ART. 70. As there are 10 mills in 1 cent, in any number of cents there are 10 times as many mills as cents. Therefore, to reduce cents to mills, multiply by 10; that is, annex one cipher. Hence, conversely, to reduce mills to cents, divide by 10; that is, cut off one figure on the right. As there are 100 cents in 1 dollar, in any number of dollars there are 100 times as many cents as dollars. Therefore, to reduce dollars to cents, multiply by 100; that is, annex two ciphers. Hence, conversely, to reduce cents to dollars, divide by 100; that is, cut off two figures on the right. As there are 1000 mills in a dollar, in any number of dollars there are 1000 times as many mills as dollars. Therefore, to reduce dollars to mills, multiply by 1000; that is, annex three ciphers. Hence, conversely, to reduce mills to dollars, divide by 1000; that is, cut off three figures on the right. ART. 71. As the operations of reduction consist in multiplying or dividing by 10, 100, or 1000, the work can be shortened by simply moving the point. ILLUSTRATIONS.-In Multiplying, move the point as many places to the right, as there are ciphers in the multiplier. Thus, $2.50=250 cents; $2.50 52505 mills. In Dividing, move the point as many places to the left, as there are ciphers in the divisor. Thus, 275 cents = $2.75; 4285 mills $4.28 5 Dollars to cents? Why? Cents to dollars? Dollars to mills? Why? Mills to dollars? 71. In what do the operations of reduction consist? How can the work be shortened? Illustrate. 3. Reduce 43 cts. and 6 m. to mills. Ans. 436 m. Ans. 49 cts. Ans. 900 cts. Ans. 10400 cts. Ans. 14020 m. Ans. $2.46 5 Ans. $3.00 7 Ans. $31.87 ADDITION OF U. S. MONEY. ART. 72. 1. Add together 4 dollars, 12 cents, 5 mills; 7 dollars, 6 cents, 2 mills; 20 dollars 43 cents; 10 dollars, 5 mills; and 16 dollars, 87 cents, 5 mills. RULE-1. Write the numbers to be added, units of the same denominations under each other; dollars under dollars, cents under cents, mills under mills, because only numbers of the same denomination can be added. OPERATION. $ cts. m. 4.12 5 7.06 2 20.43 0 10.00 5 2. Add as in Addition of Simple Num bers, and place the separating point directly under the separating points above. 16.87 5 $58.49 7 PROOF-The same as in Addition of Simple Numbers. REVIEW.-72. How write numbers in addition of U. S. money? Why? How is the addition performed? Why? Where place the point? 2. What is the sum of 17 dollars, 15 cents; 23 dollars, 43 cents; 7 dollars, 19 cents; 8 dollars, 37 cents; and 12 dollars, 31 cents? Ans. $68.45 3. Add 18 dollars, 4 cents, 1 mill; 16 dollars, 31 cents, 7 mills; 100 dollars, 50 cents, 3 mills; and 87 dollars, 33 cents, 8 mills. Ans. $222.19 9 4. William had the following bills for collection : $43.75; $29.18; $17.63; $268.95; and $718.07: how much was to be collected? Ans. $1077.58 5. Bought a gig for $200; a watch for $43.87 5; a suit of clothes for $56.93 7; hat for $8.50; and a whip for $2.31 3; what was the amount? Ans. $311.62 5 6. A person has due him, five hundred and four dollars, six cents, three mills; $420, 19 cents, 7 mills; one hundred and five dollars, fifty cents; $304 and 5 mills; $888, forty-five cents, five mills: how much is due to him?. Ans. $2222.22 7. Add five dollars, seven cents; thirty dollars, twenty cents, three mills; one hundred dollars, five mills; sixty dollars, two cents; seven hundred dollars, one cent, one mill; $1000.10; forty dollars, four mills; and $64.58 7. Ans. $2000. SUBTRACTION OF U. S. MONEY. ART. 73. From one hundred dollars, five cents, three mills, take $80, 20 cents, 7 mills. Rule. Place the less number under the greater, dollars under dollars, cents under cents, &c. Subtract as in Simple Numbers, placing the separating point under the points above. OPERATION. cts. m. $ 100.05 3 Ans. $19.84 6 PROOF.-AS in Subtraction of Simple Numbers. 5. From $3, take 3 cts. 6. From $10, take 1 mill. 7. From $50, take 50 cts., 5 mills. 8. From one thousand dollars, take cent, and one mill. Ans. $49.49 5 one dollar, ona Ans. $998.98 9 9. B owes 1000 dollars, 43 cents, 5 mills; if he pay nine hundred dollars, sixty-eight cents, seven mills, how much will he still owe? Ans. $99.74 8 MULTIPLICATION OF U. S. MONEY. ART. 74. 1. What will 13 cows cost, at 17 dollars, 12 cents, 5 mills each? SOLUTION.-Consider the cost, $17.12 5, as reduced to its lowest denomination, viz.: 17125 mills. Then, since 13 cows will cost 13 times as much as 1, multiply the cost of one, by 13, which gives for the cost of 13 cows, 222625 mills, the product being of the same denomination as the multiplicand, Art. 30. Finally, reduce the mills to dollars, Art. 70. Hence, the OPERATION. $17.125 13 51375 17125 $222.62 5 Rule-Multiply as in Simple Numbers; the product will be the answer in the lowest denomination of the multiplicand. which may then be reduced to dollars by pointing. PROOF. As in Multiplication of Simple Numbers. 2. Multiply $7, 83 cts. by 8. 3. Multiply $12, 9 cts., 3 m. by 9. Ans. 4. Multiply $23, 1 ct., 8 m. by 16. 5. Multiply $35, 14 cts. by 53. 6. Multiply $125, 2 cts. by 62. 7. Multiply $40, 4 cts. by 102. 8. Multiply 12 cts., 5 m. by 17. 9. Multiply $3, 28 cts. by 38. Ans. $62.64 $108.83 7 Ans. $368.28 8 Ans. $1862.42 $2.12 5 Ans. $124.64 REVIEW. 73. How are numbers written in subtraction? Why? How is the subtraction performed? Where is the separating point placed? 74. How is multiplication performed? How is the product pointed? 10. What cost 338 barrels of cider, at 1 dollar, 6 cents a barrel ? Ans. $358.28 11. Sold 38 cords of wood, at 5 dollars, 75 cts. a cord: to what did it amount? Ans. $218.50 12. At 7 cts. a pound, what cost 465 pounds of sugar? Ans. $32.55 NOTE.-Instead of multiplying 7 cents by 465, multiply 465 by 7, which gives the same product, Art. 30. But, in fixing the denomination of the product, remember that 7 cents is the true multiplicand. 13. What cost 89 yards of sheeting, at 34 cts. a yard? Ans. $30.26 14. What will 24 yards of cloth cost, at 5 dollars, 67 cents a yard? Ans. $136.08 15. I have 169 sheep, valued at $2.69 each: what is the value of the whole? Ans. $454.61 16. If I sell 691 bushels of wheat at 1 dollar, 25 cts. a bushel, what will it amount to? Ans. $863.75 17. I sold 73 hogsheads of molasses, of 63 gallons each, at 55 cts. a gallon: what is the sum? Ans. $2529.45 18. What cost 4 barrels of sugar, of 281 pounds each, at 6 cents, 5 mills a pound? Ans. $73.06 19. Bought 35 bolts of tape, of 10 yards each, at 1 cent a yard: what did it cost? Ans. $3.50 20. If I earn 13 cts. an hour, and work 11 hours a day, how much will I earn in 312 days? Ans. $446.16 21. I sold 18 bags of wheat, of 3 bushels each, at $1.25 a bushel what is the amount? Ans. $67.50 22. What cost 150 acres of land, at 10 dollars, 1 mill per acre? 23. What cost 17 bags of coffee, of 51 pounds each, at 14 cents, 7 mills per pound? Ans. $127.44 9 Ans. $1500.15 ART. 75. DIVISION OF U. S. MONEY. The object in Division of United States money is, 1st. To find how many times one sum of money is contained in another of the same order or denomination. Or, 2d. To divide a sum of money into a given number of equal parts, Art. 41. |