£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, 9s. 9d. ¹³/₃₀₉.
A grocer mixes 2 cwt. 15 lbs. of sugar at 11d. per pound with 14 cwt. 3 lbs. at 5d. per pound. At how much per pound must he sell the mixture so as not to lose by mixing them?
Answer, 5d. ¾ ¹⁵³/₉₀₅.
- 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 5s., then 6d., and then 1½d. 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:
- 153 tons, at £2 each ton, will cost
£306 0 0
- Since 10s. is £½, 153 tons, at 10s. each, will cost £15³/₂, which is
76 10 0
- Since 5s. is ½ of 10s., 153 tons, at 5s., will cost half as much as the same number at 10s. each, that is, ½ of £76 . 10, which is
38 5 0
- Since 6d. is ⅒ of 5s., 153 tons, at 6d. each, will cost ⅒ of what the same number costs at 5s. each, that is, ⅒ of £38 . 5, which is
3 16 6
- Since 1½ or 3 halfpence is ¼ of 6d. or 12 halfpence, 153 tons, at 1½d. each,