2. How many are 3 leaves and 2 leaves? 3 leaves and 3 leaves? How many are 3 and 1? 3 and 2? 3 and 3? 3. Jane has 3 apples and Mary has 4 apples. How many apples have both? How many are 3 and 4? 4 and 3? 4. George gave me 2 apples and Mary gave me 4. How many apples did both give me? How many are 4 and 2? 2 and 4? 5. A farmer had 2 horses and bought 6 more. How many horses had he then? How many are 2 and 6? 6 and 2? 6. Henry paid 5 cents for a pencil and 7 cents for a writing-book. How many cents did he pay for both? How many are 5 and 7? 7 and 5? 7. If a barrel of flour is worth $6, and a cord of wood $4, how much are both worth? How many are 6 and 4? 8. A man plowed 8 acres of land in one week and 6 acres the next week. How many acres did he plow in both weeks? 9. On the Fourth of July, Ned spent 10 cents for firecrackers and 6 cents for torpedoes. How many cents did he spend for both? 10. Harry is 6 years old and his sister is four How old is his sister? How many are 6 and 4? years older. 11. At Christmas, Horace received 9 gifts from his parents, and 4 from other friends. How many gifts did he receive? 12. A certain house has 5 windows in one side and 7 in another. How many windows in the two sides? 13. How many are 5 oranges and 4 oranges? 6 boys and 3 boys? 5 horses and 6 cents? 14. Why can you not tell how many 5 horses and 6 cents are? 15. Why can you tell how many 5 oranges and 4 oranges are? Numbers that express things of the same name are called Like Numbers. 16. What kind of numbers only can be united? DEFINITIONS. 44. Addition is the process of finding a number which shall be equal to two or more given numbers. 45. The Sum or Amount is the result obtained by adding. 46. The Sign of Addition is an upright cross: +. It is called plus, and is placed between numbers to be added. Thus, 3+4 is read 3 plus 4, and means that 3 and 4 are to be added. 47. The Sign of Equality is two short horizontal lines: =. It is read equals, or is equal to. Thus, 3+4=7, is read 3 plus 4 equals 7. The expression 3+4=7, or any other expression of equality, is called an Equation. 48. PRINCIPLES.-1. Only like numbers can be added. 2. The sum and numbers added must be like numbers. 1+1= 21+2 = = TABLE. 31+3 = 41+ 51 5 6 2+1 3 2+2 4 2+3= 5|2+4= 6 2 5 7 3+1 4 3+2= 5 3+3 6 3+4=73+58 4+15 4+2 64+3 7 4+4 8 459 5+1=65+2= 75+3 8 5+4 95+5=10 6+176+2 86+3 9 6+4=106+5=11 7+1= 8 7+2= 9 7+3=10|7+4=11|7+ 5=12 8+1 9 8+2-10 | 8+3=11 8+4=128+5=13 9+1=109+2=11|9+3=12|9+4 13 9+5=14 1+6 71+7 = = =11 8189|1+9= 10 | 1+10: 2+682 +7 9 2+8=10 2+9-11 2+10=12 3+6 9 3+7=10 3+8=11 3+9-12 3+10=13 4+6 10 4+7=11 4+8=124+9=13 4+10-14 5+6 11 5+7-12 5+8=13 5+9-14 5+10=15 6+6 12 6+7-13 6-8-14 6-9-15 6+10=16 7+6=13 7+7=14 7+8=15 7-9-16 7+10=17 86 14 8+7=15 8+8=16 8+9-17 8-10-18 9+6=159+7=16 9+8=17 9+9-18 9+10=19 | CASE I. 49. To add single columns. 1. A grocer sold 8 pounds of sugar to one man and 7 pounds to another. How many pounds did he sell to both? ANALYSIS. Since he sold 8 pounds to one man and 7 pounds to another, to both he sold the sum of 8 pounds and 7 pounds, which is 15 pounds. 2. A man rode 7 miles the first hour and 6 miles the second hour. How far did he ride in the two hours? 3. On one tree are 8 birds, and on another 4 birds. How many birds are there on both? 4. Carl earned $2 in May, $5 in June, and $4 in July. How much did he earn in the three months? 5. I gave 6 nuts to one boy, 5 to another, and 3 to another. How many nuts did I give to all? 6. I paid 5 cents for paper, 3 cents for pens, and 5 cents for ink. How much did I pay for all? 7. A lemon cost 5 cents, an orange 6 cents, and a pineapple 8 cents. What did they all cost? 8. Esther gave her teacher 5 pinks, 7 roses, and 4 pansies. How many flowers did she give her? 9. James shot 9 birds, Henry shot 6, and William 5. How many did they all shoot? 10. A woman picked 9 quarts of blackberries one morning, while her son picked 3 quarts. How many quarts did both pick? 11. James solved 6 examples, John 5, William 8, and Henry 7. How many examples did they solve? 12. One boy picked 6 quarts of cherries, another 4 quarts, another 5 quarts. How many quarts did they all pick? 13. I gathered from one pear-tree, this year, 2 bushels of fruit, from another 4 bushels, from another 3 bushels, and from another 2 bushels. How many bushels did I gather from these four trees? 14. A merchant sold from a piece of cloth, 3 yards at one time, 6 yards at another, 8 yards at another, and 5 yards at another. How many yards did he sell in all? 15. A man picked 8 barrels of apples on Monday, 6 barrels on Tuesday, 4 barrels on Wednesday, and 5 barrels on Thursday. How many did he pick altogether? 16. Henry learned 7 verses of poetry on one day, 5 on another, 6 on another, and 8 on another. How many verses did he learn in the four days? 17. A man paid $9 for a coat, $4 for pants, and $2 for a hat. How much did he pay for all? 18. In a garden there are 8 apple-trees, 7 plum-trees, and 9 peach-trees. How many trees are there in the garden? 19. There are 4 boys and 7 girls in one class, and 6 boys and 8 girls in another. How many pupils in both classes? 20. Homer paid 8 dollars for a fur cap, and 5 dollars for a pair of skates. How much did both cost him? 21. A boy gathered nuts for three days. The first day he brought home 8 quarts, the next day 7 quarts, the next day 9 quarts. How many quarts did he bring home? 22. Repeat the addition table of ones. Of twos. threes. Of fours. Of fives. Of sixes. Of sevens. eights. Of nines. Of tens. Of Of 23. Count by 2's from 0 to 20; thus: 0, 2, 4, 6, 8, 10, 12, etc. 24. Count by 3's from 2 to 26. 25. Count by 4's from 0 to 36. 26. Count by 5's from 3 to 43. 27. Count by 6's from 0 to 42. 28. Count by 7's from 4 to 39. 29. Count by 8's from 2 to 58. 30. Count by 9's from 7 to 70. From 26 to 41. From 5 to 53. From 7 to 72. From 4 to 46. From 11 to 60. From From 7 to 63. WRITTEN EXERCISES. 50. 1. What is the sum of 5, 4, 7, and 6? ANALYSIS.-We write the numbers to be added in a column, and begin at the bottom to add; thus: 6, 13, 17, 22; and write the sum beneath. To prove the work we may begin at the top and add downwards. If the result agrees with the one formerly obtained the work is probably correct. In adding say, 6, 13, 17, etc., instead of 6 and 7 are 13. and 4 are 17, etc. |