NOTE.—WHEN THE DIVISOR is the product of two numbers, neither of which exceeds 12, short division may be employed, by first dividing the given sum by the one number, and the quotient. thus obtained, by the other: the last quotient is the answer. Example.—Divide £376, 11s. 1ļd. by 63. £ $. d. As 63 is the product of 7 and 9, the given 7)376 11 11 sum is divided by 7,, and the quotient, 9)53 15 102 £53, 15s. 103d., by 9: the last quotient is £5 19 the answer. 61 Ans. Exercises. 1. Divide £85 13 51 by 16, . . . Ans. £ 5 7 12 05 15 37 » 21, . 3 2 7 134 7 41 27, . . " 4 19 61 247 18 on 293 14 81, 42, . . . " 6. # 853 12 81, 96, . . ! 8 17 109 33 majos fines cowalio colas color cother colas III. WHEN THE DIVISOR IS 10, 100, 1000, OR 1 WITH ANY OTHER NUMBER OF NOTHINGS ANNEXED. RULE.-Point off as many figures from the right of the highest denomination of the dividend, as there are nothings in the divisor; the remaining figures are the quotient of the denomination divided : reduce the figures pointed off to the next lower denomination, and add any of the same denomination in the given sum ; then point off as before for a further quotient, and reduce the figures pointed off to the next lower denomination; and so on. The figures that remain at each stage, after the pointing off, form the answer required. Example.—Divide £3642, 15s. 6d. by 100. £ S. d. Here there being two nothings 36,42 15 6 in the divisor, 2 figures are 20 pointed off, from the right of the dividend, at each stage of the 12 process. The figures that re main after the pointings off are 6,66 --£36, then 8s., then 6d., and 2 farthings, with a remainder of 2,64 Ans. £36 8 61 64 64, and form the answer. IV. WHEN THE DIVISOR CONTAINS A FRACTION—AS 33. RULE.—Multiply the integer or whole number of the divisor, by the under figure of the fraction, adding the upper figure to the product: multiply the dividend also by the under figure of the fraction: then divide the one product by the other. Example.—Divide £82, lõs. 8d. by 51d. £ s. d. Here the integer of the di53) 82 15 8 visor is multiplied by 4, the 4 £ s. d. under figure of the fraction, and 3, the upper figure, is added 23 )331 2 8(14 7 1142 Ans. to the product, making 23 for the divisor; the multiplicand is also multiplied by 4, making £331, 2s. 8d., the division is then proceeded with as in Rule II. Exercises. 1. Divide £36 13 51 by 31, Ans. £10 9 614 58 6 71.41, . . ! 13 14 694 87 12 10. ! 62, . . . 12 19 898 71 4 8 1 1 9 5 93 138 11 320, . 11 2 112 754 10 6 267 1 28 3 035 wiajci tinches V. WHEN THE DIVISOR IS A COMPOUND NUMBER. RULE.- Reduce both divisor and dividend to the lowest denomination that is in the one or the other; thus, if the lowest denomination in either be pence, reduce both to pence. Having now two simple numbers, proceed by long or short division, as the case may require. Example.—Divide £58, 18s. 84d. by £2, 6s. 3d. £ s. d. £ S. d. 2 6 3 58 18 82 20 20 Here the divisor and the 46 1178 dividend are both reduced to 12 farthings, and then the one sum is divided by the other, 14144 by Rule II. 2220 ) 56577( 25 1927 Ans. Exercises. 1. Divide £3 16 6 by £0 4 6,. . . Ans. 17 2. 1 15 6 8 1 0 7 4, . . " 41 ir 3. 1 56 18 0 1 17 4,. . . 30 27 4. 1 375 14 4 1 23 15 0, . in 15 iis 85 cwts. 2 qrs. 14 lbs. by 3 qrs. 7 lbs. 105 97 yds. 3 qrs. 13 yds. 2 qrs. 1 27 i 12 SIMPLE PROPORTION. PROPORTION is the method of finding an unknown number, by means of certain other given numbers to which it bears a proportion. Simple Proportion is where three numbers, or terms, as they are called, are given in order to find a fourth; hence it is also called the RULE OF THREE. Compound Proportion, as afterwards explained, is where more than three numbers or terms (usually five) are given to find out the unknown quantity. In Simple Proportion, two out of the three given numbers are always of the same kind-as, for instance, 9 yards and 18 yards; and the third is the same in kind as the fourth number sought thus, if the third were pounds, the fourth would also be pounds. RULES I. RULE FOR STATING.*_1. Write down as the third of the three terms (which are all to be placed in one line) that term which is of the same kind as the answer sought. 2. Consider, from the nature of the question, whether the answer should be greater or less than the third term : if greater, place the greater of the other two terms second ; if less, place the less second; and the remaining term in each case, first. Two dots, thus [:] are placed between the first and second term, and four dots [:: ) between the second and the third ; the three terms when stated appear thus—3:6:: 12. II. RULE FOR WORKING.-1. Reduce the first and second terms, if compound, to the same simple denomination : reduce also the third term, if compound, to its lowest given denomination. 2. Multiply the second and third terms together, and divide their product by the first. The quotient will be the answer sought, and is always of the same kind as the third term. In multiplying, the second is placed under the third term, or the third under the second, according to convenience. 3. Convert the answer, when necessary, into its highest denomination; thus, if the answer were in pence, it must be converted into pounds. NOTE.- When the second term does not exceed 12, it will be more convenient to multiply the third term as in Compound Multiplication, than to reduce it to its lowest denomination, before multiplying. See Example 1, page 58. For an explanation of the reason of the rule, see page 63. * SEE ANOTHER MODE OF STATING THE RULE, PAGE 59. |