2 cwt. 1 qr. 21 lbs. 7 oz. × 53 = 129 cwt. 1 qr. 16 lbs. 3 oz. 2ᵈ 4ʰ 3ᵐ 27ˢ × 109 = 236ᵈ 10ʰ 16ᵐ 3ˢ £27 . 10 . 8 × 569 = £15666 . 9 . 4 £7 . 4 . 8 × 123 = £889 . 14 £166 × ₈/₃₃ = £40 . 4 . 10⁶/₃₃ £187 . 6 . 7 × ³/₁₀₀ = £5 . 12 . 4¾ ²/₂₅ 4_s._ 6½_d._ × 1121 = £254 . 11 . 2½ 4_s._ 4_d._ × 4260 = 6_s._ 6_d._ × 2840 229. Suppose it required to find how many times 1s. 4¼_d._ is contained in £3. 19. 10¾. The way to do this is to find the number of farthings in each. By 219, in the first there are 65, and in the second 3835 farthings. Now, 3835 contains 65 59 times; and therefore the second quantity is 59 times as great as the first. In the case, however, of pounds, shillings, and pence, it would be best to use decimals of a pound, which will give a sufficiently exact answer. Thus 1s. 4¼_d._ is £·067, and £3. 19. 10¾ is £3·994, and 3·994 divided by ·067 is 3994 by 67, or 59⁴¹/₆₇. This is an extreme case, for the smaller the divisor, the greater the effect of an error in a given place of decimals. EXERCISES. How many times does 6 cwt. 2 qrs. contain 1 qr. 14 lbs. 1 oz.? and 1ᵈ 2ʰ 0ᵐ 47ˢ contain 3ᵐ 46ˢ? _Answer_, 17·30758 and 414·367257. If 2 cwt. 3 qrs. 1 lb. cost £150. 13. 10, how much does 1 lb. cost? _Answer_, 9_s._ 9_d._ ¹³/₃₀₉. A grocer mixes 2 cwt. 15 lbs. of sugar at 11_d._ per pound with 14 cwt. 3 lbs. at 5_d._ per pound. At how much per pound must he sell the mixture so as not to lose by mixing them? _Answer_, 5_d._ ¾ ¹⁵³/₉₀₅. 230. There is a convenient method of multiplication called PRACTICE. Suppose I ask, How much do 153 tons cost if each ton cost £2. 15. 7½? It is plain that if this sum be multiplied by 153, the product is the price of the whole. But this is also evident, that, if I buy 153 tons at £2. 15. 7½ each ton, payment may be made by first putting down £2 for each ton, then 10s. for each, then 5_s._, then 6_d._, and then 1½_d._ These sums together make up £2. 15. 7½, and the reason for this separation of £2. 15 . 7½ into different parts will be soon apparent. The process may be carried on as follows: 1. 153 tons, at £2 each ton, will cost £306 0 0 2. Since 10s. is £½, 153 tons, at 10_s._ each, will cost £15³/₂, which is 76 10 0 3. Since 5_s._ is ½ of 10_s._, 153 tons, at 5_s._, will cost half as much as the same number at 10_s._ each, that is, ½ of £76 . 10, which is 38 5 0 4. Since 6_d._ is ⅒ of 5_s._, 153 tons, at 6_d._ each, will cost ⅒ of what the same number costs at 5_s._each, that is, ⅒ of £38 . 5, which is 3 16 6