1. In 1857 the total quantity of sheep, lamb, and alpaca wool imported into Britain was 129749898 lbs. ; how many lbs. were imported on an average daily, allowing 365 days to the year? Ans. 355479635 63 lbs. 2. The population of London in 1851 was 2362236, on a surface of 122 square miles; what was the average population per square mile? Ans. 19362722. 3. In 1851 the south of Scotland contained a population of 1813562 on a surface of 9000 square miles; what was the average population per square mile? Ans. 2013588. 4. The surface of the earth is about 197140100 square miles, and the surface of Great Britain and Ireland is 122550 square miles; how often is the surface of the United Kingdom of Great Britain and Ireland contained in the whole earth? Ans. 1608-78700 5. The surface of Great Britain is 90038 square miles, and in 1851 it contained a population of 20959477; what was then the average population per square mile? Ans. 23238658. 122550. 6. In 1853 the population of the Russian empire was 65237437, and the number of inhabitants to each square geographical mile was 174; find the number of square geographical miles in the Russian empire, Ans. 37492714. Exercises on Simple Addition, Subtraction, Multiplication, and Division. 1. Multiply the sum of six thousand seven hundred and two, fifteen thousand nine hundred and twenty-six, and two millions seven hundred and thirty-nine thousand three hundred and eighty-nine, by six thousand seven hundred and forty-five, and divide the product by one thousand seven hundred and twentynine, Ans. 10774901729 836 2. Add together 1894, 37592, 1006, 283597, 8463925, 173964, 2157184, and 327; from the sum subtract 3578961, multiply the remainder by 78359, and divide the product by 9385, Ans. 629587888173. 3. Divide the sum of 237965843, 3921726, 58379, and 83796254, by the difference between 71689 and 140942, Ans. 4703453. 4. Multiply 675392619 by 8735, and divide the product by Ans. 1086054103. 54321, 5. Perform the operations indicated below: 7183102 +61534-17916 6. Perform the operations indicated below: 312570 × 598 + 76125 × 47318÷3-79583 6139 x 15 Ans. 206789843. 7. Perform the operations indicated below: (7 +75) × 43 + (4698 + 315) ÷ 9 (73 +142) – (16 ÷ 2 + 4 × 7) Ans. 8348. 8. Divide the continued product of 2, 3, 4, 5, 6, 7, 8, and 9 by the continued product 12, 13, and 14, Ans. 166. 9. Divide 731 × 437 × 596 by 71 × 24 × 89, Ans. 125511636 ALL CALCULATIONS IN ARITHMETIC are made by means of one or other of the four fundamental rules, Addition, Subtraction, Multiplication, and Division, or by combining them in various ways, according to the Rules given in the remaining portion of this work. COMPOUND NUMBERS. COMPOUND NUMBERS are those which consist of two or more kinds or denominations. When we speak of a pound, a simple number is expressed, it is one kind of thing; but when we speak of a sum consisting of pounds, shillings, and pence, then we refer to various denominations or kinds; in other words, a sum compounded, of various kinds of money, and hence termed a compound number. All questions which refer to sums of money, and to calculations of weights, measures, &c., which consist of various kinds or denominations, are placed under the head of Compound Numbers. Calculations in simple numbers are the same in every country, and must continue without change throughout all time; for example, that 2 and 2 are equal to 4, is a universal truth, which all mankind cannot alter. The rules of Simple Addition, Subtraction, Multiplication, and Division, are therefore in use in every country in the world. With calculations in compound numbers, the case is entirely different, as almost every country has its own standards of money, weights, and measures, and the arithmetical rules for working differ accordingly. These calculations, however, could be rendered as easy as those in simple numbers, if the standards of money, weights, and measures, were constructed on the same decimal principle of advancing by tens. In Great Britain and Ireland, the standards of money, weights, and measures are mixed and various, as may be learned from the following tables. It is necessary that the pupil commit these tables to memory, before proceeding with the calculations in compound numbers. In the gold coinage, 22 parts (commonly called carats) = 11 oz. of fine gold, and 2 parts (carats) = 1 oz. of copper are melted together, and 40 troy pounds of this mixture are coined into 1869 sovereigns. The weight of a sovereign is 123 grains. In the silver coinage, 11 oz. 2 dwt. of fine silver are melted with an alloy of 18 dwt. of copper, and 66 shillings are coined from a troy pound of this mixture. The weight of a shilling is 87 grains. In the copper coinage, 24 pence are made from an avoirdupois pound of copper. All accounts are kept and reckoned by pounds, shillings, pence, and farthings. L. or £ is the initial letter of the Latin word libra, a pound, and is used to denote pounds; s., from the Latin word solidus, stands for shillings; and d., from denarius, for pence: £ s. d. are therefore respectively placed over columns of pounds, shillings, and pence. The mark for a half-penny is for a farthing, or fourth of a penny,; and for three farthings,. The old Scottish pound was equal to 1s. 8d. sterling: hence £100 Scots was = £8, 6s. 8d. of our present money. NOTE. For an account of a new system of reckoning money deci mally, that has been proposed as a substitute for the present mode of reckoning, see Appendix. 7000 Troy grains = 1 lb. Avoirdupois. Gold, silver, and precious stones are weighed by troy weight. In determining the purity of gold, the gold is supposed to be divided into 24 carats, and if pure, is said to be 24 carats fine; if there be 23 carats of pure gold, and 1 of alloy, it is said to be 23 carats fine; and so on. The ounce and pound are the same as in the troy weight. This weight is used only in preparing medicines. 112 = 2240 = 16 = 448 = 1792 = 28672 256 7168 35840 = 573440 1 = 20 = 80 = All ordinary articles are weighed by this weight, which is known as the imperial standard, and is in universal use in this country. A standard imperial pound avoirdupois is equal to the weight of 27.727 cubic inches of distilled water (or the tenth of a gallon) at the temperature of 62° Fahrenheit, and when the barometer stands at 30 inches. = 1 league. A Fathom is 6 feet: a Hand, 4 inches: a Military pace, 2§ feet. |