11. 12 boys were playing together, and 3 went home. How many were left? 3 from 12 leave how many? 12. A man bought several sheep for 19 dollars. He sold them for 14 dollars. How many dollars did he lose? 14 from 19 leave how many? 13. A boy had 16 marbles, and gave away 11. How many had he left? 11 from 16 leave how many? 14. In a school, consisting of 20 boys, 13 learn different studies, and the rest learn grammar. How many learn grammar? 13 from 20 leave how many? 15. A man bought some goods worth 18 dollars, and to pay for them, gave a barrel of flour worth 8 dollars, and the rest in money. How much money did he give? 8 from 18 leave how many ? 16. A farmer had 21 sheep, and a dog killed 5. many had he left? 5 from 21 leave how many? How 17. In an orchard, consisting of 27 trees, 12 bear apples, and the rest bear pears. How many bear pears ? 12 from 27 leave how many? 18. George had 26 cents, and spent 11. How many had he left? 11 from 26 leave how many? 19. Samuel had 12 books, and lost 3. How many had he left? 3 from 12 leave how many? 5 from 12 leave how many? 6 from 12? 8 from 12? 11 from 12? 2 from 12 7 from 12? 10 from 12? 20. 4 from 15 leave how many? 10 from 15? 9 from 15? 8 from 15? 3 from 15? 12 from 15? 2 from 15? 13 from 15? 14 from 15? 7 from 15? 5 from 15? 6 from 15? 11 from 15? 21. 6 from 17 leave how many? 5 from 17? 7 from 17? 4 from 17? 8 from 17? 9 from 17? 3 from 17? 2 from 17 11 from 17? 10 from 17? 12 from 17? 22. 16 men were in a boat. The boat upset and 12 were drowned. How many were left? 12 from 16 leave how many? 5 from 16? 4 from 16? 3 from 16? 7 from 16? 8 from 16? 13 from 16? 15 from 16? 9 from 16? 10 from 16? 6 from 16? 23. 5 from 13 leave how many? 4 from 13? 10 from 13? 7 from 13? 9 from 13? 12 from 13? 8 from 13? 6 from 13? 11 from 13? 24. 8 from 14 leave how many? 6 from 14? 4 from 14? 10 from 14? 7 from 14? 2 from 14? 12 from 14? 11 from 14? 3 from 14? 5 from 14? 9 from 14? 25. 6 from 18 leave how many? 7 from 18? 8 from 18? 10 from 18? 9 from 18? 5 from 18? 4 from 18? 3. from 18? 2 from 18? 11 from 18? 12 from 18? 13 from 18? 14 from 18? 15 from 18? 16 from 18? 26. 7 from 19 leave how many? 8 from 19? 6 from 19? 5 from 19? 4 from 19? 3 from 19? 2 from 19? 9 from 19? 10 from 19? 11 from 19? 12 from 19? 13 from 19? 14 from 19? 15 from 19? 27. Repeat the SUBTRACTION TABLE. 1 from 1 leaves 04 from 4 leaves 0 7 from 7 leaves 0 28. 2 from 9 are how many? 2 from 19? 2 from 29? 2 from 39? 2 from 49? 2 from 59? 2 from 69 ? 2 from 79? 2 from 89? 2 from 99? 2 from 109 ? [Let the teacher here take 3 from 9, 3 from 19, and so on, until he has gone through all the combinations, that can be made in this way, in the same manner as directed in Addition, $VII.] 29. 4 from 7 leave how many? 4 from 17? 4 from 27? 4 from 37? 4 from 57? 4 from 87? 4 from 47? 4 from 67? 4 from 77? 4 from 97? 4 from 107? 30. 8 from 16 leave how many? 8 from 26? 8 from 36 8 from 46? 8 from 56? 8 from 66? 8 from 76? 8 from 86? 8 from 96? 8 from 106? 31.7 from 15 leave how many? 7 from 25? 7 from 35? 7 from 45? 7 from 55? 7 from 65? 7 from 85? 7 from 95? 7 from 105? 32. 9 from 9 leave how many? 9 from 19? 9 from 29? 9 from 39? 9 from 49? 9 from 59? 9 from 69? 9 from 79? 9 from 89? 9 from 109 ? 33. 6 from 15 leave how many? 6 from 25? 6 from 45 ? 6 from 35? 6 from 55? 6, from 65? 6 from 75? 6 from 85? 6 from 95 ? 6 from 105? 34. 5 from 7 leave how many? 5 from 6? 5 from 9? 5 from 8? 5 from 11? 5 from 10? 5 from 12? § XXI. 1. Write the following numbers on your slate, take away, or subtract the lower one from the upper, and set down the difference in figures. 7 8 6 5 8 9 4 5 7 98 5 3 5 2 3 4 7 3 2 5 6 6 4 2. Take an example of some higher orders. 90 80 60 40 70 50 30 90 200 500 600 30 70 20 30 50 20 10 60 100 200 300 800 3000 8000 90000 400000 7000000 90000000 3. Take an example where several significant figures are used. 20800 38009 570308 60805 47023 580321469 10400 17006 Hence, it is evident, that, in finding the differences of numbers, units of the same orders must be taken from each other, and their differences put in the places of the orders employed. [The pupil should be taught to explain operations in Subtraction by repeating the process aloud as in Addition.] 16. Here are some further examples. 93570224 76583424 56249879 45987688 5795786314 The pupil will observe, that it matters not on which side he begins to perform the above examples. He will find it best, however, to accustom himself to commence on the right, as this will be necessary in most of the examples, which follow. Neither is it of any consequence how the given numbers are set down, nor which is written uppermost, if units are always taken from units, tens from tens, &c. But the mode whieh we have used above, is altogether the most convenient; viz., to place the larger number above the other, in such a manner that the same orders may stand under each other; that is, units under units, tens under tens, &c. We must caution the pupil against subtracting units of different orders from one another, since 6 tens from 9 hundreds are neither 3 tens nor 3 hundreds. But 6 tens from 9 tens are 3 tens, and 6 hundreds from 9 hundreds are 3 hundreds. 19. A man, having 26 acres of land, sold 9. How many had he left? 9 units cannot be taken from 6 units. 26 9 17 Ans. But 9 units can be taken from 26 units, and the remainder is 17. 20. A merchant had 53 yards of cloth, and sold 16 yards; how many had he left? 53 16 - 37 Ans. 6 units cannot be taken from 3 units. But 6 239 38 29 1542 2187 58632 32984 53890 3124 1213 1234 13472 15763 41763 1216 We might perform all examples in Subtraction in this manner : but an easier method is the following. 22. In a cistern there were 73 gallons of water, and 25 were used How many were left? out. Instead of proceeding as before, I first separate the 73, which is 7 tens and 3 units, into 6 tens, and 1 ten and 3 units; or 6 tens and 13 units, thus, I then separate the 25 into 2 tens, and 5 units, thus, Then 5 units from 13 units, leave 8 units; 60 13 73 20 = 25 40+ 8 48 and 2 tens from 6 tens, leave 4 tens. The answer therefore is 4 tens and 8 units, or 48. This process is nothing more than taking one of the tens, and writing it with the units, for the sake of convenience. This is called BORROWING, and is the reverse of carrying in Addition. 23. The United States declared themselves independent on the 4th of July, 1776. How many years from that time, to the 4th of July, 1829? Here, the tens in the less number are more than those of the greater. We must, therefore, borrow one of the hundreds. Separating then as before, we have 1000+700+120+9=1829 And, 1000+700 70+6=1776 Therefore, the answer is 0+0+ 50+3= 53 years. Now, this process may be performed in the mind, without any actual separation of the parts. For, we see, that the figure from which we borrow, becomes one less, and, the number to which we unite what we borrowed, becomes 10 greater, because it is of a lower order. 24. A man raised 763 bushels of wheat, one year, and 851, the next. How much more did he raise the second year than the first? Here, we increase the 1 unit by 10, making it 11 units, from which we subtract the 3 units, leaving 8. We then diminish the 5 851 763 88 Ans. tens by 1 ten, leaving 4 tens. But we cannot take 6 tens from this. Therefore, we borrow again in like manner. In the same manner, perform the following. 25. From a garrison containing 9,563 men, there were sent away 2,764. How many were left? 1ns 6,769 26. In 1,800 there were 903 post-offices in the United States, and in 1,828 there were 7,530. How much had their number increas ed. Ans. 6,627 27. During the whole American revolution, the continental troops employed were 231,971, and the militia 56,163. How many more continental troops, than militia? Ans. 175,808 You have now been learning to perform SUBTRACTION. Then, SUBTRACTION IS FINDING THE DIFFERENCE BETWEEN TWO NUMBERS. Of course, it is exactly the reverse of Addition. THE DIFFERENCE FOUND IS CALLED THE REMAINDER, THE NUMBER, SUBTRACTED, IS CALLED THE SUBTRAHEND, THE NUMBER, FROM WHICH THE SUBTRACTION IS MADE, IS CALLED THE MINUEND. |