more than B?

(8) From 43 take 23; and from 5 take 211. 9) Multiply 21 of 7 by 2% of 67.

(10) Add together of 5s. 6d., of 2s. 6d., and

(11) Two men could reap a field separately in 4 days and 6 days, in what time could they do it together?

7 19

(12) Which is the greater or and by how much? 9 24'

(13) Divide 4 of 1 by 32 of 11.

(14) A and B have each £4. If A spend

8

of his money,

15

and B spend £2 16s., what fraction is A's remaining money of B's?

(15) Find the value 23 of 2 miles 3 fur. 120 yds. 2 ft. (16) Simplify 51-3+2-13.

(17) If 3 tons cost £23 178. 318d., what is the price of a ton?

(19) How many miles an hour does a person walk who takes two steps a second, and 1900 steps in a mile?

(20) A sum of £20 is divided among four persons; the first having; the second, of the remainder; and the

3

II

third, of the sum still remaining. Find the share of the fourth.

(21) What fraction of 31 tons 10 cwt. 2 qrs. 24 lbs. is 21 tons 13 cwt. 2 qrs. 13 lbs. ?

(22) Find the wages for 17 wks. 5 dys. at £1 28. 3d. per week.

(23) Simplify 1+38−271⁄2+428-315.

(24) A sovereign being worth 25 franes, and a napoleon 20 francs, express 15s. as the fraction of a napoleon.

4

(25) After spending and of his money, what fraction

3 8

of the whole will a man have left? and if the sum left is 98. 9d., what was the original amount?

I

(26) What fraction is lb. troy of lb. avoir.? and

what fraction is lb. troy of lb. avoir.?

I 7

9

(27) Add together 46 days, 55 hrs., 7

70

min., and 25 sec. (28) Subtract from 2 its fourth, fifth, and tenth parts, multiply the remainder by 2 of 14, and divide this product by 1 of 2.

(29) If a train takes 3 hours to travel 1044 miles, determine its average time for travelling a mile.

(30) Simplify (48 +14+11) of (85—63).

(31) Find the quantity, of which of 1 of 8 is 25 lbs. 4 OZ. 16 dwts.

(32) Express 1 of 5s. 6d. as the fraction of 128. 3d. (33) What fraction added to 19, 33, and 57, will make a sum total of 12?

(34) Find the value of 13 of 4 dys. 6 hrs. 10′ 23′′-82 of 5 dys. 3 hrs. 7′ 21′′.

(35) In the score made by one side at a cricket match,

4

5

four players made of the whole, the four next of the

6

12

remainder, and the other three, of the number still re

7

maining: and there were 4 byes, &c. What was the whole score?

(36) A cistern which holds 100 gallons can be filled from a tap in 25 minutes, and emptied by a waste pipe in 45 minutes. If both are opened together how long will it take to fill, and how much water will have been wasted?

5-(23+1)

(37) Simplify 3+2 of (+2)

(38) Find the value of 2 of 4+1 of 27 of 2; and of 2 of (4+18) of (2-1) of 23.

2 1

(39) What fraction added to will make-1?

5-4

5층 4층

(40) If

13
of one line A is equal to
15

which is the greater, and what fraction of it is the less?

(41) An ounce troy of gold being worth £3 178. 10ld., what is the value of a pound avoirdupois?

(42) What sum is the same fraction of £2 48. Id. that 5s. 91d. is of 10s. 2d.?

2

(44) One partner in a business whose share is of the

II

whole receives from it £214 16s. profit: what share has another who receives £492 58.?

(45) A and B commence some work on Monday mornnig, and by Tuesday evening have done of it; A then leaves, and B completes it by Saturday evening. In how many days could A have done it alone?

2

2

a mile in min.; and C, of a mile in

3

19

7

the quickest runner? and if he can run a certain distance in 3′ 10′′, how much longer will each of the others take?

(49) If the wheel of a railway carriage is 3 times 23 of 2 feet in circumference, how many times does it turn in a minute when the carriage is travelling at the rate of 23 of 33 miles in 5% of hours?

(50) Divide the difference of 13((2-2)× 1} and 13(29-21)×1 by 133-2-2×1.

CHAPTER V.

DECIMALS.

34.-IN the first chapter, the common system of notation was explained in its application to integral numbers, i. e. to those which contain an exact number of units. The same system may be extended to numbers which do not contain the unit exactly.

To express, for example, an integral number containing less than a thousand units, we write down first the number of hundreds of units it contains, then the number of tens of units in the remainder, and then the number of units still remaining: and so, in the same manner if there be yet left a remainder less than the unit, we may write down the number of tenths of the unit which it contains, then the number of hundredths of the unit contained in the remainder, and so on.

A

D

B

K

M

Suppose, for example, A B, an inch long, to be the unit of length by which a given distance is to be measured; and suppose the distance to have contained 5 hundreds of A B, 4 tens of A B, and 7 A B; and a remainder KL to be left, less than AB. Take a tenth of AB, AC; and let KL contain AC 3 times, with remainder ML less than AC. Again suppose AD, a tenth of AC (i. e., a hundredth of A B), to be taken, and to be contained in M L 6 times, with a remainder smaller than itself. And lastly, let the tenth of A D (i. e., a thousandth of A B), be contained in this remainder 9 times. Then the whole distance, expressed in terms of A B, will be 500+40+7 3 6

9 + + +

13 100 1000

If then we make the same convention respecting the local value of the figures (2 c) as is adopted in integral numbers, i. e. that it decreases tenfold for each place from left to right; we may express such a quantity by a horizontal series of figures, only separating the integer from the frac