unit figure as usual; and for every ten, place a dot against that figure which makes ten or more than ten, and add the excess to the figure above it, and thus proceed to the top of the column. Write the excess of ten at the foot of the column added, then count the dots, and as many as they are, so many carry to the next left hand column. 3 4.9.5. 27687 3978 76 3.4 SUBTRACTION. 1. John's father gave him 6 apples. He gave his brother 4 of them. How many had he left? 2. Joseph bought sixpence worth of candies and ninepence worth of hazelnuts. How much more did he give for the hazelnuts than for the candies? 3. Henry was 10 years old when his mother died, his sister was 6. How much older was Henry than his sister? 4. Carolus Good Luck, as he was going to school, found a purse containing 10 dollars. As a reward for his honesty in faithfully delivering it to the owner, he received 3 dollars; how many were there left? 5. Peter's father gave him 10 cents. As he was going to school he found 25 more; but, for dishonesty in trying to conceal his prize from the rightful owner, his father took from him the 10 cents which he gave him. How much more did he find than he lost? 6. Timothy bought a slate for 18 cents, and a spelling book for 28 cents, how much more did he give for the book than for the slate? 7. Susan had 6 frocks; 4 of them she burnt; how many had she left? SIMPLE SUBTRACTION, Teaches to find the difference between two numbers of the same name or kind. (See note p. 19.) To perform the operation, two numbers are required, the larger is called the Minuend, the less the Subtrahend; the difference between them is called the Remainder. RULE. 1. Place the numbers, the less under the greater; units under units, tens under tens, hundreds under hundreds, &c. Begin at the right hand, or unit's place, and take each figure in the lower line from the one above it, and set down the remainder. If either of the lower figures be greater than the one above it, suppose ten to be added to the upper figure, subtract the lower figure from it, and set down the difference, observing to carry one to the next left hand figure. Proof.-Add the remainder and lower line together; if the work be right, the amount will correspond with the upper line. Beginning at the right hand, we say, 1 from 2 and 1 remains, which we set down; then, because 6, the next left hand figure, cannot be taken from 5, the figure above it, we suppose 10 to be added to 5, which is 15; then 6 from 15 and 9 remain, which we set down. We now carry 1 to 5, the next figure, because we borrowed 10, and say, 6 from 14, borrowing 10 again, and 8 remain. And, last ly, I to carry to 2 is 3-3 from 3 and nothing remains. QUESTIONS. 1. What does Simple Subtraction teach ? 2. Why is it called simple ? 3. To perform the operation, how many numbers are required? 4. Which is the minuend? 5. Which is the subtrahend? 6. What is the remainder? 7. What is the rule for simple subtraction? 8. How do you prove subtraction? From 39670 From 506789 From 67023491 Take 57216532 5. From four hundred and seventy-nine, take three hundred and seventy-five. 6. Take twenty-five thousand, nine hundred and twentythree, from forty-four thousand, five hundred and twenty. 7. What number must be subtracted from 2081 that the remainder may be 1104? Answer, 977. 8. From thirty-four thousand, take seventeen thousand and ninety-one. EXERCISES. 1. John's uncle gave him 20 cents. He lost 5 of them; how many had he left? 2. In a school of 48 scholars, 21 left; how many remained? Answer, 27. 3. A western hunter met with 45 buffaloes in one drove -killed all but 18; how many did he kill? Ans. 27. 4. Sir Isaac Newton was born in the year 1642, and died in 1727; how old was he when he died? Answer, 85 years. 5. The mariner's compass was invented about the year 1302; how long after that period was Sir Isaac Newton born? Answer, 340 years. 6. The first settlement in New-England was made at Plymouth, by the Puritans, in the year 1620; how long is Ans. 217 years. it since that time, to the year 1837? How 7. Gun-powder was invented in the year 1330. long was it after the invention of the mariner's compass? Ans. 28. 8. Virginia contains 64000 square miles; New-York contains 46000. What is the difference? Ans. 18000. 9. The library of Dartmouth College contains 12,800 volumes; Harvard University contains 34,600 volumes. How many does one contain more than the other? Answer, 21800. QUESTIONS. 9. In the first example how do you subtract 6 from 5? 10. How do you pay the 10 which you borrowed? 11. Why is the 1, which you carry, equal to the 10, which ydu borrowed? Answer. Because 1, in the left hand column, is equal to 10 in the right. C 10. Dartmouth College was incorporated in the year 1769, Harvard University in the year 1638. What is the difference in time? Answer, 131 years. 11. The population of the State of New-York, in 1820, was 1,372,812; in the year 1835 it was 1,616,482. How many years between these two periods, and how much was the increase? Answer, 15 years. Increase,243,670. 12. An officer with a company of 102 soldiers, was met by a party of Indians, who killed all his army but 17 men. How many were killed? Answer, 85. 13. A merchant bought 40 tons of wine, containing 10080 gallons, which cost him 2410 dollars. He sold 28 tons, containing 7056 gallons, for 1814 dollars. How many gallons had he left, and how much money did he want to make up the first cost? Ans. {3024 galls. 596 dolls. ADDITION. 1. If a harness is worth SUBTRACTION. 2. If a horse cost 86 dol 18 dollars, and the horse is lars, and the harness 18 dolworth 68 dolls. more than lars, how much more than the harness, what is the value the harness did the horse of the horse? cost? 3. If a merchant have 1734 yards of cloth, after selling 6588 yds., how many had he at first? 4. A merchant having 8322 yds. sells 6588 yds.; how many has he left? 6. What number must be 5. What is the amount of added to 8625 to make 2269+8625 ? 7. Dr. Franklin was born in 1706,-93 years before 10894 ? S. How many years before the death of Washington, in the death of Washington. In 1799, was the birth of Frankwhat year did Washington lin? die? 9. The mariner's compass was invented in 1302; Sir Isaac Newton was born 28 years after. In what year was he born? 11. If a piece of land be bought for 550 dolls., and is 10. Sir Isaac Newton was born in 1330; the mariner's compass was invented 28 years before.. In what year was it invented? 12. If a piece of land sell for 800 dolls., which is 250 sold for 250 more than it more than it cost, what was cost, for how much was it the first cost? sold? 13. Peter the Great died 14. Peter the Great died in 1725-112 years before in the year 1725. How mathe independence of Texas ny years from that period to was acknowledged by the the acknowledging of the United States. In what year independence of Texas, in was the independence ac- 1837? knowledged? 15. Supposing a man to be born in the year 1738; lived 98 years; in what year did he die? 16. Supposing a man to be 98 years old in the year 1836, in what year was he born? 17. Columbus first sailed for 18. The independence of America in the year 1492; America was declared in the the independence of Ameri-year 1776; 284 years before ca was declared 284 years Columbus first sailed for after. In what year was it America; in what year did declared? he sail? PRACTICAL QUESTIONS IN ADDITION AND SUBTRACTION. 1. Add 900, 400, and 752; subtract from their sum 647. Answer, 1405. 2. Charles had 18 peaches. He gave his mother 6 and his sister 4. How many had he left. Ans. 8. 3. A man buys at one store 84 eggs, at another 4 dozen, at another 3 dozen. As he returns, he sells 5 dozen. How many did he purchase, and how many had he left, when he arrived at home? Answer, 168-108. 4. James owes A 20 cents; B 30; C 40; D 50.John owes A 18 cents; B 23; C 35, D 47. do they both owe, and which owes the most? How much A merchant owes A 1300 dollars; B 1900 dollars; C 2500 dollars. He is worth 3500 dollars. How much does he owe, and how much more than he is worth? 6. A man borrowed of his friend at one time 100 dolls., at another 150 dolls., at another 175 dolls. He paid 275 |