eighty-five, Nine millions and six, Ninety millions and nine thousand. A. 99101026. SIMPLE SUBTRACTION. ¶ VIII. 1. George had 10 apples, and gave 6 of them to William; how many did he have left? Why? A. Because 4 and 6 are 10. 2. Rufus, having 20 dollars, gave 12 to James; how many had he left? Why? 3. A man, owing 30 dollars, paid 20; how many did he then owe? 4. A man, having 100 dollars, lost 50 of them; how many had he left? 5. A merchant bought a piece of cloth for 120 dollars, and sold it for 140 dollars; how much did he make by the bargain? 6. From 100 take 20; take 10; take 40; take 60; take 70; take 80; take 90; take 95; take 85; take 75; take 5; take 15. 7. John, having 75 apples, gave 20 to his oldest brother, 20 to his youngest, and 20 to his sister; how many had he left? 8. Harry had 25 marbles in both pockets; he lost 9 out of one pocket, and 7 out of the other; how many had he left? 9. William has two pockets, both of which will hold 75 peaches; he has in one 15, and in the other 45; how many more will both hold? 10. A boy, returning with a basket full of oranges, containing 100, and meeting his cousin by the way, gave him 20; how many did he carry home? 11. Two boys were playing at marbles; each had 20 when they began; John lost 5; how many did each have then? When the unfortunate boy had lost all but 2, how many had James won from John? 12. You bought 100 new marbles for 50 cents, and sold Peter 10 for 15 cents; Harry 6 for 10 cents, and Thomas 34 for 20 cents; how many marbles had you remaining? and how much more did you pay for them than what you sold came to ? 13. How many quarters to an apple, or any thing? How many thirds? How many fifths? How many sixths? Seventas? 14. If you had 4 pencils, and should give away, how many Would you have left? 15. If you had 3 cents, and should give away, how many Would you have left? 16. If you had 8 pencils, and should give away, how many Would you have left? 17. How many would you have left each time, if you should give away,, 4, §, 7? 18. If you had 16 marbles, and should give away. †, 16, 16, 16, 16, 18, 18, 16, how many would you have left each time? Q. What is this which you have now been doing called? A. Subtraction. Q. What, then, is the taking of one number from another of the same name, or denomination, called? A. Simple Subtrac tion? Q. What do you mean by the same name, or denomination? A. When the numbers are either all dollars, or all days, or all shillings, or all seconds, &c. Q. In Addition, you recollect that you were required to put together two or more numbers, to find their amount; now it seums that we are to take one number from another to find their difference: how, then, does Subtraction appear to differ from Addition? A. It is exactly the opposite of Addition. Q. What is the largest number called? A. The Minuend Q. What is the smaller number called? A. The Subtrahend. Q. What is that which is left after subtracting called? A. The Difference, or Remainder. Q. From the above, how many parts do there appear to be in Subtraction, and what are they? A. Three-Minuend, Subtrahend, and Difference. Operation by Slate illustrated. 1. A man, having 387 dollars, lost 134 dollars; how many had he left? OPERATION. He had 387 dollars, the Minuend. He lost 134 dollars, the Subtrahend. Had left 253 dollars, the Remainder. In this example how do you obtain the 3, 5. and 2, in the Remainder? A. I say 4 (units) from 7 (units) leaves the 3 (units); 3 tens from 8 (tens) leaves the 5 (tens), and 1 (hundreds) from 3 (hundreds) leaves the 2 hundreds. 2. A man bought a wagon for 62 dollars, and a harness for 39 dollars; what did the wagon cost him more than the har OPERATION. Wagon, 62 dollars. PROOF, 62 dollars. In this example we have a little difficulty in attempting to subtract as before, by saying 9 (units) from 2 (units); but suppose we take one ten from the 6 tens, the next upper figure, which would leave 5 (tens), and join or add this 1 (ten), that is, 10 units, to the 2 units, making 12 units; how would you, then, proceed to get the 3? A. I would say, 9 (units) from 12 (units) leaves 3 (units). Now, as we took 1 ten from the 6 tens, it is evident that we must call the 6 tens 5 tens, and say, 3 tens from 5 tens leave 2 tens; but suppose that, instead of making the upper figure 1 less, calling it 5, we should make the lower figure one more, calling it 4, what would be the result, and how would you proceed? A. I would say, 1 to carry to 3 makes 4, and 4 from 6 leaves 2,the same as before. What is this taking 1 from 6, and adding it to 2, the upper figure, called? A. Borrowing ten. PROOF.-If 8 from 14 leaves 6,because 6 and 8 are 14, how would you proceed to prove the operation? A. I add 23 (the Difference) to 39, (the Subtrahend,) making 62, an amount like the Minu end-therefore right. From these illustrations we derive the following RULE. I. How do you write the numbers down? A. The less under the greater. II. How do you place units, tens, &c.? A. Units under units, tens under tens, &c. III. At which hand do you begin to subtract? A. The right, IV. How do you subtract each figure in the lower line? A. From the figure above it. do V. What do you set down? A. The Difference. VI. If the lower figure be greater than that above it, what you do? A. Add ten to the upper figure. VII. What do you do then? A. From this amount take the lower figure. VIII. What do you set down? A. The Difference. IX. How many do you carry in all cases, when the lower figure is greater than that above it? A. One. PROOF-Which numbers do you add together to prove the operation? A. The Difference and Subtrahend. 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 Jamies 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? Ꭿ. 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. The pupil should be required in all rules to prove his results It is of practical importance, besides, it occasions less trouble to the teacher in detecting mistakes. 18. From 99 take 22; take 55. A. 121. A. 252. A. 162. Ꭿ. 750. A. 3153. A. 2077. A. 1999989. A. 8999997. A. 18999981. 35. From nineteen millions take nineteen. SIMPLE MULTIPLICATION. IX. 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. At 3. What will 2 cows come to, at 10 dollars a head? At 12 dollars? At 14 dollars? At 18 dollars? At 20 dollars? 25 dollars? How many are 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 vards of cloth come to, at 10 cents per vard What will 4 yards? 6 yards? 12 yaras 20 yards? 30 vards? 60 yards? 80 yards? How many are 10 times 3? 47 6 12? 20? 30? 60? 80? |