ARITHMETIC. The subject of Arithmetic is divided into Four Sections: SECTION A.-Vulgar Fractions-Four Questions-5 marks each. Marks allotted, 20. SECTION B.-Decimal Fractions-Four Questions-5 marks each. Marks allotted, 20. SECTION C.-Compound Proportion and Interest-Four Questions-6 marks each. Two of each kind as a rule. Marks allotted, 24 SECTION D.-Miscellaneous Problems-Four Questions-9 marks each. Marks allotted, 36. Full marks for Arithmetic, 100. Qualifying marks, 50 (of which 18 must be obtained in Section D). Time allowed, 34 hours, inclusive of the time occupied in completing the printed papers, which is to be done by the men about to be examined, at the dictation of the superintending officer, or some other person in his presence. NOTE.-By the foregoing remarks it will be seen that the time to work the paper is nearly exactly 3 hours. The Candidate is earnestly requested never to work by rules of thumb but as far as time will allow, to shew clearly and intelligently, the reasons for the methods and processes employed, by the style of working; to make all figures most distinctly, and where necessary, directly underneath each other; and to use the scribbling Column only for his rough work. SECTION A. Vulgar Fractions-Four Questions-5 marks each. For the elementary explanation of Vulgar and Decimal Fractions, see "Guide to 2nd Class Certificate," their further development only being treated in this work. The style of the questions, which are intended to embrace all that pertains to the subject, is best seen by few examples. ADDITION AND SUBTRACTION OF VULGAR FRACTIONS. Ex. (a) Add together of of 5 guineas; of of £1,, 10,, 0; of 23 florins; 23 of 2 crowns; and 74d. 9d. 19 2 of 2 crowns= 3 9 (G×?x5). =,=286.××”)a =དིམ་= Ex. (b) Add together of a ton; % of a cwt.; % of a lb. Ex. (c). Find the difference between 73£ and 3 of 7£. £73 = £7 + (3 of 1£) = ( ~ × 20). 40 S.. -s.=133s. 1 Ι 4 of a shill of 12 pence=(x)d. ={d.=4d. NOTE. The sign is employed to denote the difference of two quantities, without indicating which of them is the greater. MULTIPLICATION AND DIVISION OF VULGAR FRACTIONS. In these examples, brackets are of frequent occurrence, and assume the forms ( ); { }; (); indicating that the compound quantity enclosed, is to be reduced to a simple fraction. A complex fraction is one which has a fraction for its numera1 3 10 tor, or denominator, or both, thus 21311; are complex fractions. To reduce a Complex fraction to a simple quantity, divide the numerator by the denominator. A whole number may be regarded as a fraction, with 1 for a denominator, thus 7=1, &c. For division of fractions, invert the divisor, and proceed as in multiplication. This rule is deduced from the fact that if both dividend and divisor be both multiplied by the same number, i.e., their common denominator, the value will remain the same, and the quotient is not thereby altered. Thus in the complex fraction the divisor and dividend are reduced to quantities having the 24 same denomination, viz. :-halves, there being two halves in 1 and 5 halves in 2. 1 is therefore of 24. SOLUTION |