TEMA 1. NÚMEROS ENTEROS (SOLUCIONES)

 

📘 Soluciones – Hoja de Trabajo

---

Nivel 1: Conceptos básicos

1. Divisores de 15: 1, 3, 5, 15.

2. Múltiplos de 7: 7, 14, 21, 28, 35, 42, 49, 56. Mayores que 40: 42, 49, 56.

3. Opuesto de –4: +4 (misma distancia a 0 en la recta numérica).

4. $|-12| = 12$.

5. Orden: –9 < –7 < –2 < 0 < 5.

6. Divisores de 20: 1, 2, 4, 5, 10, 20. El 21 no divide a 20.

7. Múltiplos de 9 hasta 90: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. Pares: 18, 36, 54, 72, 90.

8. $|8| + |-5| = 8 + 5 = 13$.

9. El opuesto de 0 es 0.

10. Ordenados: –7 < –1 < 0 < 3 < 5.

---

Nivel 2: M.C.M., M.C.D. y operaciones simples

11. m.c.m.(6, 8) = 24.

12. m.c.d.(18, 24) = 6.

13. m.c.m.(9, 12, 15) = 180.

14. m.c.d.(32, 48, 64) = 16.

15. (–7) + (–3) = –10.

16. 5 – (–4) = 9.

17. (–12) + 8 = –4.

18. (–9) – 6 = –15.

19. (–3) × (–7) = +21.

20. (–48) ÷ 12 = –4.

---

Nivel 3: Operaciones combinadas y potencias

21. 15 + (–8) = 7.

22. (–20) + 30 = 10.

23. 7 – (–15) = 22.

24. (–12) – (–5) = (–12) + 5 = –7.

25. (–6) × 4 = –24.

26. (–40) ÷ (–5) = +8.

27. (–2)⁴ = 16.

28. (–2)⁵ = –32.

29. –2⁴ = –16 (diferente de (–2)⁴ = +16).

30. (–5)³ + (–5)² = –125 + 25 = –100.

---

Nivel 4: Problemas de aplicación

31. m.c.m.(30, 45) = 90 s.

32. m.c.d.(40, 60) = 20 → 20 cestas. Cada cesta: 2 manzanas y 3 naranjas.

33. 50 – (9 × 12) = 50 – 108 = –58 puntos.

34. 20 – (6 × 4) = 20 – 24 = –4 ºC.

35. √225 = 15 cm.

36. √81 = 9, √100 = 10.

37. √–49 → no existe en los números enteros.

38. 17² = 289 cm².

39. 180 = 2² · 3² · 5; 252 = 2² · 3² · 7 → m.c.d. = 36, m.c.m. = 1260.

40. Orden: –25 < –10 < –3 < 0 < 8 < 15.

---

Nivel extra: Operaciones combinadas largas

41. (–3) + 5 – (–7) = 9.

42. 12 – [(–4) + 6] = 10.

43. (–8) + 15 – 9 + (–6) = –8.

44. 25 – (–12) + (–7) = 30.

45. [(–5) + 9] – [(–3) + 2] = 5.

46. (–4) × (3 + (–2)) = –4.

47. (12 – 15) × (–3) = 9.

48. (–2)³ + (–2)² – 4 = –8 + 4 – 4 = –8.

49. (–5)² – [(–3) × (–2)] = 25 – 6 = 19.

50. 20 – {3 × [(–4) + 7]} = 20 – 9 = 11.

51. [(–6) + 4] × [(–2) – (–3)] = (–2) × 1 = –2.

52. {(–8) + 12} ÷ (–2) = 4 ÷ (–2) = –2.

53. (–3)² + (–4)² – (5)² = 9 + 16 – 25 = 0.

54. [15 – (–7)] ÷ [(–3) + 5] = 22 ÷ 2 = 11.

55. {(–10) + 6} × (–2) – 5 = (–4) × (–2) – 5 = 8 – 5 = 3.

56. (–2)⁴ – (–3)² + (–1)⁵ = 16 – 9 – 1 = 6.

57. [(–12) + 20] ÷ (–2) + 7 = 8 ÷ (–2) + 7 = –4 + 7 = 3.

58. {(–8) + 2³} × (–3) = (–8 + 8) × (–3) = 0. → 0 (⚠ antes lo puse mal, era 0, no 6).

59. (–5)² + (–4)×(–3) – 2³ = 25 + 12 – 8 = 29.

60. {[(–6) + 9] × (–2)} – 12 = (3 × –2) – 12 = –6 – 12 = –18.