Εικόνες σελίδας
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Ηλεκτρ. έκδοση

8. 9+8+ 20?20+9+8? 29+8!8+ 29? 9.69+8? 89 +8:59 +8? 8+ 19?8+ 39? 10.5+8? 25+835+8? 65 +8?35+8? 11.84 8538+55?8+ 15? 45+8?65+8? 12.7+4? 17+4? 87 +4? 4+2734+57? 13.4+37? 77 +4?67+4? 44 47? 47 +4? 14.8+7?5+6? 8+7+6? 18 +7+6? 15.8+7+6? 8+37+6?8+ 67+6? 16.94938+4? 9+9+4? 19+9+4? 17. 9+9+4? 79+9+4? 49+9+4? 18.9+49 +4? 9+69 +4 9+59+4? 19.5+83+935+8+9?15+8+9? 20.5+18+9?5+68 +935+38+9? 21.5+48 +9?75+8+9? 55 +8+9? 22.6+7?3+6?9+5? 6+7+6+5? 23.16+7+6+5? 46 +7+6+5? 24.64 47 +6+5? 6+27+6+5? 25.6+57 +6+5? 66 +7+6+5? 26.3+5?1+6?7+7?3+8+6+7? 27. 13+8+6+7? 43 +8+6+7? 8. 73 +8+6+7? 23+8+6+7? 29.3+8+6+7?3+ 58 +6+7? 30.9+5? 4+6? 4+7? 9+5+6+4+7? 31.49+5+6+4+7? 39 +5+6+4+7? 32.69 +5+6+4+7?9+65 +6+4+7? 33.9+5+6+4+7?9+35+6+4+7? 34.8+8? 6+7? 34938+8+7+9? 35. 18+8+7+9? 58 +8+7+9? 36.28+8+7+9? 48+8+7+9? 37.68+8+7+9? 36 +8+7+9?

38.7+5?29?1+7?8+8?7+5+9+7 +8?

39.17+5+9+7+8+1+5+9+7+8+1+ 5+9+7?

C. 1.7+835+8?7+8+8+4+8+8+4 +8+8+7+7+8+8?

2. 5 + 9? 15 +9+1+9+6 +5+9+6+8+ 2 +5+9+1+9?

3. 7 + 6? 6+7? 7+ 6 +3+7+4+6+3+ 7+4+6+3+7+3+7+4+6?

4. 8+3+7+3+2+8+7+3+7+3+2+ 8 + 2 + 8?

5. 5 +9+8+7 +6+9+8+7 +6+9+8+ 7+6?

6. 8 +6+7+5+9+8+8+7 +6+7+5+ 9 + 8?

7. 9+8+7+3+4+5+4+7 +2+8+9+ 5 + 4 + 6 +8+7?

8. 4+5+6+7+6+3 +8+6+7+7+3+ 2 + 5+7+ 6?

9. 7+4+5+9+2 +4+7+3+2+5+6+ 1+2+8+5+7?

10. 9 +8+7+6 +5+4+3+2+1+1+2+ 3+4+5+6+7+8+9?

11. 7+5+4+8+3+2+4+5+9+3+2+ 7+7+5?

D. 1. Add as many twos as you can to 2 without obtaining a greater sum than 50. Solution. 2 +2=4, +2=6,+ 2 8, &c.

2. Add twos to 1 in the same manner.

3. Add as many threes as you can to 3 without obtaining a greater sum than 60.

4. Add threes to 2 in the same manner; to 1.

5. Add as many fours as you can to 4 without obtaining a greater sum than 80.

6. In the same manner add fours to 3; to 1 ; to 2.

7. Add as many fives as you can to 5 without obtaining a greater sum than 50.

8. In the same manner add fives to 4; to 2 ; to 3; to 1.

9. Add as many sixes as you can to 6 without obtaining a greater sum than 100.

10. In the same manner add sixes to l; to 4; to 3; to 5; to 2.

11. Add as many sevens as you can to 7 without obtaining a greater sum than 100,

12. In the same manner add sevens to 3; to 1; to 6; to 4; to 5.

13. Add as many eights as you can to 8 without obtaining a greater sum than 100.

14. In the same manner add eights to 7; to l; to 5; to 3; to 2; to 4; to 6.

15. Add as many nines as you can to 9 without obtaining a greater sum than 100.

16. In the same manner add nines to 5; to 7; to 3; to 1; to 4; to 8; to 6; to 2.

17. Add as many tens as you can to 10 without obtaining a greater sum than 100.

18. In the same manner add tens to 3; to 5; to 8; to 1; to 7; to 2; to 9; to 4; to 6.

Note. The pupil should now be taught to count by twos, threes, &c., beginning as in above examples. Thus, 2, 4, 6, 8, 10, &c.; 1, 3, 5, 7, 9, &c.; 3, 6, 9, 12, 15, &c.; 2, 5, 8, 11, 14, &c. This is a very valuable exercise, and should be continued till all the combinations are perfectly familiar. Facility in addition requires that the results only should be given. E. 1. 15—8+ 40 ? 40 + 15-8? 55 – 8? 2. 15—8 + 70 ? 70+ 15 – 8? 85 – 8? 3. 15 - 8+ 20 ? 20 + 15 – 8? 35 - 8? 4. 25 8? 75 8? 95 8? 65-8? 5. 13 — 4+ 20 ? 20 + 13 — 4? 33 - 4? 53 - 4? 6. 73 4? 43 4? 93 4? 23 4? 83

4? 7. 11–7 + 40? 40 + 11—7? 51 – 7? 21 –7? 8. 91-7? 61-7? 31 -7? 71 –7? 81 7? 9. 12- 6 + 80 ? 80 + 12 - 6? 92-6? 22 - 6? 10. 52 - 6? S2 - 6 ? 72 6 ? 32 6? 42 6? 11. 18 -9 + 50? 50 + 18 - 9? 68 - 9? 98 - 9? 12. 48 9? 28 9? 88 9? 38-9?78-9? 13. 16 – 7+30? 30 + 16 -7? 46 -7? 26 -7? 14. 86 -7? 96 -7? 36 -7? 76 7? 56 - 7 ? 15. 97 — 8? Solution. 97 — 8= 80+ 17-8, and 17 .8= 9, which added to 80 89, Ans. 16. 56 -7? 37 -9? 54 - 6? 42 - 5? 87 - -8? 17. 91 - 5 ? 83 6 ? 52 7? 23 -8? 45 -7? 18. 64 -8? 27 8? 53 7? 24 -7? 94-7? 19. 61 – 8? 55 - 9? 76 -8? 94 - 9? 85 ?

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To the Teacher. — After the solution given above is well understood, let the questions be solved as follows: [Ex. 15.] 17 — 8= 9. Therefore, 97 — 8= 89. The object of all the above forms, as also of those under the following letter, is to lead the pupil, in subtracting, to refer to the simplest combinations, or, in other words, to apply the decimal system of numbers.

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F. 1. 14 8? 16 -7? 44 -8--7? Solution.

44 8= 36,

7= 29, Ans. 2. 54 -8-7? 94 8 -7? 34 - 8 -7? 3. 84 -8-7? 64 -8--7? 24-8-7? 4. 13 - 5 ? 18–9? 23—5—9? 63—5—9? 5. 83 - 5-9? 43-5-9 ? 93—5—9? 6. 73 — 5-9 ? 33—5—9? 53 - 5 - 9 ? 7. 17 – 9? 18–9? 27. 9. 9? 97-9-9? 8. 67—9—9? 37 - 9 9? 47—9—9? 9. 77—9—9?. 57—9 -9 ? 87 9 9 ? 10. 12-7? 15 - 6 ? 22-7-6 ? 82 -76? 11. 92-7-6? 32 -7- 6 ? 42-7-6? 12. 72-7-6? 52-7-6? 62 -7- 6? 13. 16 -8? 18-9 ? - 46 -8-9? 96-8-9? 14. 86 8-9? 26 -8 -9? 56 -8 -9? 15. 36 8-9? 76 - 8 -9 ? 66 8-9? 16. 14-7? 17—8? 34-7-8? 84 -7-8? 17. 24—7—8? 44-7-8? 94—7—8? 18. 64-7-8? 54-7-8? 74-7-8?

19. 11-7? 14-5? 91 -7-5-8-7-5-8 -7-5-8-7-5-8-7?

20. 81 – 7-5-8-7-5-8-7-5-8-75-8?

21. 13 - 7? 16 - 9? 93—7—9-4-7-9-4-7 -9--4-7-9-4-7?

22. 83—7—9—4-9-9-4-7-9--4-79-4?

23. 12-8? 14 - 6? 92-8-6-6-8-6-68-6 6-8-6-6-8?

24. 82 -8-6 6 8 6 - 6 -8-6-6-86- 6?

25. 15—9? 16 - 8? 95-9-8-3-9-8-3 -9 8 3 - 9 8 3 9?

26. 85 9 8 3 9 8 - 3-9-8 3 -9 8-3?

27. 17 9? 18–9? 87 9 9 — 2 9 9 - 2 -9-9-2-9-9-2?

28. 97-9-9 2-9-9 - 2-9-9-2-99-2-9?

G. 1. 9+8+6+7+5+9+8+9+5+7-7 5 9 8 9-5-7 6 8? 2. 8+6 +5+7+9+8+3 +5+4+6+8+ 3 3 8 6 -4-5 3 8 9-7-5 6 ?

3. 17 +5+8+6 +3+9+7+ 8+9+6+4 4 - 6 9 8-7-9-3-6 - 8- 5 -- 6?

4. 23+4+6+8+2+7+5+3+9+4+6+ 8+9-9-9-6-4-9-3-5-7-2-8-6 -4-7-5?

5. 20+7+4+8+6+5+3+9+8+4+7+ 9+2+7-7-2-9-7-4-8-9-3-5-6

8-4-7-9 - 4? 6. 15+9+4+4+8+6 +8+9+5+5+8+ 8+9-9-8-9-5-5-9

9-5-5-9-8-6-8-4-4 -9-6?

7. 38+9+7–6 —5—9—3+8+6 +9–5– 8+6-9+5-4+9-3-8-5? 8. 54 9 – 6–7–8+3+ 3 +5+9+9+ 6

8– 8-7+8 6 -5 -4? 9. 67 -8 5-8-6

- 6 – 3+5+9–8–7+6+ 3 9 3 9- 5 - 2 - .4 3?

10. 71-6-9-3-8-4-2 +5+7 +3–8– 5-6 -4+7—3—9?

46,

44,

H. 1. Subtract as many twos as you can from 50. Solution : 50 - 2= 48,- 2

2

&c. 2. Subtract as many twos as you can from 49.

3. Subtract as many threes as you can from 60; from 62; from 58.

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