Example 2.-Ifcwt. cost £21, what will Since cwt. cost £35 16 1% cwt. cost? then I cwt. will cost £ 35×8 12X7 5 and, therefore, cwt. will cost £12x7x16= £5 2 £1 17s. 6d. Example 3.-A person spending, and his money had £119 left; how much had he at first? I of After spending 193 of his money he would have 123 or 17% of it left. 03 126 of his money = £119. Multiplying by the reciprocal of 1% 7 Example 4.-After spending of my money, I find that of what is then left amounts to 5s. 8d. ; how much had I at first? After spending of my money I had of it left. of what is left = 2 of 2 = of the money of the money at first = 5s. 8d. the whole sum at first IIS. 4d. Example 5.-A can do a piece of work in 9 days, and B in 12 days; in what time will they do it together? A can do of the work in 1 day, and B 12 ... A and B together can do +10% of the 36 work in 1 day; as many times, then, as of the work is contained in the whole work, so many days will A and B together require. ... No. of days required = 1 ÷ 36 EXERCISE 29. = 36 = 57. A. (1) Find the value of of 10s. + of 275. (2) Express the difference of of 2 guineas and of 6s. 8d. as the fraction of £3. (3) Reduce of 16s. old. to the fraction of 17s. 6d. (4) Find the value of 3 of a ton + of a cwt. + of a lb. (5) Compare of £1, of 1 guinea, and of a crown; and express their sum in guineas. (6) Find the cost of of a ton at £1 3s. 81d. per ton. (7) At £2 175. 93d. per cwt., what is the cost of I cwt.? (8) If of a yard cost £1 13s. 7 d., what is the price per yard? (9) If 24 gallons cost £3 14s. 2d., what is the price per gallon? (10) If of of a lb. ? of a lb. cost 13s. 51d., what is the cost B. (1) Find the value of of an acre, when § of an acre is worth £42 os. 71⁄2d. II (2) A sum of £11 12s. 3d. is divided amongst four persons, so that the first has, the second 12, and the third 13 of the sum; find the fourth person's share. (3) A sum of £20 is divided amongst four persons, so that the first has, the second of the remainder, and the third of what still remains; find the share of the fourth. (4) One-half of a post is in the mud, of it in the water, and 2 ft. above the water; find the length of the post. (5) After paying 1 of 11, 1 of 1, and 1 of 11⁄2 of his debts, a man still owes 13 175. 9}d; how much did he owe altogether? (6) Out of £3 7s. 41d., one-third is paid to A and one-seventh to B; after this ths of the remainder is paid to A and the rest to B: how much was paid to A and B respectively? (7) A cistern can be filled by one pipe in 20 minutes and emptied by another in 30 minutes; in what time would it be filled if both pipes were open together? (8) A and B can do a piece of work separately in 12 days and 18 days respectively; in what time could they do the work together?' (9) A man can do a piece of work in 12 days, but with a boy's assistance he can finish the work in 9 days; how long would the boy take to do the work by himself? (10) If 4 men or 5 women can do a piece of work in 12 days, in what time will 5 men and 4 women do the same? Find the cost of- C. (1) 8 yds. I qr. 3 nls. at £7 15s. 9 d. per yd. (2) 5 cwt. 3 qrs. 16 lbs. at £5 13s. 7 d. per cwt. (3) 2 cwt. I qr. 4 lbs. at £7 15s. 3 d. per cwt. (4) 7 ewt. 3 qrs. 22 lbs. at £15 10s. 8d. per cwt. (5) 15 cwt. I qr. 26 lbs. at £5 7s. 2d. per cwt. D. (1) Express as a fraction of £3 the difference between £3 and £3×4. Ι (2) What fraction of I drachm is 1 dwt.? (3) Reduce £3 55. of £1 to the fraction of 1 of = (4) If 13 of a sum of money of 5s. 10d., find the sum. (5) If of a bushel cost £1, what part of a bushel can be bought for 7s. ? (6) If 3 men or 7 boys can do a piece of work in 29 days, in how many days will 7 men and 3 boys do the work? (7) If 26 francs are equivalent to a pound, what fraction of a shilling is a franc? (8) There are two numbers whose difference is 25, and.one number is of the other; what are the numbers ? (9) If of a sheep be worth £, and 10 of a sheep be worth given for 20 oxen? of an ox, how much must be of 5 ft. 4 in. CHAPTER XI. DECIMALS. 112. A decimal number is the number of units, tens, hundreds, thousands, &c., contained in that number. A decimal fraction, or, as it is commonly called, a decimal, is the number of tenths, hundredths, thousandths, &c., contained in that fraction. 113. From the law of decimal notation we see DC BA that in the number 3 3 3 3, the figure under c, which represents 300, is a tenth of the foure under D, which represents 3000; and that the figure under B is a tenth of that under c, and the figure under A is a tenth of that under B. Thus, in a decimal number the value of every successive digit decreases in a ten-fold degree as we proceed from left to right. 114. Supposing this law to hold good for successive digits to the right of the unit's place, then in the A C d number 3 3 3 3, if a denote the unit's place, the figure under b will be a tenth of the figure under a, or a tenth of 3, that is 3 tenths; similarly the figure under c will be a tenth of that under b, or 3 hundredths, and the figure under da tenth of that under c, or 3 thousandths. 115. Hence in the following number where 8 is the unit's figure it appears that the denomination or local value of the digits to the right of the unit's place may be determined by a similar rule to that given for the determination of the value of the integral digits. Thus, a digit one place to the left of the unit's figure is tens, one place to the right, tenths; a digit two places to the left of the unit's figure is hundreds, two places to the right, hundredths; a digit three places to the left, thousands, three places to the right, thousandths, &c. |