XII. SIMPLE SUBTRACTION. 1 A man owing 9 dollars paid 3 dollars. How many dol lars did he still owe? 5. If we take 6 miles from 27 miles, we have 21 miles left; because 21 and 6 are 27: thus,— 10. Observe that like Addition, units must be placed under units, tens under tens, hundreds under hundreds, &c. 11. From 6235 dollars take 2111 dollars? A. 4124 dollars. 12. From 89659 bushels take 7216 bushels? A. 82443 bushels. 13. A merchant having 13,069 bags of coffee sold 9,020 bags; how many bags had he remaining on hand? Minuend,' 1 3 0 69 Proof. 49 1 3069 Say 0 from 9 leaves 9; 2 from 6 leaves 4; 0 from 0 leaves 0· 9 from 13 leaves 4. A. 4049 bags. 14. In like manner perform and prove the following examples,— 18. Two brothers engaged in mercantile business; one gained 1,584 dollars and the other 920 dollars. more than the other? 19. A father gave 36,540 dollars to his daughter. How much greater was his daughter's? 20. Subtract 13 million from 27 million. How much did one gain XII. Q. How are units, tens, &c., to be placed in subtraction? 10. Why does 6 from 27 leave 21? 5. How do you subtract 0 from 9? 13. O from 0? 13. 9 from 13? 13. In subtracting 9,020 from 13,069 which number is the minuend? 13. Which is the subtrahend? 13. What is the answer called? 13 1 SUBTRACTION, [L. subtractio.] The taking a part from the rest 2 MINUEND, [L. minuendus.] To be diminished or lessened 3 SUBTRAHEND, from subtrahendus L. to be taken from. (1.) A 6 dollars. (2.) A. 23. (3.) 307 (4) A. 2,330 21. Subtract 85 thousand from 96 thousand A. 11,000. 22. What is the difference between one inillion eight hundred thousand, and six hundred thousand? A. 1,200,000. 23. A man bought a chaise for 262 dollars, and a harness for 39 How much did one cost more than the other? dollars. 262 A. 2 2 3 P. 2 6 2 We can't take 9 from 2, but we can take 1 ten, which is 10 units, from 6 tens. The 10 units (borrowed) added to the 2 units make 12. Then 9 from 12 leaves 3. Now instead of calling the 6 a 5, we may add the 1 ten, which we borrowed, to the 3 tens, the next lower figure, since it can make no difference in the result, for 4 from 6 is the same as 3 from 5. Therefore say, 1 to carry to 3 is 4, which from 6 leaves 2, &c. 24. Hence, when the lower figure is greater than the one above it, add 10 to the upper figure, and only 10 in any case, then take the. difference, being particularly careful to carry 1 to the next lower figure. (27.) 30. If we take 4,508 from 67,297, how many will remain ? 33. A gentleman purchased a farm for 4,000 dollars, and paid 5 991 earnest money. dollars as 66 5 A. 3 9 9 5 How much did he still owe? Say 5 from 10 leaves 5; 1 to carry from 10 leaves 9; 1 to carry again from 10 leaves 9; 1 to carry from 4 leaves 3. 34. Since in the last example, there are no tens nor hundreds in the upper line, we do in reality borrow the 10 from the 4 thousands 35. For if we call the 4 thousands 10 less, making 3990, and subtract the 5 without carrying any, the result will be the same as before. 36. Hence the 10 is always borrowed from the first significant figure on the left in the upper line. 37. From 10,000 cents take 1 cent. 38. From 10,000 mills take 9,999 mills. A. 9,999 cents. Q. In taking 39 from 262, how do you subtract the 9 from 2? 23. Do you borrow the 10 units from the upper figure 6, or the lower figure 3? 23. To which figure do you pay it again, or carry it? 23. How happens it that you borrow from one and pay to another? 23. How then do you proceed in all such cases! 24. In subtracting 5 from 400, for instance, from what is the 10 borrowed, and why? 34. From which figure is the 10 always borrowed? 36. J EARNEST. Seriousness; a reality; first fruits; money given to bind a bargain. A. 10002. A. 765,433 39 How much does 110,001 exceed 99,999 ? 40. How much does 1,234,567 lack of 2 million? 41. How much greater is 1 million than 1,000 ? 42. How much smaller is 5,000 than 500,000? 43. Find how much must be added to fifteen thousand and five o make twenty-three thousand. A. 7,995. A. 495,000. 44. The deluge happened A. M.1 1656, and our Saviour was born A. M. 4,004. How many years intervened between these two events? A. 2348 years. 45. How many years from the birth of our Saviour, to the discovery of America by Columbus, which occurred A. M. 5,496 ? A. A. D. 1492. 46. Find by the following list, the length of time each President of the United States held that office. 47. George Washington, from 1789 to 1797. RECAPITULATION. A. 8 years. A. 8 years A. 8 years A. 8 years. A. 4 years. A. 8 years. A. 4 years. A. 4 years. 56. SUBTRACTION is the taking of a less number from a greater. 57. SUBTRACTION then is exactly the reverse of Addition. 58. The MINUEND is the greater number, and the one from which the subtraction is to be made. 59. The SUBTRAHEND is the smaller number, and the one which is to be subtracted. 60. The REMAINDER is the difference between any two numbers. 61. SIMPLE SUBTRACTION is the subtracting of one number from another, when both are of the same denomination. RULE. 62. Place the less number under the greater, so that units may stand under units, tens under tens, &c. 63. Begin on the right and take each figure separately, from the figure over it. 64. If the upper figure be too small, add 10 to it, then subtract, and carry 1 to the next lower figure. Q. What is Subtraction? 56. Does it resemble Addition? 57. What is the Minuend? 58. Subtrahend? 59. Remainder? 60. Simple Subtraction? 61 Rule? 62, 63, 64. Order? 65. Proof? 66. Reason of the rule? 67. 1 A. M. The A. stands for Anno, L., meaning, in the year, and the M. for Mundi, of the world; hence A. M. 1656, means so many years since the creation of the world. 2 A. D. in the year of our Lord, See xi. 45. 65. ORDER. WRITE DOWN: SUBTRACT: AND CARRY. 66. PROOF. Add together the remainder, and subtrahend, and if their sum equal the minuend, the work is right. 67. The rule and proof proceed both on the same general principle, viz.; "That the sum of the parts is equal to the whole." (68.) (69.) (70.) 65001039 2 7 3 4 20 A. 999,001. A. 999,991. 71. From one million take 999. 72. From one million take nine. 73. What number added to four hundred and fifty-nine thousano 77. Suppose a man is worth 100,000 dollars lacking 1000 dollars How much is he worth? A. 99,000. A. 9,191,000 78. Subtract 376,000 from 9,567,000. 79. A father divided his estate, amounting to 75,000 dollars, between his son and daughter, giving to the former 37,560 dollars. How many dollars did he give to the daughter? A. 37,440 dollars. 80. A merchant bought goods worth 125,000 dollars, on four months credit, but is offered a discount' of 825 dollars for cash down. What would be the cost of the goods for cash? A. 124,175 dollars. 81. Suppose you buy goods worth 35,765 dollars on six months credit, and are offered the same goods for 35,565 dollars ready money. What is the discount offered you? A. 200 dollars. (3.) From Ten million, Take Forty-five. A. 9,999,95 5. (4.) From One billion and fifty, A. 999,00 0,049. 5. A farmer having 500 dollars, paid away 200 dollars for a chaise and 100 dollars for a harness. How many dollars had he left? A. 200 dollars. 6. A gentleman has an annual income of 4,000 dollars; his family expenses are 1,500 dollars, and he contributes 500 dollars to charitable objects. How much can he lay up at the year's end? A. 2,000 dollars. 7. A merchant owing 2,345 dollars, paid 1,400 dollars at one time and 549 dollars at another. How much more will it require to pay the debt? A. 396 dollars. 8. A father divided his property, which amounted to 35,000 dollars, among his three children. He gave to the oldest 13,456 dollars; to What was the other child's part? A. 11,544 dollars. the youngest 10,000 dollars. 9. A man bought a house, a horse and a chaise for 3,700 dollars. He paid 115 dollars for the horse and 210 dollars for the chaise. What did the house cost him? A. 3,375. 10. Suppose the distance from Boston to New York be 210 miles; thence to Philadelphia 90 miles, and thence to Baltimore 100 miles, how many miles are Philadelphia and Baltimore from Boston? A. Pa. 300 miles; Be. 400 miles. 11. The population of the United States in 1820, was 9,638,166; in 1830 it was 12,858,670; and in 1840, was, according to the Census returns of that year, 17,063,353. At these estimates what was the increase of population from the first period of time to the second; from the second period to the third; and from the first period to the third? A. 3,220,504; 4,204,683; 7,425,187. SIMPLE MULTIPLICATION. XIV. 1. Suppose a man earns 9 dollars a week, for 5 successive 9 dollars. weeks; how many dollars will he earn in all? XIV. Q. By what two methods can you find how many 5 times 9 are? 1. Which is the shortest method? 1. Multiplying 9 by 5 making 45; what are the numbers severally called? 1. 1 MULTIPLICATION, [L. Multiplicatio.] The act of multiplying or of increasing any number a given number of times. |