MULTIPLICATION OF DUODECIMALS. 102. SUPPOSE we wish to multiply 14f. 7' by 2f. 3' we should proceed as follows: 14f. 7 2f. 3' 31. 7' 9" 29f. 2' Ans. 32f. 9′ 9′′=32f+ of a foot of a foot. EXPLANATION. We begin on the right hand, and multiply the multiplicand through, first by the primes of the multiplier, then by the feet of the multiplier, thus: 3'x7'-x=2 of a foot, which is 21"1'9"; we write down the 9", and reserve the 1' for the next product; again, 14ƒ. × 3′ = 14 × of a foot, which is 42'; now adding in the 1', which was reserved from the last product, we have 43′= 3f. 7', which we write down, thus finishing the first line of products. Again, we have 2f.x7=2x=1 of a foot, which is 14'1f. 2'; we write the 2′ under the primes of the line above, and reserve the 1f. for the next product; 2f.x 14f.=28f., to which, adding in the 1f. reserved from the last product, we have 29f., which we place underneath the feet of the line above. Taking the sum, we find 32f. 9' 9", for the answer. From the above we infer, that if we consider the index of the feet to be 0, then the denomination of each product will be denoted by the sum of the indices of the factors. Thus, feet by feet, produces feet; feet by primes, produces primes; primes by primes, produces seconds, &c. Hence, to multiply a number consisting of feet, inches, seconds, &c., by another number consisting of like quantities, we have this RULE. Place the several terms of the multiplier under the corresponding ones of the multiplicand. Beginning at the right hand, multiply the several terms of the multiplicand by the several terms of the multiplier successively, placing the right-hand term of each of the partial products under its multiplier; then add the partial products together, observing to carry one for every twelve, both in multiplying and adding. The sum of the partial products will be the answer. Repeat this Rule. EXAMPLES. 1 What is the product of 3f. 7′ 2′′ by 7ƒ. 6′ 3′′? 2. Multiply 7f. 8' by 6f. 4′ 3′′? Ans. 48f. 8' 7". Ans. 28f. 3′ 11′′ 2′′". 3. Multiply 6f. 9' 7" by 4f. 2'? 4. What is the area of a marble slab, whose length is 7f. 3', and breadth 2f 11'? Ans. 21f. 1′ 9′′. 5. How many square feet are contained in the floor of a hall 37f. 3' long, by 10f. 7' wide? Ans. 394f. 2′ 9′′. 6. How many square feet are contained in a garden 100f. 6' in length, by 39f. 7' in width? Ans. 3978f. 1' 6". 7. How many yards of carpeting, one yard in width, will it require to cover a room 16f. 5′ by 13f. 7' ? 5' Ans. 24yd 6f. 11′ 11′′. REDUCTION OF CURRENCIES. 103. Before the adoption of Federal money in this country, accounts were generally kept in the denominations of English money. Different States considered the pound as having different values, as given in the following TABLE. $1 in England 4s. 6d. £%, called Sterling money. 81 in { South Carolina =4s. 8d.=£, called Georgia $1 in Georgia S Canada {Canada coti} } = currency. 5s.=£4, called Canada currency. How were accounts kept before the adoption of Federal money? Did all the States estimate the pound at the same value? What fraction of a £ is $1 in Sterling money? What part of a £ is $1 in Georgia currency? What part of a £ is $1 Canada currency? What part of a £ is $1 New England currency? What part in Pennsylvania currency? What part in New York currency? CASE I. 104. To reduce Federal money to pounds, shillings, and pence, we obviously have this RULE. Multiply the sum in Federal money by the value of $1 expressed in the fraction of a pound, as given in the above Table; the product will be pounds. If there are decimals of a pound, they must be reduced to shillings and pence by Rule under ART. 99. What is the fraction by which we multiply Federal money to reduce it to Sterling money? What fraction do we multiply to reduce it to Georgia currency? What is the fraction for Canada currency? What for New England currency? What for Pennsylvania currency? What for New York currency? If in the product there are decimals of a pound, how do you dispose of them? EXAMPLES. 1. Reduce $100-20 to the different currencies, as given in the preceding Table. |
