III. WHEN THE MULTIPLIER DOES NOT EXCEED 144, BUT CANNOT BE RESOLVED INTO TWO FACTORS. RULE.—Multiply by the nearest factors, as in Rule II., then the original sum by the remainder of the multiplier, and add the two last products together for the answer. Example.—Multiply £17, 13s. 6d. by 23. £ $. d. 10 176 15 0 Here we multiply the given sum by 10, then the product by 2, and the original sum by the remainder, 3, and add the two 353 10 0 last products together, for the answer. 53 0 6 £406 10 6 Ans. Exercises. 1. Multiply £1 17 64 by 17, . . . Ans. £31 17 104 2 3 9 34, . . 74 9 71 7 9 8 58, . 434 0 8 4. ! 13 14 541 65, . . 1 891 18 51 43 18 31 , 78, 1 3425 6 99 6. 1 3 16 87 , 106, . . 406 11 1 n . 1 3 91 123, . 146 3 9.2 8. 14 cwts. 2 qrs. 9 lbs. by 97, Ans. 1414 cwts. 1 qr. 5 lbs. 87 yds. 3 qrs. 2 nls. i 135, 11863 yds. O qr. 2 nls. wiach i no conicos IV. WHEN THE MULTIPLIER EXCEEDS 144. RULE.-Multiply as in Rule I.; only, instead of performing the process mentally, the figures, from their quantity, require to be written down separately, in order to be calculated. Example.—Multiply £23, 14s. 7{d. by 374. £ s. d. Here we first multiply the 2 farthings by 23 14 374, and convert them to pence, making 1878. 374 and no farthings over. Carry the 187d. to the pence, then multiply the 7d. by 374, and £8875 99 Ans. include the 187d. from the farthings: the 7d. X 374, and adding 187, are 2805d., which, converted to shillings, make 233s., and 9d. over. Place the 9d. below the pence, carry 233s. to the shillings, then multiply the 14s. by 374, and include the 233s. from the pence, making 5469s., which, converted to pounds, are £273, and 9s, over. Place the 9s. below the shillings, carry £273 to the pounds, then multiply the £23 as in Simple Multiplication, and include the £273, making £8875. NOTE.--As it is generally more convenient to multiply the greater number by the less, than to multiply the less by the greater, in the above example instead of multiplying 2 farthings, &c., by 374, we multiply 374 by 2; and so on. V. WHEN THE MULTIPLIER CONTAINS A FRACTION-AS 8%. Rule.—Multiply first by the integer or whole number of the multiplier, and then by the fraction (see Simple Multiplication, Rule IV., page 19), and add the products together for the answer. Examples.—Multiply £3, 15s. 4{d. by 83. £ s. d. Here we first multiply £ S. d. 3 15 41 the given sum by 8, then 3 15 41 X. 8 separately by , and add 30 30 the two products for the 5)116 l; * 2 5 21 of dividing £11, 6s. 13d. . £25 23 £32 8 21 4 Ans. by 5, see page 50. COMPOUND DIVISION. COMPOUND DIVISION is the method of dividing a compound by a simple number. RULES. I. WHEN THE DIVISOR DOES NOT EXCEED 12. RULE.--Divide the highest denomination of the dividend as in Simple Division, placing the quotient below the figures divided. If there is any remainder, reduce it to the next lower denomination, add to it any of that denomination in the given quantity, and divide the amount as before: if there be again a remainder, reduce it to the next lower denomination, &c.; and so on, proceeding in this way till all the denominations have been divided. The various quotients will be of the same denomination as the dividends from which they arise. Example.- Divide £87, 14s. 92d. by 7. The 87 pounds are divided by 7; the answer is 7)87 14 92 £12, and £3 over: the £3, reduced to shillings, £12 10 87 make 60s., and adding the 14s. in the dividend, amount tó 74s., which, being divided by 7, give 10s., and 4s, over : the 4 shillings are 48 pence, to which adding the 9d, in the dividend, the sum is 57d., and these divided by 7, give 8d., and 1 penny over: a penny is 4 farthings; add to these the 3 in the dividend, making 7, which, divided by 7, give l; that is, 4d. Exercises. 1. Divide £34 13 44 by 2, . . Ans. £17 6 81 17 12 81 i 3, 5 17 63 23 15 88, 9, 2 12 103 83 9515, 16 13 101 ; 57 17 7 4 73 Ž 93 19 71 108 109 124 13 87, 5, 24 18 8 137 16 4 110, . 13 15 71 345 8 6 1 11, 1 31 8 01 : 417 13 43 # 12, . 34 16 111 11. 85 lbs. 8 oz. io drs.' by 8, Ans. 10 lbs. 11 oz. 14 drs. 136 tons 14 cwts. 2 grs. 1 9, 15 tons 3 cwts. 34 qrs. 1 158 miles 7 fur. 26 per. . 7, 1.22 miles 5.fur.264 per. I 76 acres 3 ro. 30 per. » 12, 6 acres 1 ro. 25% per. 15. 216 yds. 2 qrs. 3 nails , 8, 1. 27 yds. O qrs. 15 nail. ! 167 days 14 h. 34 min., 7, 1 23 days 22 h. 394 m. Gio si acconcos o O si 12 14. II. WHEN THE DIVISOR EXCEEDS 12. RULE.—Divide as in Rule I., only employ long instead of short division, Example.—Divide £484, 198. 78d. by 73. £ S. d. £ s. d. 73) 484 1972(6 12 101 54 Ans. The pounds are first di438 vided by 73; the answer is 46 £6, and £46 over: the £46 are reduced to shillings, by 20 multiplying by 20, and the 939 (12 19s. in the dividend being 73 added, make together 939 shillings, which, divided by 209 73, give 12s., and 638. over: 146 the 63 shillings are reduced 63 to pence, and the 7d. being added, make 763d., which, divided by 73, give 10d., and 763 (10 33 pence over: the 33d. being reduced to farthings, make, with the addition of the 3 farthings in the sum, 135, and these, divided by 135(1 73, give d., and 62 over. The whole answer is thus £6, 12s. 62 = 43 104d.43. |