(19) Show by two examples that a number which exactly divides two other numbers will exactly divide their sum. (20) Show that 36 divides 87264, 4932, 38304, and also their sum without remainder. (21) Show that the same is true with 5765, 4830, 2785, 1850, divided by 5, and also 134475, 94325, 7276720, 60225, divided by 55. (22) Show by three examples that any number which exactly divides two others without remainder will exactly divide their difference. (23) At an election there were 3 candidates and 7232 votes polled. The first had a majority of 186 over the second, and 209 over the third: how many votes were given for each candidate ? (24) Divide the square of 3875 by the square of 25. (25) A reservoir is supplied by a pipe which brings in 98 gallons an hour; it also feeds an outlet pipe which takes out 76 gallons an hour. The reservoir is empty at noon on Monday, when the supply pipe is turned on. At noon on Tuesday the outlet is opened, and both continue to run until noon on Wednesday: how many gallons will there then be in the reservoir? (26) If a person walking 9 hours a day makes a journey of 432 miles in 16 days, what is the rate he travels per hour? (27) In one of two towns 1 person out of every 39 dies in a year, and in the other 1 in 45. The population of the first is 287,001, and of the second 38,475: how long will it be before there is a total of 205,350 deaths in the two? Additional Exercises. (1) Take out any number of figures from Part I. of the table on page 10, and divide by 9. Also take out the corresponding number from Part II., and divide by 9. The two remainders added together make 9. (2) Take any two numbers. Find half their sum and square it. Find half their difference and square it. Subtract the one result from the other, divide by one of the numbers, and the answer will be the other number. Averages. 55. If three persons have together £12, and this sum were divided equally among them, they would have £4 each. This is expressed by saying the average amount possessed by each person is £4. A person spends 25 pence on Monday, 34 on Tuesday, 58 on Wednesday, and 23 on Thursday: what is his average daily expenditure? He spent on the four days 140 pence. This is at the average rate of 35 pence each day, 35 being the average of 25, 34, 58, and 23. 56. RULE.-To find the average of several numbers, add them together and divide by their number. Thus in the above question there are four numbers, the sum of which is 140, and 140÷4 gives 35 as the average. Find the average of (1) 86, 17, 25, 7, 30 Ex. 35. (7) 21, 386, 4156, 7282, 1875 (8) 16, 38, 415, 687, 213, 741, 87 (9) 28, 19, 68, 73, 195, 48, 15 (10) 23, 415, 776, 218, 173, 415, 0,4 (11) 160, 136, 718, 386, 29, 46, 7, (12) 298, 386, 741, 584, 8, 600 (13) In a town the deaths for 5 years were 278, 576, 589, 689, 682, and 695: what was the average number of deaths? (14) The average age of 18 boys is 15; the oldest is 17 and the youngest 6: find the average age of the rest. (15) In a school there are 22 boys whose age is 17 years, 35 boys aged 16, 48 boys aged 15, 94 boys aged 15, 95 boys aged 13, 48 aged 12, and 24 aged 11: what was the average age in the school? (16) A man worked on an average 9 hours a day for 6 days, the next week he worked 10 hours on Monday, 9 on Tuesday, 11 on Wednesday, 9 on Thursday, O on Friday and Saturday. The next week he worked on an average 81 hours a day how many hours daily on an average did he work during the 3 weeks (6 days in each week). 12 Pence.... Money Rules. TABLES OF ENGLISH MONEY. PENCE TABLE. 2 Farthings make 1 Halfpenny, written thus, d. 2 Halfpence id. 1s. 20 Shillings 1 Pound, £1 57. The same value may be expressed in different forms; thus, 7 shillings, and 84 pence, are the same in value, but different in name. 58. When a value is expressed in one form, the process by which we find its equivalent value in another form, is termed REDUCTION. 59. We speak of farthing as a lower name than shillings, and o shillings as a higher name than pence. Reduction is therefore of two kinds,-ascending and descending; the money table written thus will show the relation of these processes to each other. pound shillings shillings pence farthings Descending. D དྷ=ནྟཾ=ཙྪཱ=ཙ 960f. 60. If we have a number of farthings given to find their value in pence, shillings, or pounds, we do so by ascending reduction. 61. If we wish to find the number of shillings, pence, or farthings in so many pounds, we use descending reduction. 62. Descending Reduction. RULE.-Multiply the number of the highest name mentioned, by as many units of the next lower name as make one of the higher. Add to the product any units of this lower name that may be contained in the given sum, and proceed thus, step by step, to the units of the name required. EXAMPLE:-Reduce £367 16s. 8d. to farthings. £367 16s. 8d. Reduce to farthings: Ex. 36. (1-6) 4d.; 8d. ; 7d.; 11d. ; 13d.; 15d. " (7-13) 44d.; 61d.; 81d.; 174d.; 94d.; 12дd.; 113d. (14-22) Is.; 3s.; 5s.; 17s.; 16s.; 28s.; 19s.; 14s.; 25s. (23-30) 13s. 2d.; 15s. 5d.; 16s. 7d.; 19s. 8d.; 21s. 2d.; 14s. 5d.; 18s. 9d.; 11s. 11d.; (31-39) 16s. 8d.; 17s. 94d.; 11s. 114d.; 12s. 9jd.; 15s. 63d.; 25s. 44d.; 38s. 64d.; 27s. 5d.; 29s. 113d. (40-53) £1; £2; £3; £8; £12; £15; £17; £28; £49; £386; £217; £914; £388; £126. (54-60) £1 11s.; £3 14s.; £4 7s.; £2 12s.; £17 5s.; £186 15s.; £214 13s. (61-68) £19 8s. 6d.; £17 15s. 4d.; £13 Os. 8d.; £164 14s. 5d.; £386 17s. 2d. ; £17 13s. 9d.; £386 14s. 2d.; £178 18s. 9d. ; (69-73) £179 14s. 6d. ; £215 13s. 84d.; £386 13s. 81d.; £169 11s. 5d. £177 15s. 8d. (74-78) Reduce to pence :-£17; £13 15s. 4d.; £19 16s. 8d.; 2168s.; £38 15s. 5d. (79-83) Reduce to shillings :-£38 15s.; £2968 17s.; 875 guineas; 396 guineas; £287 19s. (84-89) Reduce to halfpence :-£4 19s. 2d.; £9 9s. 9d.; £376 Os. 31d.; £309 7s.; 2179 guineas; £18 12s. 11 d. 63. Ascending Reduction. RULE.-Divide the given amount by as many units of the same name as make one of the next higher, and proceed thus, step by step, to the units of the name required. EXAMPLE:-Reduce 21856 pence to pounds. 20)1821 shillings. 4 pence. £91 1s. 4d. Ex. 37. (1-5) Reduce to pence :-2168 farthings; 3872 farthings; 21986 farthings; 1773 farthings; 18675634 farthings. (6-9) Reduce to shillings:-8167 pence; 937124 farthings; 9284 groats; 72148 threepenny-pieces. (10-20) Reduce to pounds : 2349 shillings; 67931 farthings; 247899 farthings; 476937 threepenny-pieces; 7000 groats; 1789 guineas; 4897 half-crowns; 14289 sixpences; 999 florins; 6879119 farthings; 740987 pence. (21-30) Reduce to guineas :-£668; 973698 farthings; 2769 pence; 300 half-crowns; 7390 farthings; 8876914 groats; 37911 crowns; 17943 half-sovereigns; 99813 halfpence; 76139 threepenny-pieces. (31-38) Reduce to crowns:-£786; 21733 farthings; 3976410 halfpence; 2197 pence; 699 guineas; 34779 groats; 943 threepenny-pieces; 4297 half-guineas. (39-50) Reduce to florins:-£39 16s.; 428 farthings; 7296 groats; 6890 guineas; 741 half-crowns; 8900 halfpence; 72 crowns; 98476 pence; 7217930 farthings; 3670 sixpences; 9763 threepenny-pieces; 81919730849 farthings. (51-59) Reduce to sixpences :-904 crowns; 27896 farthings; £379; 41837 halfpence; 274 guineas; 1780 pence; £891 10s. 6d.; 716 half-crowns; 81907 groats. (60-71) Reduce to groats:-£86; 9107 farthings; 721904 pence; 1617 shillings; 2179 crowns; 32710 pence; 34219 threepenny-pieces; 702 guineas; £6921 17s. 8d.; 41679 farthings; 92718493 halfpence; 73814 half-crowns. |