A. Units under units, tens under tens, &c. A. The right. Q. How do you subtract each figure in the lower line? Q. What do you set down? A. The Difference. Q. If the lower figure be greater than that above it, what do you do? A. Add ten to the upper figure. Q. What do you do then? A. From this amount take the lower figure. Q. What do you set down? A. The Difference. Q. How many do you carry, in all cases, when the lower figure is greater than that above it? 'A. One. PROOF. Q. Which numbers do you add together to prove the operation? A. The Difference and Subtrahend. Q. What must the amount be like? A. The Minuend. More Exercises for the Slate. 3. A man, having 98 dollars, paid away 49; how many had he left? A. 49 dollars. 4. James bought 78 marbles, and lost 29 of them; how many had he left? A. 49 marbles. 5. A man paid 175 dollars for a gold watch, and 55 dollars for a horse; how much more did he pay for the watch than for the horse? A. 120 dollars. 6. A man bought a chaise for 215 dollars, and to pay for it gave a wagon, worth 37 dollars, and the rest in money; how much money did he pay? A. 178 dollars. 7. A merchant bought a piece of cloth, containing 489 yards, and sold 365 yards; how many yards had he left? A. 124 yards. 8. If you have 20 dollars in your pocket, and owe 15 dollars, how many dollars will you have left in your pocket, when your debts are paid? 9. If you have 2560 dollars' worth of stock, and owe 1500 dollars, how much worth of stock will you have, after your debts are paid? A. 1060 dollars. 10. America was discovered by Christopher Columbus, in 1492; how many years had elapsed at the time when hostilities commenced, in the revolutionary war, 1775? A. 283 years. 11. Gen. Washington was born in 1732, and died in 1799; how old was he? A. 67 years. 12. William has 15 cents; he owes Rufus 6 cents, and James 4; now how many will he have left, after paying Rufus and James? 13. A merchant owes to the Exchange Bank 2365 dollars, to the Bank of North America 15000 dollars, and his whole stock is worth no more than 42000 dollars; how much will he have left, after paying both banks? A. 24635. 14. If you buy 20 apples for 40 cents, and sell 15 for 35 cents, how many apples will you have left, and how much will they cost you? 15. A grocer buys 560 bushels of rye for 530 dollars, and sells 200 bushels for 400 dollars; how many bushels will he have left, and what will they cost him? A. 360 bushels, and they cost him 130 dollars. 16. A wine merchant bought 3600 gallons of wine; and sold at one time 2400 gallons, at another 1000 gallons; how many gallons has he on hand? A. 200. 17. From 200 take 150; take 190. To prevent the learner from copying his answer from the book, the following examples have answers formed by adding together two separate results. Each of these results is, in all such cases, however simple the process, given in the Key, which goes along with this work. 18. From 99 take 22; take 55. A. 121. A. 252. A. 162. A. 750. .A. 1000. .9. 3153. A. 2077. A. 15666014. 33. From 1000000 take 1; take 10. 34. From nine million take 3. 35. From nineteen million take nineteen. 36. From forty million take one million. A. 1999989. A. 8999997. A. 39000000. SIMPLE MULTIPLICATION. TIX. 1. What will 3 books come to, at 20 cents apiece? Why? A. Because 20 and 20 are 40, and 20 are 60; that is, 3 times 20 are 60. 2. What will 3 bushels of apples come to, at 30 cents a bushel? Why? A. Because 30 and 30 are 60, and 30 more are 90; that is, 3 times 30 are 90. 3. What will 2 cows come to, at 10 dollars a head? At 12 dollars? At 14 dollars? At 18 dollars? At 20 dollars? At 25 dollars? How many are 2 times 10, then? 2 times 12? 2 times 14? 2 times 18? 2 times 20? 2 times 25? 4. What will 30 yards of cloth come to, at 2 cents per yard? What will 14 yards? 16 yards? 12 yards? 25 yards? 30 yards? 60 yards? 80 yards? How many are 2 times 30? 14? 16? 12? 25? 30? 60? 80? 5. What will 3 yards of cloth come to, at 10 cents per yard? What will 4 yards? 6 yards? 12 yards? 20 yards? 30 yards? 60 yards? 80 yards? How many are 10 times 3? 4? 6? 12? 20? 30? 60? 80? 6. What will 4 oranges cost, at 10 cents apiece? Why? A. Because 10 and 10 are 20, and 10 are 30, and 10 more are 40; that is, 4 times 10 are 40. Q. What, then, is multiplication a quick way of performing? Q. What is the number called, which is to be added to itself, or repeated several times? A. The Multiplicand. Q. What is the number, which shows how many times the multipli cand is to be repeated, called? A. The Multiplier. Q. What are both multiplier and multiplicand sometimes called? Q. What is the result, or number found by multiplying, called? ¶ X. WHEN THE MULTIPLIER IS 12, OR LESS. Operation by Slate illustrated. 1. How much will 4 barrels of pork come to, at 17 dollars a barrel? Q. Since 4 times 7 are the same as 7 times 4, we see that it makes no difference which number is considered the multiplier why is the 4, then, made the multiplier in this example? 4. For the sake of convenience, it being the smaller number. Q. How do you get the 8 units in the product? A. I say, 4 times 7 (units) are 28 (units), or 2 tens and 8 units, writing down the 8 units, and carrying the 2 (tens), as in Addition. Q. How do you obtain the 6 (tens)? A. I say, 4 timeș 1 (ten) are 4 (tens), and 2 (tens), to carry, make 6 (tens). 17 PROOF. 3 less than 4, the former multiplier. 51 17 the multiplicand. 68 like the result of the other operation,therefore right. PROOF. Q. As 3 times 17 and 1 time 17 evidently make 4 times 17, how can you prove the above operation? A. I can multiply 17 by 3, one less than 4, making 51; then add 17 (the multiplicand) to 51, making 68; which, being like the result in the first operation, proves the work to be right. From these remarks and illustrations we derive the following RULE. Q. How are the terms to be placed? A. The less under the greater, with units under units, tens under tens, &c. Q. At which hand do you begin to multiply? A. At the right hand. Q. How are the figures of the multiplicand to be multiplied by the multiplier? A. Separately. Q. How do you carry and write down? More Exercises for the Slate. 2. What will 125 pounds of cheese cost, at 6 cents a pound? A. 750 cents. 3. What will 420 pounds of pork come to, at 9 cents a pound? A. 3780 cents. 4. What will 167 barrels of flour come to, at 9 dollars a barrel? A. 1503 dollars. 5. What will be the price of 8 hogsheads of wine, at 129 dollars per hogshead? A. 1032 dollars. 6. A merchant sold 895 oranges, at 11 cents apiece; what did they come to? A. 9845 cents. 7. What will 236 lemons come to, at 8 cents apiece? At 6 cents? 236 1416 236 1888 1888 3304 Ans. For the answers to each individual process, the teacher can consult the Key. 8. Multiply 120 by 2 2; by 3. 9. Multiply 1211 by 5; by 6. 10. Multiply 1211 by 7; by 8. 11. Multiply 65321 by 9; by 6. 12. Multiply 65321 by 8; by 10. 13. Multiply 123456 by 11; by 4. 14. Multiply 123456 by 3; by 5. 15. Multiply 345612 by 3; by 8. 16. Multiply 345612 by 12; by 7. 17. Multiply 12345006789 by 3; by 4. 18. Multiply 12345006789 by 5; by 6. 19. Multiply 236120013 by 2; by 3. A. 600. A. 13321. Ꭿ. 18165. A. 979815. A. 1851840. A. 86415047523. ¶ XI. WHEN THE MULTIPLIER IS MORE THAN 12. 1. There are 365 days in one year; how many are there in |