OPERATION. First bag, 876 Second bag, 653 524 2053 Writing down the numbers as already directed, we begin with the right hand, or unit column, and find the amount to be 13, that is, 3 units and 1 ten. Setting down the 3 units, or right hand figure, in unit's place, directly under the column, we reserve the 1 ten, or left hand figure, to be added with the other tens, in the next column, saying, 1, which we reserved, to 2 makes 3, and 5 are 8, and 7 are 15, which is 5 units of its own order, and 1 unit of the next higher order, that is, 5 tens and 1 hundred. Setting down the 5 tens, or right hand figure, directly under the column of tens, we reserve the left hand figure, or 1 hundred, to be added in the column of hundreds, saying, 1 to 5 is 6, and 6 are 12, and 8 are 20, which being the last column, we set down the whole number, writing the 0, or right hand figure, directly under the column, and carrying forward the 2, or left hand figure, to the next place, or place of thousands. Wherefore, we find the whole amount of money contained in the three bags to be 2053 dollars, the answer. PROOF. We may reverse the order, and, beginning at the top, add the figures downward. If the two results are alike, the work is supposed to be right. From the examples and illustrations now given, we derive the following RULE. I. Write the numbers to be added, one under another, placing units under units, tens under tens, &c., and draw a line underneath. II. Begin at the right hand or unit column, and add to gether all the figures contained in that column: if the amount does not exceed 9, write it under the column; but if the amount exceed 9, so that it shall require two or more figures to express it, write down the unit figure only under the column; the figure or figures to the left hand of units, being tens, are so many units of the next higher order, which, being reserved, must be carried forward, and added to the first figure in the next column. III. Add each succeeding column in the same manner, and set down the whole amount at the last column. EXAMPLES FOR PRACTICE. 19. A man bought four loads of hay; one load weighed 1817 pounds, another weighed 1950 pounds, another 2156 pounds, and another 2210 pounds; what was the amount of hay purchased? 20. A person owes A 100 dollars, B 2160 dollars, C 785 dollars, D 92 dollars; what is the amount of his debts? 21. A farmer raised in one year 1200 bushels of wheat, 850 bushels of Indian corn, 1000 bushels of oats, 1086 bushels of barley, and 74 bushels of pease; what was the whole amount? Ans. 4210. 22. St. Paul's Cathedral, in London, cost 800,000 pounds sterling; the Royal Exchange 80,000 pounds; the MansionHouse 40,000 pounds; Black Friars Bridge 152,840 pounds; Westminster Bridge 389,000 pounds, and the Monument 13,000 pounds; what is the amount of these sums? Ans. 1,474,840 pounds. 23. At the census in 1820, the number of inhabitants in the New England States was as follows:-Maine, 298,335; New Hampshire, 244,161; Vermont, 235,764; Massachusetts, 253,287; Rhode Island, 83,059; Connecticut, 275,248; what was the whole number of inhabitants, at that time, in hose States? Ans. 1,389,854. 24. From the creation to the departure of the Israelites from Egypt was 2513 years; to the siege of Troy, 307 years more; to the building of Solomon's Temple, 180 years; to the building of Rome, 251 years; to the expulsion of the kings from Rome, 244 years; to the destruction of Carthage, 363 years; to the death of Julius Cæsar, 102 years; to the Christian era, 44 years; required the time from the Creation to the Christian era. Ans. 4004 years. 25. 28 6 3 7 0 5 4 2 1 0 6 1 3 1 0 7 4 2 9 3 1 5 6 3 8 6 2 5 3 0 3 4 7.9 2 247135 8673 26. 4 3 6 7 5 8 3 0 2 1 4 6 3 1 7 5 2 3 4 9 7 1 3 6 20 6 08127 5 3 0 6 217 5 6 5 2 17 4 6 3 0 1 28 8 7 0 3 26 3 4 7 2 0 1 3 B* 27. 5 3 6 4 2 0 7 6 3 1 0 2 3 28 1 2 3 4 5 6 7 29 48 6057042087094 3 1 6 2 8 3 590 6718 760428 6 5 3 7 8 9 2 28. 902375 4 6 8 2 1 35 28349 6 7 326 708 9 306 34 2 1 6 7 3 2 1 2 3 6 5 4 780 24369 80 50 60 70 3 900 29. What is the amount of 46723, 6742, and 986 dollars? 30. A man has three orchards; in the first there are 140 trees that bear apples, and 64 trees that bear peaches; in the second, 234 trees bear apples, and 73 bear cherries; in the third, 47 trees bear plums, 36 bear pears, and 25 bear cherries; how many trees in all the orchards? SUPPLEMENT TO NUMERATION AND ADDITION. QUESTIONS. 1. What is a single or individual thing called? 2. Wha? is notation? 3. What are the methods of notation now in use? 4. How many are the Arabic characters or figures? 5. What is numeration? 6. What is a fundamental law in notation? 7. What is addition? 8. What is the rule for addition ? 9. What is the result, or number sought, called? 10. What is the sign of addition? 11. equality? 12. How is addition proved? EXERCISES. of 1. Washington was born in the year of our Lord 1732; he was 67 years old when he died; in what year of our Lord did he die? 2. The invasion of Greece by Xerxes took place 481 years before Christ; how long ago is that this current year 1827? 3. There are two numbers, the less number is 8671, the difference between the numbers is 597; what is the greater number? 4. A man borrowed a sum of money, and paid in part 684 dollars; the sum left unpaid was 876 dollars; what was the sum borrowed? 5. There are four numbers, the first 317, the second 812, the third 1350, and the fourth as much as the other three; what is the sum of them all? 6. A gentleman left his daughter 16 thousand, 16 hundred and 16 dollars; he left his son 1800 more than his daughter; what was his son's portion, and what was the amount of the whole estate ? Son's portion, 19,416. Whole estate, 37,032. Ans. 7. A man, at his death, left his estate to his four children, who, after paying debts to the amount of 1476 dollars, received 4768 dollars each; how much was the whole estate? Ans. 20548, 8. A man bought four hogs, each weighing 375 pounds, how much did they all weigh? Ans. 1500. 9. The fore quarters of an ox weigh one hundred and eight pounds each, the hind quarters weigh one hundre and twenty-four pounds each, the hide seventy-six pounds. and the tallow sixty pounds; what is the whole weight o. the ox? Ans. 600 10. A man, being asked his age, said he was thirty-four years old when his eldest son was born, who was then fifteen years of age; what was the age of the father? 11. A man sold two cows for sixteen dollars each, twen ty bushels of corn for twelve dollars, and one hundred pounds of tallow for eight dollars; what was his due ? SUBTRACTION OF SIMPLE NUMBERS. 6. 1. Charles, having 18 cents, bought a book, for which he gave 6 cents; how many cents had he left? 2. John had 12 apples; he gave 5 of them to his brother; how many had he left? 3. Peter played at marbles; he had 23 when he began, but when he had done he had only 12; how many did he lose? 4. A man bought a cow for 17 dollars, and sold her again for 22 dollars; how many dollars did he gain? 5. Charles is 9 years old, and Andrew is 13; what is the difference in their ages? 6. A man borrowed 50 dollars, and paid all but 18; how many dollars did he pay? that is, take 18 from 50, and how many would there be left? 7. John bought a book and slate for 33 cents; he gave 8 cents for the book; what did the slate cost him? 8. Peter bought a waggon for 36 cents, and sold it for 45 cents; how many cents did he gain by the bargain? 9. Peter sold a waggon for 45 cents, which was 9 cents more than he gave for it; how many cents did he give for the waggon? 10. A boy, being asked how old he was, said that he was 25 years younger than his father, whose age was 33 years; how old was the boy? The taking of a less number from a greater (as in the foregoing examples) is called Subtraction. The greater number is called the minuend, the less number the subtrahend, and what is left after subtraction is called the differ ence, or remainder. 11. If the minuend be 8, and the subtrahend 3, what is the difference or remainder? Ans. 5. 12. If the subtrahend be 4, and the minuend 16, what is the remainder? 13. Samuel bought a book for 20 cents; he paid down 12 cents; how many cents more must he pay? SIGN. A short horizontal line, --, is the sign of subtraction. It is usually read minus, which is a Latin word signifying less. It shows that the number after it is to be taken from the number before it. Thus, 8. -3: 5, is read 8 minus or less 3 is equal to 5; or, 3 from 8 leaves 5. latter expression is to be used by the pupil in committing the following The |