6+8=14 7+8=15 8+5=16 9+8=17 6+9=15 7+9=16 8+9=17 9918 T 5. When the numbers to be added are small, the addition is readily performed in the mind; but it will frequently be more convenient, and even necessary, to write the numbers down before adding them. 13. Harry had 43 cents, his father gave him 25 cents more; how many cents had he then ? One of these numbers contains 4 tens and 3 units. The other number contains 2 tens and 5 units. To unite these two numbers together into one, write them down one under the other, placing the units of one number directly under units of the other, and the tens of one number directly under tens of the other, thus: 43 cents. Having written the numbers in this man25 cents. ner, draw a line underneath. 43 cents. 8 43 cents. 25 cents. Ans. 68 cents. We then begin at the right hand, and add the 5 units of the lower number to the 3 units of the upper number, making 8 units, which we set down in unit's place. We then proceed to the next column, and add the 2 tens of the lower number to the 4 tens of the upper number, making 6 tens, or 60, which we set down in ten's place, and the work is done. It now appears that Harry's whole number of cents is € tens and 8 units, or 68 cents; that is, 43 +25= 68. 14. A farmer bought a chaise for 210 dollars, a horse for 70 dollars, and a saddle for 3 dollars; what was the whole amount? Write the numbers as before directed, with units under units, tens under tens, &c. OPERATION. Chaise, 210 dollars, Saddle, 9 dollars. Answer, 289 dollars. Add as before. The units will be 9, the tens 8, and the hundreds 2; that is, 210+70+9289. After the same manner are performed the following examples: 15. A man had 15 sheep in one pasture, 20 in another pasture, and 143 in another; how many sheep had he in the three pastures? 15+20+143 how many? 16. A man has three farms, one containing 500 acres, another 213 acres, and another 76 acres; how many acres in the three farms? 500+213 +76 how many? 17. Bought a farm for 2316 dollars, and afterwards sold it so as to gain 550 dollars; what did I sell the farm for? 2316+550 how many? Hitherto the amount of any one column, when added up, has not exceeded 9; consequently has been expressed by a single figure. But it will frequently happen that the amount of a single column will exceed 9, requiring two or more figures to express it. 18. There are three bags of money. The first contains 876 dollars, the second, 653 dollars, the third, 524 dollars, what is the amount contained in all the bags ? 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 Sgure, directly under the clumn 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 band or unit column, and add together 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 those 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. 286370542106 1 3107429 3 1 5 6 3 8 6 25 3034792 247135 8673 26. 4367583 0 2 1 463 175 2 3 4 9 7 13 620 608127 5 3 0 6 217 5 6 5 2 17 4 6 3 0 1 28 870 3 26 3 4 7 2013 B* 27. 5 3 6 4 20 7 6 3 1 0 2 3 28 1 2 3 4 5 6 7 29 48 605 7042087094 31 6 2 8 3 5 9 0 6 7 18 76 0 4 28 6 5 3 7 6 9 2 28. 902375 4 6 8 2135 283496 7 3 2 6 7 08 9 3 0 6 3 4 2 1 6 7 321 2 3 6 5 4 7 8 0 2 4 3 69 3050607 80900 29. What is the amount of 46723, 6742, and 986 dollars? 30. A man has three orchards; in the first there are 140 ees that bear apples, and 64 trees that bear peaches; in the second, 234 trees bear apples, and 73 bear cherries; in the ward, 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. What 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 697; what is the greater number. |