45. A man bought a house for $15675; he paid $5096 for furniture, $3.40 for repairs, and $35 for insurance. How much did he pay in all for the house? 46. Lake Superior covers an area of 32290 square miles; Lake Erie, 9493; and Lake Ontario, 7654. What is the area covered by them all? SUBTRACTION. ORAL EXERCISES. 43. 1. A farmer, having 14 cows, sold 6 of them. How many had he left? SOLUTION. - Fourteen cows less 6 cows are 8 cows. He had 8 cows left. 2. Stephen, having 9 marbles, lost 4 of them. How had he left? many 3. If a man earns 10 dollars a week, and spends 6 dollars for provisions, how many dollars has he left? 4. A merchant, having 16 barrels of flour, sells 9 of them. How many barrels has he left? 5. Charles had 18 cents, and gave 10 of them for a book. How many cents had he left? 6. James is 17 years old, and his sister Julia is 5 years younger. How old is Julia? 7. A grocer, having 20 boxes of lemons, sold 11 boxes. How many boxes had he left? 8. From a cistern containing 25 barrels of water, 15 barrels leaked out. How many barrels remained? 9. I paid $16 for a coat, and $7 for a vest. How much more did the coat cost than the vest? 44. Subtraction is the process of taking away part of a number or of finding the difference between two numbers of the same kind. 45. The Minuend is the number from which another is to be subtracted. 46. The Subtrahend is the number to be subtracted. 47. The Remainder or Difference is the result obtained by the process of subtraction. The minuend and subtrahend must be like numbers; thus, 5 dollars taken from 9 dollars leaves 4 dollars; 5 apples taken from 9 apples leaves 4 apples; but it would be absurd to try to take 5 apples from 9 dollars, or 5 dollars from 9 apples. 48. The sign, -, is called minus, which signifies less. When placed between two numbers, it denotes that the number following it is to be taken from the one preceding it. Thus, 862 is read 8 minus 6 equals 2, or 8 less 6 is 2, and shows that 6, the subtrahend, taken from 8, the minuend, equals 2, the remainder. EXAMPLES. 49. When no figure in the subtrahend is greater than the corresponding figure in the minuend. 1. From 574 take 323. OPERATION. Minuend, 574 Subtrahend, 323 Remainder, 251 SOLUTION. We write the less number under the greater, with units under units, tens under tens, etc., and draw a line underneath. Then, beginning at the right hand, we subtract separately each figure of the subtrahend from the figure above it in the minuend. Thus, 3 taken from 4 leaves 1, which is the difference of the units; 2 taken from 7 leaves 5, the difference of the tens; 3 taken from 5 leaves 2, the difference of the hundreds. The whole difference is 2 hundreds 5 tens and 1 unit, or 251. 22203. 32343. 604400. 313241. 10. From 3276 take 2143. 11. From 7634 take 3132. 12. From 41763 take 11521. 13. From 18346 take 5215. 15. Subtract 47321 from 69524. 16. Subtract 16330 from 48673. 17. Subtract 291352 from 895752. 18. Subtract 84321 from 397562. 19. A farmer paid $645 for a span of horses and a carriage, and sold them for $522. What did he lose? 20. A man bought a mill for $3724, and sold it for $4856. What did he gain? Ans. $1132. 21. A drover bought 1566 sheep, and sold 435 of them. How many had he left? Ans. 1131 sheep. 22. A piece of land was sold for $2945, which was $832 more than it cost. What did it cost? 23. A man willed to his son $15768, and to his daughter $4537. How much more did he will to his son than to his daughter? Ans. $11231. 24. A merchant sold goods to the amount of $6742, and by so doing gained $2540. What did the goods cost him? 25. If I borrow $15475 of a person, and pay him $4050, what do I still owe him? 50. When any figure in the subtrahend is greater than the corresponding figure in the minuend. 1. From 846 take 359. OPERATION. Minuend, ∞ ∞ Hunds. c e Tens. Units. 846 Subtrahend, 359 Remainder, 487 SOLUTION. Since we cannot take 9 units from 6 units, we add 10 units to 6 units, making 16 units; 9 units taken from 16 units leaves 7 units. But as we have added 10 units, or 1 ten, to the minuend, we shall have a remainder 1 ten too large, to avoid which, we add 1 ten to the 5 tens in the subtrahend, making 6 tens. We cannot take 6 tens from 4 tens; so we add 10 tens to 4, making 14 tens; 6 tens taken from 14 tens leaves 8 tens. Now, having added 10 tens, or 1 hundred, to the minuend, we shall have a remainder 1 hundred too large, unless we add 1 hundred to the 3 hundreds in the subtrahend, making 4 hundreds; 4 hundreds taken from 8 hundreds leaves 4 hundreds, and we have for the total remainder, 487, the same as before. 51. The following method is preferred by some, as being simpler. OPERATION. (7) (13) (16) Minuend, 8 46 Subtrahend, 3 59 Remainder, 487 SOLUTION. In this example we cannot take 9 units from 6 units. From the 4 tens we take 1 ten, which equals 10 units, and add it to the 6 units, making 16 units; 9 units taken from 16 units leaves 7 units, which we write in the remainder in units' place. As we have taken 1 ten from the 4 tens, only 3 tens are left. We cannot take 5 tens from 3 tens; so from the 8 hundreds we take 1 hundred, which equals 10 tens, and add it to the 3 tens, making 13 tens; 5 tens from 13 tens leaves 8 tens, which we write in the remainder in tens' place. As we have taken 1 hundred from the 8 hundreds, only 7 hundreds are left; 3 hundreds taken from 7 hundreds leaves 4 hundreds, which we write in the remainder in hundreds' place, and we have the whole remainder, 487. The numbers written over the minuend are used simply to explain more clearly the method of subtracting; in practice the process should be performed mentally, and these numbers should be omitted. |