§ 11. John has three apples and Charles has two; how many apples have they between them. Every boy will answer, five. Here a single apple is the unit, and the number five contains as many units as the two numbers three and two. The operation by which this result is obtained is called addition. Hence, ADDITION is the uniting together of several numbers, in such a way, that all the units which they contain may be expressed by a single number. Such single number is called the sum or sum total of the other numbers. Thus, 5 is the sum of the apples possessed by John and Charles. What is the sum of 2 and 4? of 3 and 5? of 6 and 3? of 4, 3 and 1? of 2, 3 and 4? of 1, 2, 3 and 4? of 5 and 7? How many units in 4 and 6? How many units in 9 and 4? Q. What is addition? What is the single number called which expresses all the units of the numbers added? What is the sum of 2 and 4? What is six called? OF THE SIGNS. § 12. The sign +, is called plus, which signifies more. When placed between two numbers it denotes that they are to be added together. Thus, 3+2 denotes that 3 and 2 are to be added together.. The sign, is called the sign of equality. When placed between two numbers it denotes that they are equal to each other. Thus, 3+2-5. When the numbers are small we generally read them, by saying, 3 and 2 are 5. Q. What is the sign of addition? What is it called? What does it signify? When placed between two numbers what does it express? Express the sign of equality. When placed between two numbers what does it show? Give an example. § 13. Before adding large numbers the pupil should be able to add, in his mind, any two of the ten figures. Let him commit to memory the following table, which is read, two and 0 are two; two and one are three; two and two are four, &c. EXAMPLES. 1. What is the sum of the numbers 375, 6321 and 598. In this example, the small figure placed under the 4, shows how many are to be carried from the first column to the second, and the small figure under the 9, how many are to be carried from the second column to the third. OPERATION. 375 6321 598 7294 11 In like manner, in the examples below, the small figure under each column, shows how many are to be carried to the next column at the left. Beginners had better set down the numbers to be carried as in the examples. § 15. Begin at the right hand figure of the upper line, and add all the columns downwards, carrying from one column to the other, as before. If the two results agree the work is supposed right. SECOND PROOF. Draw a line under the upper number. Add the lower numbers together, and then add their sum to the upper If the last sum is the same as the sum total, first found, the work may be regarded as right. number. Q. What do the small figures under the columns denote? How do you prove addition by the first method? How do you prove addition by the second method? 7. Add 8635, 2194, 7421, 5063, 2196, and 1245 together. Ans. 8. Add 246034, 298765, 47321, 58653, 64218, 5376, 9821, and 340 together. Ans. 730528. 9. Add 27104, 32547, 10758, 6256, 704321, 730491, 2787316, and 2749104 together. Ans. 10. Add 1, 37, 29504, 6790312, 18757421, and 265 together. Ans. 25577540. 11. Add 562163, 21964, 56321, 18536, 4340, 279, and 83 together. Ans. 12. What is the sum of the following numbers: viz., Seventy-five; one thousand and ninety-five; six thousand four hundred and thirty-five; two hundred and sixty-seven thousand; one thousand four hundred and fifty-five; twenty seven millions and eighteen; two hundred and seventy millions and twenty-seven thousand. Ans. 297303078. APPLICATIONS. 1. How many days are there in the twelve calendar months? January has 31, February 28, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, and December 31. Ans. 365 days. 2. A merchant on settling his accounts finds that he owes A 60 dollars, B 150 dollars, C 240 dollars, and to D 100 dollars. How much does he owe in all? Ans. 3. What is the total weight of seven casks of merchandise: viz. No. 1, weighing 960 pounds, No. 2, 725 pounds, No. 3, 830 pounds, No. 4, 798 pounds, No. 5, 698 pounds, No. 6, 569 pounds No. 7, 987 pounds? Ans. 5567 pounds. 4. A man borrowed a sum of money and paid in part 267 dollars, and afterwards paid the remainder 325 dollars: How much did he borrow? Ans. dollars. 5. At the Custom House, on the first day of June, there were entered 1800 yards of linen; on the 10th, 2500 yards; on the 25th, 600 yards; on the day following, 7500 yards; and on the three last days of the month, 1325, yards each day: What was the whole amount entered during the month? Ans. yards 6. A farmer has his live stock distributed in the following manner in pasture No. 1, there are 5 horses, 14 cows, 8 oxen, and colts; in pasture No. 2, 3 horses, 4 colts, 6 cows, 20 calves, and 12 head of young cattle; in pasture No. 4, 320 sheep, 16 calves, 2 colts, and 5 head of young cattle. How much live stock had he of each kind, and how many head had he altogether? Ans. 8 horses, 20 cows, 8 oxen, 12 colts, 36 calves, 17 head of young cattle, and 320 sheep. Total live stock, 421 head. 7. What is the interval of time between a transaction which happened 125 years ago, and one that will happen 267 years hence? Ans. years. 8. An army consists of 4000 foot soldiers, 4006 cavalry or horse, 3093 artillery-men, 1224 riflemen, 1400 pioneers |