DEFINITIONS. 1. Numbers having units of the same kind are called Like Numbers. 2. Addition is the process of uniting two or more numbers into a single number, called their Sum. 3. The sum, then, is the result obtained by adding. 4. The Sign of Addition is an upright cross (+) called plus (more); it is placed between the numbers to be added. 7 + 4 is read "7 plus 4." 5. The Sign of Equality is two parallel horizontal 74 11 is read "7 plus 4 equals 11." lines, =. 6. 7 + 4 = 11, being an expression of equality, is called an Equation. PRINCIPLES. 1. Only like numbers can be added. 2. The sum and the numbers added are like numbers. EXERCISES. 1. The digits are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. What numbers do they represent? 2. Answer the following questions at sight: 1. 0+1=? 8.7+0=? 15. 45? 10. 8, 4, 2, 3. 15. 7, 8, 4, 9. 5. 5, 3, 2. 3. Begin at the uppermost 3 in A, and give orally and at sight the sum of the numbers in each line thus: 3, 5, 10, sum of first line of A. 4. Begin at the same place and give in the same manner the sum of each column thus: 3, 7, 12, 18, 23, the sum of the first column of A. ORAL PROBLEMS. 1. How many fingers are 6 fingers and 4 fingers? Answer: 6 fingers + 4 fingers 10 fingers. 2. If an apple cost 3 cents and an orange 5 cents, how much did both cost? 3. A girl paid 6 cents for a pencil and 5 cents for sugar-plums. How much did she How much did she pay for both? 4. A boy spent 7 cents for some paper and 5 cents for an orange. How much did he spend for both? 5. A man rode on his bicycle 8 miles the first hour and 7 miles the second hour. How far did he ride in the two hours? 6. A horse travels 9 miles the first hour and 8 miles the second hour. How far does he go in two hours? 7. A farmer who had 5 horses, bought 5 more at one time, and at another time 4 more. How many did he then have? 8. A matron bought 8 quarts of strawberries of one man, 5 quarts of another, and 5 of another. How many quarts did she buy in all? 9. A traveller bought for lunch 5 cents' worth of crackers, 4 cents' worth of milk, and 8 cents' worth of berries. What did his lunch cost him? 10. How many animals are in a field, there being 6 cows, 4 oxen, and 8 sheep? 11. Margaret gave $2.00 for an atlas, $3.00 for a history, and $8.00 for a dictionary. How much did she pay for all? 12. A man earns $9.00, while a boy and a girl earn each $5.00. How much do all earn when the man has earned $9.00? 13. Add 2, 6, 8, 7, 1, 2. Also, 8, 5, 3, 2, 4, 9. 14. A house has 8 windows on the east side, 7 on the west, and 9 on the south. How many are there in all? 15. A rose-bush has on one branch 8 roses, on another roses, and on a third 6 roses. How many roses on the three branches? 7 How 16. In one part of a building there are 9 offices, in another part 5 offices, in a third part 6 offices. many in the three parts? 17. Jennie sold to a lady 4 quarts of berries, 8 quarts of peaches, 2 quarts of beans, and 1 quart of peas. How many quarts did the lady buy? 18. A gentleman selected for a bouquet 8 white carnations, 6 pink ones, and 6 red ones. How many in all in the bouquet? 19. Sarah wrote on Monday 9 letters, on Tuesday 8 letters, on Wednesday 7 letters. How many letters did she write in the three days? 20. A foot-ball team won 2 games in September, 3 games in October, 4 games in November, not counting the game won on Thanksgiving Day. How many games were won in the three months? 21. Count by 2's from 0 to 50; 22. Count by 3's from 0 to 51. 23. Count by 4's from 0 to 52. 24. Count by 6's from 0 to 72. 25. Count by 7's from 0 to 84. 26. Count by 8's from 0 to 96. 37. Count by 9's from 7 to 115. thus: 0, 2, 4, 6, etc. Addition of Single Columns. WRITTEN EXERCISES. 1. What is the sum of 3, 6, 8, 7? Explanation. Explain, speaking thus: "For convenience, we write the numbers in a column. We then add thus: 7+ 8 = 15; 15 +6=21; 21 + 3 = 24, the sum." Process. 3 6 8 7 24 sum = To prove the correctness of the result, we add the column downwards: 36 9; 98 17; 17 +7 24, the We may explain more briefly, saying "3, 9, 17, 24; again, 7, 15, 21, 24." What is the first principle of Addition? 2. In a similar manner add and explain these : (21.) (22.) (23.) (24.) (25.) (26.) (27.) (28.) (29) (30.) 3 5 1 8 1 5 66724 7 6 6 7 5 9 3 (31.) (32.) (33.) (34.) (35.) (36.) (37.) (38.) (39.) (40.) |