REDUCTION DESCENDING. 245. 1. How many farthings are there in 2 pence? In 5 pence? In 7 pence? In 8 pence? In 6 pence? 2. How many pence are there in 2 shillings? In 5 shillings? In 7 shillings? In 8 shillings? In 6 shillings? 3. How many pence are there in 5s.? In 5s. and 3d.? In 7s. 4d.? In 4s. 5d.? In 6s. 8d.? 4. How many farthings are there in 5d.? In 6d. 3 far.? In 51d.? In 61d.? In 83d.? In 91d.? In 103d.? 5. How many shillings are there in £2 5s.? In £3 5s.? 246. Reduction of a denominate number is the process of changing it from one denomination to another without altering its value. 247. Reduction Descending is the process of changing a denominate number to an equivalent number of a lower denomination. WRITTEN EXERCISES. 1. How many farthings are there in £3 5s. 63d.? 786d. 4 3147 far. £3 5s. 6d. ANALYSIS. Since in 1 pound there are 20 shillings, in 3 pounds there are 3 times 20 shillings, or 60 shillings; and 60 shillings +5 shillings 65 shillings. Since in 1 shilling there are 12 pence, in 65 shillings there are 65 times 12 pence, or 780 pence; and 780 pence + 6 pence: 786 pence. Since in 1 penny there are 4 farthings, in 786 pence there are 3144 farthings; and 3144 farthings + 3 farthings 3147 farthings. Hence in £3 5s. 6d. there are 3147 farthings. 2. How many pence are there in £2 10s. 6d.? = PROCESS. 4 of 20 s. = 60s. 60s. of 12d.=72od. 72o d. = 1024 d. ANALYSIS. Since in 1 pound there are 20 shillings, in of a pound there are of 20 shillings, or of a shilling. Since in 1 shilling there are 12 pence, in 60 of a shilling there are 60 of 12 pence, or 120 pence; and 720 pence = 102§d. Therefore in £ there are 1029d. RULE.-Multiply the number of the highest denomination given, by the number of units of the next lower denomination which is equal to one of the next higher, and to the product add the number given of this lower denomination. Proceed in like manner with this and each successive result thus obtained, until the number is reduced to the denomination required. 6. How many pence are there in £3? 10. How many shillings are there in £5 6s.? How many farthings? 11. Reduce 12s. 5d. 2 far. to farthings. 12. How many pence are there in £7 9s. 5d.? 13. Reduce 17s. 6d. to farthings. 14. What is the value of £ in units of lower denomina tions? 15. Find the number of farthings in £5 13s. 3d. 16. Reduce £35 6s. 8d. to pence. 17. Reduce £45 3s. 93d. to farthings. 18. Reduce £29 18s. 5d. to farthings. REDUCTION ASCENDING. 248. 1. How many pence are there in 12 farthings? In 16 farthings? In 20 farthings? 2. How many shillings are there in 24 pence? In 60 pence? 84 pence? 96 pence? 3. How many pounds are there in 40 shillings? In 60 shillings? In 120 shillings? 4. How many pounds sterling must be paid for 10 pairs of boots at 6 shillings a pair? 5. At 5 shillings each how many pounds sterling must be paid for 16 hats? For 20 hats? 6. Sold 8 pairs of skates at 5 shillings a pair. How many pounds sterling did I receive for them? Reduction Ascending is the process of changing a denominate number to an equivalent number of a higher denomination. WRITTEN EXERCISES. 1. How many pounds sterling are there in 7254 pence? PROCESS. 12)7254 20)604...6 30....4 7254 d. £30 4s. 6d. ANALYSIS. Since 12 pence are equal to 1 shilling, there must be as many shillings in 7254 pence as 12 pence are contained times in that number. 12 pence are contained in 7254 pence 604 times with a remainder of 6 pence, therefore 7254 pence are equal to 604s. 6d. Since 20 shillings are equal to 1 pound, there must be as many pounds in 604 shillings as 20 shillings are contained times in that number. 20 shillings are contained in 604 shillings 30 times and a remainder of 4 shillings. Therefore 7254 pence are equal to £30 4s. 6d. 2. How many shillings are there in 345 farthings? 6. Reduce 3d. to a fraction of a pound. PROCESS. 4d. = 4 of 12s. = 333⁄44S. ANALYSIS. Since 1 penny is of a shilling, of a penny is equal to of of a shilling, or £16804 of a shilling. 348.34 of £20 = £1880 S.= Since 1 shilling is pound, of a shilling is equal to of of a pound, or pound. 20 of a of a RULE.-Divide the given number by the number of that denomination which is equal to a unit of the next higher denomination. Divide the quotient in like manner, and thus proceed until the required denomination is reached. The last quotient and the several remainders will be the result sought. 7. Change of a shilling to a fraction of a pound. 8. Change of a farthing to a fraction of a shilling. 9. Change 384 pence to units of higher denominations. 10. Change 3146 shillings to pounds. Reduce: 11. 3596d. to pounds. Reduce: 20. £15 8s. to farthings. FRENCH MONEY. 249. In France the currency is decimal. Franc. TABLE. The unit is the 10 Centimes (ct.) [pronounced son-teems] 1 Decime 10 Decimes [pronounced des-seems] = 1 Franc . The value of the franc, as determined by the Secretary of the Treasury, is $.193 in United States money. 1. How many centimes are there in 1 franc? In 5 francs? 2. How many decimes are there in 1 franc? In 7 francs? 3. How many centimes are there in 4 decimes? 4. How many dollars are there in 10 francs? In 20 francs? 5. In 3684 centimes how many francs are there? 6. How many francs are there in $19.30? In $9.65? In $3.86? MEASURES OF SPACE. 250. Space is extension in any direction. It has three dimensions or measurements-length, breadth and thickness. 251. A Line is that which has only length. Thus, the edge of any thing, or the distance between any two objects or places, is a line. 252. A Surface is that which has only length and breadth. Thus, the floor, this page, or the outside of any thing, is a surface. 253. A Solid is that which has length, breadth and thickness. Thus, a stone, an apple, a block, a book, etc., are solids. |