6 ) 36 4 an * 3. Multiply 36 by 48 quotient being properly the product of a part of a unit , the product of the unit figure is placed 6=of 36 directly under. 144 Ans. 156 4. Multiply 34 by 57 5. Multiply 55 by 5+. 34 Ans. 286. 6. Multiply 365 by 67, 17= of 34 ) Ans. 22421 81=1 of 34 and 7, Multiply 264 by 103. 170 Ans. 2673. 1952 Ans. 8. Multiply 6742 by 65. NOTE.To multi6742 ply by a fraction, we 6 sometimes find it 421355 of 6742. more convenient to † 40452 multiply the multi plicand by the numeAns. 446658 rator of the fraction 6742 x by and divide the pro5 Numerator. duct by the denominDenominator 8 ) 33710 ator; see the quo42135= of 6742. tient is then the pro duct of the fraction; which product* in all cases must be added, as in this 8th example, with the produett of the whole number. 9. Multiply 2456 by 941. Ans. 243552. 10. Multiply 346 by 24. Ans. 9397. 11. Multiply 4673 by ž. Ans. 36345. 12. Multiply 6621 by *. Ans. 4965 FAMILIAR EXAMPLES. To exercise the learner in Addition, Subtraction, Multipli cotion, and Division. 1. If you add 444, 375, 250, and subtract 300 from the amount; what will remain ? Ans, 769, 2. John borrowed of George at one time 500 dollars, at another $250; John paid at one e time 150 dollars, at another 120 dollars; how much is John indebted to George? Ans. $480. 3. What number is that which being multiplied by 30 the product will be 1350 ? Ans. 45. 4. What number is that which being divided by 72 the quotient will be 36? Ans. 2592. 5. What will 48 yards of broadcloth come to at $44 per yard? Ans. $216. 6. What will 96 yards of Irish linen come to at of a dollar per yard? Ans. $72. 7. At one dollar and a half per yard; what will fifty yards cost? $75. 8. Four men in partnership have, in stock, 6346 dollars ; of which A put in $1500, B $900, and C $2500; what did D put in ? Ans. 1446. 9. If 4 yards of broadcloth cost 16 dollars; what will 8 yards cost? Ans. $32. Note.-From this exam. 4) 16 ple, the student may draw $ 4 the price of 1 yard. very important instruction, which may be employed in 8 almost all the transactions of business in buying and sellAns. $ 3 2 the price of 8 yards. ing. Where the price of a quantity is given to obtain the price of a unit, we divide the price of the quantity by the quantity; the quotient is then the price of the unit, that is, one pound, one yard, &c. “And when we have the price of a unit given, to obtain the price of a quantity we multiply the price of a unit by the number expressing the quantity. Consequently when the price of a quantity is given to find the price of some other quantity, we only have to observe the following rule. RULE.-Divide the price of the given quantity by the number expressing the quantity, and your quotient will be the price of one; then multiply the price of one by the number expressing the other quantity, and the product will be the price of the required quantity. 10. If 8 yards of calico cost 24 shillings; what will 4 yards cost? Ans. 12s. Dem. It is plain, that 1 yard must cost the eighth part of the price of eight yards; and by dividing 24 shillings, the price of eight yards, by 8, our quotient, 3 shillings, is an eighth part of 24 shillings; consequently 3 shillings is the price of 1 yard; it is also evident, that 4 yards Shillings. must cost 4 times as much 8) 24 as one yard; then by mul tiplying 3 shillings, the 3 the price of · yard. price of one yard, by 4, 4 our product must be the Ans. 1 2 s. the price of 4 yards. it is repeating 3 shillings, price of 4 yards; because the price of 1 yard, 4 times. 11. If 4 barrels of flour cost 20 dollars; what will 30 barrels cost? Ans. $150. 12. If 28 cords of wood cost 42 dollars; what will 6 cords cost? Ans. $9. 13. If a man receive 7 cents for the loan of 1 dollar per year; what should he receive for the use of 100 dollars the same time? Ans. $7. Note. To reduce cents to dollars, cut off two of the right hand figures; and all to the left will be dollars; the two figures cut off will be cents; thus 1450 cents=$14,50 cts.; to bring mills into dollars, cut off three of the right hand figures; thus, 14505 mills=14 dollars, 50 cts. and 5 mills. 14. If a man receive 49 cents for the use of 7 dollars; what should he receive for the use of 50 dollars, the same time? Ans. $3,50 cts. 15. If a man receive 28 dollars for the use of 400 dollars a year; what should he receive for the use of $1000 the same time? Ans. $70. 16. If a man's wages for 365 days amount to $456,25 cents; what will his wages amount to for 60 days ? Ans. $75. 17. Suppose you receive $36, for 24 yards of fine linen; what should you receive for 48 yards? Ans. $72. 18. What will 127 yards of cloth come to, at $4 per yard ? Ans. $50. 19. Suppose 50 yards.cost $37,50 cents; what is the cost of one yard? Ans. ,75 cts. 20. If one yard cost seventy-five cents; what will fifty cost? Ans. $37,50 cts. QUESTIONS. What is à mixed number ? A. A whole number and a fraction, as 44, express 4 and two sevenths. How do you multiply by ? A. By taking half of the multiplicand, that is, dividing the multiplicand by 2, and taking the quotient for the product. How do you multiply by one third ? A. Take one third of the multiplicand. How do you multiply by t? A. Take one twelfth of the multiplicand. What is multiplying by one? A. It is taking the multiplicand once ? What is multiplying by 3? A. It is taking the multiplicand three times. When you multiply by a whole number and a fraction, where do you place the product of the fraction ? A. Directly under the product of the unit figure of the multiplier, because multiplying by a simple fraction is only multiplying by a part of a unit. Where the price of a quantity is given, how do you find the price of any other quantity? A. Divide the price of the given quantity by the given quantity, which will give the price of a unit, then multiply the price of a unit , by the other quantity, and the product will be the price of the required quantity: If six yards of cloth cost 12 shillings, how would you find the cost of 3 yards ? A. I would divide 12 shillings by six, the number of yards, the quotient will then be the price of 1 yard; then multiply the price of one yard by 3, the number of yards, and the product will be the price of 3 yards. How much more should a merchant receive for 3 yards than for 1? A. Three times as much. REDUCTION, Is the changing of numbers from one denomination to another with. out altering their value. It is of two kinds, Descending and Ascending. Reduction Descending is changing higher denominations into Lower, as pounds into shillings, and shillings into pence, &c.; it is performed by multiplication. Reduction Ascending is changing lower denominations into higher, as pence into shillings, shillings into pounds; performed by division. REDUCTION DESCENDING. RULE.-Multiply the number in the highest denomination given by as many of the next lower as make one in that higher; and remember to add to the product, the figures of the next lower denomination, and in like manner proceed till your given sum is reduced to the denomination required. Proof. Reduction descending is proved by reduction ascending, and reduction ascending, by reduction descending; and, if by reverse (ing the work, the given sum be produced, the work is right. FEDERAL MONEY. 10 Mills make 1 Cent, ct. 10 Cents make 1 Dime, di. 10 Dimes, or 100 cts. make 1 Dollar, $. 10 Dollars make 1 Eagle, E. 9.7 The following is a brief account of the coin in use in the United States, abstracted from an act establishing a mint, and regulating the coins of the United States,” pessed April 2d, 1792. The money of account of the United States shall be expressed in dollars or units, dimes or tenths of a dollar, cents or hundredths of a dollar, and mills or thousandths of a dollar. The following are the denominations of coin in the United States. The Eagle shall be of the value of ten dollars. Gold- The Half Eagle five dollars. The Quarter Eagle two and a half dollars. The Dollar Spanish milled dollar. The Half Dollar half the d., or 50 cts. Silver- The Quarter Dollar 1-4th the d., or 25 cts. The Dime 1 tenth the d., or 10 cts. The Half Dime 1-20th the dollar, or 5 cts. The Cent 1 hundredth of the dollar. 1 half the cent. The standard for gold coin, shall be eleven parts of pure gold and one part of alloy, so that every twelfth part is alloy. The alloy must be silver and copper, but the silver must not exceed one hælf in the alloy. The weight of the Eagle, shall be two hundred and forty-seven and a half grains of pure gold, or two hundred and seventy grains of standard gold; and the other gold coins shall be proportional. The standard proportion for silver coin of the United States, shall be one thousand four hundred and eighty-five parts of pure silver, and one hundred and seventy-nine parts of alloy; and the alloy must be purt copper. The weight of the Dollar, shall be three hundred and seventy-one and one fourth grains of pure silver, or four hundred and sixteel grains of standard silver; and the other silver coins must weigh pro portional according to their value. The copper coins shall be of pure copper. The weight of the Cent shall be eleven penny weights of copper; and the Half Cent shall weigh in the same proportion. The proportional value of gold to silver is as fifteen to one, or by a law of Congress, fifteen pounds in weight of pure silver, shall be equal in value to one pound in weight of pure gold. All coins issued from the mint of the United States, shall be a lawful tender for the payment of any debt at the values here given, but should they fail in weight, the valueş must be proportional to their weight, EXAMPLES 1. In ? dollars; how many cents ? Ans, 200 cts. DEMONSTRATION.- It is plain, that we must have one hundred times as many cents as dollars to equal our dollars in value, because it takes a hundred cents to equal à dollar; and by multiplying by 100, |