SUBTRACTION. 40. 1. John has 8 marbles, and his brother 5. How many more marbles has John than his brother? 2. Thomas had 9 apples, and gave 4 of them to Peter How many had he left? 3. How much more are 11 cents than 6 cents? 4. How many dollars are $ 13 less $7 ? 5. Ella is 14 years old, and Mary is 9 years old. How many years older is Ella than Mary? 6. Sold a knife for 15 cents and a ball for 7 cents. How much more did I get for the knife than for the ball? 41. Subtraction is taking one of two like numbers from the other. 42. The Difference is the result of a subtraction. 43. The Minuend is the number subtracted from. 44. The Subtrahend is the number subtracted. 45. The Sign of Subtraction is named minus. It means less. Thus, 1596 is read fifteen less nine are six. ORAL EXERCISES. 7. A boy raised 13 melons and sold 6. How many had he left? 8. Arthur had 11 cents and gave away 7. How many had he left? 9. In a nest there were 14 eggs, but 5 have been taken away. How many remain in the nest ? 10. In a pool were 13 lilies, and 8 have been carried away. How many remain? 11. If of 16 peaches 8 should be eaten, how many would be left? 30. Subtract by 2's from 40 back to 20, naming only re sults. 1. Only like numbers and units of the same order can be subtracted one from the other. 2. The difference and subtrahend together must equal the minuend. WRITTEN EXERCISES. 44. Find the difference between 865 and 242. Minuend 865 Solution. For convenience, we write the subtrahend under the minuend, so that units of the same order may be in the same column. 2 ones from 5 ones leave 3 ones, which we write beneath in ones' place; 4 tens from 6 tens leave 2 tens, which we write beneath in tens' place; and 2 hundreds from 8 hundreds leave 6 hundreds, which we write beneath in hundreds' place. The difference is 6 hundreds 2 tens 3 ones, or 623. To test or prove the work, we add together the difference and subtrahend, and the sum equals the minuend (Art. 46). 53. A farmer raised 1896 bushels of wheat, and sold 675. How many bushels had he left? 54. A man bought a house for $2550, and sold it for $2875. How much did he gain? ORAL EXERCISES. 55. Henry gave 13 cents to John and 9 to James. How many more cents did John receive than James? 56. William is 17 years old and Albert is 9. What is the difference in their ages? 57. A boy had 25 cents, and spent 9. How many cents had he left? 58. Ellen had 23 roses, and gave her teacher 4 and her playmates 6. How many had she left? 59. Gave $25 for an overcoat, and $8 for a vest. How much more did the one cost than the other? 60. John had 33 peaches and gave 9 away. had he left? How many are: How many 70. How many are 52 37? 63 49? 84-29 ? 71. Sold a horse which cost me $100 for $ 80. did I lose? How much 72. I have a book of 56 pages, and have read 39 of the How many pages remain to be read? pages. 73. John travels 35 miles a day and Edwin 60 miles. How many more miles does the one travel than the other? 74. A boy had 51 cents and spent 38. How many cents had he left? WRITTEN EXERCISES. 75. What is the difference between 1624 and 342? Minuend 1624 Subtrahend 342 Difference 1282 1624 Solution.-2 ones from 4 ones leave 2 ones, which we write beneath in the place of ones. 4 tens cannot be taken from 2 tens; we therefore take 1 hundred, or 10 tens, from the 6 hundreds of the minuend, leaving 5 hundreds, and adding the 10 tens to the 2 tens we have 12 tens; 4 tens from 12 tens leave 8 tens, which we write beneath in the place of tens. 3 hundreds from 5 hundreds leave 2 hundreds, which we write in hundreds' place; no thousands from 1 thousand leaves 1 thousand, which we write in thousands' place. The difference is 1282. This we prove by adding the difference and subtrahend, and finding the sum to be equal to the minuend. 76. Find the difference between 167 and 476. Minuend Difference 46.65 Solution. We make the decimal places the same in the two numbers by filling the place of hundredths in the minuend by 0. 5 hundredths cannot be taken from 0 hundredths; we therefore take 1 tenth, or 10 hundredths, from the 8 tenths, leaving 7 tenths; 5 hundredths from the 10 hundredths leave 5 hundredths, which we write beneath in hundredths' place. 1 tenth from 7 tenths leaves 6 tenths, which we write beneath in tenths' place; and subtracting the ones and tens, and writing the result beneath, we have 46.65 as the result required. 80. Subtract 167.807 from 970.96. 81. Take $158.55 from $549.60. 82. How much more than $91.97 is $147.11 ? 83. How much and $ 6711.45 make $7050.25 ? 47. Rule for Subtraction, Write the subtrahend under the minuend, placing units of the same order in the same column. Begin with the units of the lowest order to subtract, and proceed to the highest, writing the result beneath. If any order of the minuend has less units than the same order of the subtrahend, increase its units by ten, and subtract; consider the units of the next minuend order one less, and proceed as before. 48. PROOF. Add the subtrahend and the difference together; the sum should equal the minuend (Art. 46). (3)(9)(9)(10) 34000 21345 12655 Solution. There being 0 ones, O tens, hundreds in the minuend, we take 1 of the 4 thousands (leaving 3 thousands), or 10 hundreds; then taking 1 of the 10 hundreds (leaving 9 hundreds), or 10 tens; and 1 of the 10 tens (leaving 9 tens), or 10 ones; the minuend |