(22.) Eagles. 271135 260 3 5 7 311070582 1 2 1 6 2 5 515 37 4 2 3 2 813 6 0 2 115 6 0 1 535126100812 (23.) Dollars. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 98 7 6 5 4 3 2 1 9 8 7 6 5 4 3 2 0 5 5 4 4 3 3 2 2112233 4 4 2 2 6 6 5 5 4 4 33 2211001133 776 6 5 5 4 4 3 3 2 211 0011 (24.) Pennyweights. 987 6 5 4 3 2 1 9 8 7 6 5 4 3 2 9879543 987 654 9 8 7 6 5 1234 123 12 1 (25.) Degrees. 13000 895 965 721 3 (26). Furlongs. A to No. 17. 50 6 5 5 57 24 764007 611 4 5 3 26 9181 8 5 21498110 4 1 1035914702 58885 22 25 3 6 5 7 9 4 6 9 5 2 4 5 5 4 0 4871 253 684 222 22190020371507746 X3 Total amount, 2 052 69774325927004 6 2 9731' 28. Add 8541, 1256, 3560, and 2456 together. A. 15813. W Ja 29. Add-15000 dolls. 2500 dolls. 36594 dolls. 29321 dolls. together. A. 83415 dolls. 30: Add 11000 mills, 1100 mills, 110 mills, and 11 mills, together. A. 12221 milló. 31. Add 555555 ounces, 3333 ounces, 66 ounces, 4444444 ounces, and 22222 ounces, together. A. 5025620. 32. What is the sum of the following numbers ? viz. Twenty-five, Three hundred sixty-five, Two thousand one hundred and forty-five, Eighty-nine thousand, Four hundred eighty-five, Nine million and six, Ninety million and nine thousand. A. 99101026. SIMPLE SUBTRACTION. mai 1 sho 1 BE ea how many same I 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; 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 liis 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 ? il. 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 12. You bought 100 new marbles for fifty 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? Sevenths? 14. If you had 4 pencils, and should give away 7, 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 $, g, 4, 5, 7? 18. If you had 16 marbles, and should give away I fe, 1969 162 163 , 16, 17, 18, how many would you have left each time? Q: What is this which you have now been doing called ? Q. What, then, is the taking of one number from another of the same name, or denomination, called ? A. Simple Subtraction. 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 seems 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. 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. Q. In this He had 3.87 dollars, the Minuend. example, how do you obtain He lost 134 dollars, the Subtrahend. the 3, 5, and 2, in the ReHad left 253 dollars, the Remainder. mainder ? 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. À man bought a wagon for 62 dollars, and a harness for 39 dollars; what did the wagon cost him more than the harness ? OPERATION. Q. In this example, we have a Wagon, 62 dollars. little difficulty in attempting to subtract as before, by saying 9 Harness, 39 dollars. (units) from 2 (units); but sup pose we take 1 ten from the 6 Difference, 23 dollars. tens, the next upper figure, which would leave 5 (tens), and join or 62 dollars. 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.) Q. 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. Q. What is this taking 1 from 6, and adding it to 2, the upper figure, called ? A. Borrowing ten. PROOF. Q. 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 02, an amount like the Minuend—therefore right. From these illustrations we derive the following RULE. PROOF, you do? A. Units under units, tens under tens, &c. 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. 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 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? Ă. 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 2500 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 |