The Sign of Addition is an erect cross, +, and is called plus. Thus, 32, which is read three plus two, denotes that 3 and 2 are to be added. The Sign of Equality is two short parallel horizontal lines, and is read equals, or equal to. Thus, 3+2=5, is read, three plus two are equal to five. Recite the column 1 and 1. 2 and 1. 3 and 1. 4 and 1. 5 and 1. 6 and 1. 7 and 1. 8 and 1. 9 and 1. 10 and 1. What is a Sign? What is the Sign of Addition? Of Equality? 1. 2 and 4 are 2. 5 and 1 are 3. 4 and 3 are 4. 3 and 7 are 5. 8 and 2 are 6. 6 and 5 are 7. 9 and 6 are 8. 3 and 8 are how many? how many? how many? how many? how many? how many? how many? how many? EXERCISES ON THE TABLES. 9. 3 and 5 are how many? 10. 7 and 4 are how many? REVIEW.-What is Notation? (32.) Numeration? (36.) What is the Rule for writing numbers? (35.) For reading numbers? (37.) 44. How many are 11 and 7? 21 and 7? 51 and 7? 71 and 7? 12 and 3? 32 and 3? 83 and 3? 45. How many are 16 and 2? 66 and 5? 96 and 5? 17 and 3? 37 and 3? 46. How many are 18 and 7? 28 and 7? 98 and 7? 14 and 7? 27 and 7? 46 and 2? 46 and 5? 68 and 7? 69 and 8? 47. How many are 19 and 8? 29 and 8? 89 and 9? 10 and 9? 20 and 9? 80 and 9? MENTAL EXERCISES. 1. John has 4 apples, Arthur 3, and Henry 2; how many have they in all? SOLUTION. They have the sum of 4 apples, 3 apples, and 2 apples; 4 and 3 are 7, and 2 are 9. Therefore, they have in all 9 apples. 2. Paid for paper eight cents, and for pencils 6; how much was paid for the whole? 3. James caught 7 fishes, Ernest 5, and Albert 6; how many were caught by them all? 4. Gave 9 dollars for coal, and 11 dollars for wood; how many dollars were given for both? 5. If a writing-book costs 10 cents, a pen 5 cents, and a slate 9 cents, how much do they all cost? 6. A clothier sold a hat for 5 dollars, a vest for 9, and a coat for as much as he sold both the hat and vest for; for how much was the coat sold? 7. Jane has 5 books at school, 7 at home, and has loaned 6; how many has she in all? 8. In one pasture are 10 sheep, in another 7, and in a third 8; how many are there in all? 9. A farmer had 27 cows and bought 8 more; how many had he then? REVIEW.-What is the method of expressing numbers by figures called? (32.) 10. In a garden are 30 peach-trees, 7 pear-trees, and 9 apple-trees; how many trees are there in the garden? 11. How many are 33 and 29? SOLUTION. · As many as the sum of 33 and 29; 33 is 3 tens and 3 units, and 29 is 2 tens and 9 units; 3 tens and 2 tens are 5 tens, and 3 units and 9 units are 12 units, or 1 ten and 2 units; 5 tens and 1 ten are 6 tens, or 60 units; and 60 units and 2 units are 62. Therefore 33 and 29 are 62. 35 and 25? 12. How many are 25 and 35? 13. How many are 20+23+16? 16+23+20? 14. A lady paid 55 dollars for a carpet, 20 dollars for a chair, and 15 dollars for a table; how much did she pay for the whole? A PRINCIPLE OF ADDITION. 41. The sum of numbers is the same in whatever order they are added. WRITTEN EXERCISES. 42. 1. Required the sum of 236, 541, and 102. OPERATION. 236 541 102 Sum, 879 For convenience, we write the given numbers so that all the figures of the same order stand in the same column, and begin with units to add.. 2, 1, and 6 units are 9 units, which we write for the units of the sum. 0, 4, and 3 tens are 7 tens, which we write for the tens of the sum. 1, 5, and 2 hundreds are 8 hundreds, which we write for the hundreds of the sum. The sum required is 8 hundreds 7 tens 9 units, or 879. How are the given numbers written in the operation? 2. Required the sum of 595, 361, and 723. OPERATION. Sum, 1679 For convenience we write, as before, the figures of the same order in the same column, and begin with units to add. 3, 1, and 5 units are 9 units; we write the 9. 2, 6, and 9 are 17 tens, or 1 hundred and 7 tens; we write the 7, and add the 1 in with hundreds. 1, 7, 3, and 5 hundreds are 16 hundreds, or 1 thousand and 6 hundreds, which we write. The sum is 1 thousand 6 hundreds 7 tens 9 units, or 1679. In practice, it is sufficient to name only results. Thus, In the operation we may say: three, four, nine, — write 9; two, eight, seventeen, -write 7 and add 1 with next column; eight, eleven, sixteen, write 16; answer, 1679. Rule.Write the numbers to be added so that figures of the same order shall stand in the same column. Beginning with units, add each column separately, and write the sum underneath, if less than ten of the order added. If, however, the sum is ten or more, write the right-hand figure, and add the number expressed by the other figure or figures with the numbers of the next column. Write the whole sum of the last column. PROOF. Add the numbers a second time, but so that they shall have been added the one time upwards and the other downwards. Why is it convenient to have figures of the same order in the same column? Ans. Because only units of the same order can be directly added. How do you write the numbers to be added? How do you add each column? Recite the Rule. The Proof. |