Ejercicios de fracciones: Prácticas de aritmética

1. Opera y simplifica
1. $$\dfrac 13 - \dfrac 15 \cdot \left( 1 - \dfrac 12\right)$$
2. $$\left(\dfrac 12 - \dfrac 23\right) : 3 - \dfrac 12$$
3. $$3 - \dfrac 52 \cdot \left(1 - \dfrac 35\right)$$
4. $$\left(1-\dfrac 15\right) : 2 - \dfrac 75$$
5. $$\dfrac 23 - \dfrac 12 \left(1 - \dfrac 32\right)$$
6. $$\left(1-\dfrac 52\right) : \dfrac 13 - 3$$
2. Opera y simplifica
1. $$\dfrac 12 - \dfrac 13 \left(\dfrac 25 - 3\right)$$
2. $$\left(\dfrac 12 - \dfrac 52\right) : \dfrac 13 -2$$
3. $$\left(\dfrac 13 : \dfrac 25 - \dfrac 12\right) \dfrac 13 - 1$$
4. $$\dfrac 13 - \dfrac 52 : \left(1 - \dfrac 52\right)$$
5. $$\left(\dfrac 12 - \dfrac 37\right) \dfrac 23 - \dfrac 17$$
6. $$\left(\dfrac 12 + \dfrac 34\right) \dfrac 15$$
3. Opera y simplifica
1. $$\left(\dfrac 32 - 3\right) : \dfrac 15 + 1$$
2. $$\left(\dfrac 12 - \dfrac 16\right) 6$$
3. $$\left(1 - \dfrac 38\right) \dfrac 85$$
4. $$\left(3 + \dfrac 12\right) \cdot\left(3 + \dfrac 13\right)$$
5. $$\left(\dfrac 72 - \dfrac 18 - \dfrac 1{16}\right) \dfrac 23$$
6. $$\left(\dfrac 23 - \dfrac 14\right)\left(\dfrac 23 + \dfrac 34\right)$$
4. Opera y simplifica
1. $$\dfrac 12 - \dfrac 13 \left(1 - \dfrac 15\right)$$
2. $$1 - \dfrac 23 \dfrac 15 - \dfrac 3{10}$$
3. $$\left(1 - \dfrac 23\right) : \dfrac 12 + \dfrac 25$$
4. $$\dfrac 12 - \left(\dfrac 25 + 3 - \dfrac 12\right) + \dfrac 15$$
5. $$\dfrac 12 - \left(\dfrac 15 + \dfrac 23 \dfrac 52\right)$$
6. $$\dfrac 32 - \dfrac 13 \left(1 - \dfrac 53\right)$$
5.  Opera y simplifica
1. $$\left(\dfrac 12 - \dfrac 35\right): \dfrac 34 - 1$$
2. $$\left(\dfrac 12 - 1\right) : 2 + \dfrac 13$$
3. $$\dfrac 23 - \dfrac{\dfrac 15 - 2 \left(1 - \dfrac 32\right)}{-\dfrac 12 : \dfrac 23} -1$$
4. $$\dfrac 32 - \dfrac{1 - \dfrac 13}3$$
5. $$1 - \dfrac 12 : \dfrac{1 + \dfrac 12}3$$
6. $$\dfrac 32 - \left(\dfrac 12 - \dfrac 15 : 3\right)$$
6. Opera y simplifica
1. $$\left(\dfrac 32 - 1\right) : \left(\dfrac 25 + 1\right)$$
2. $$\left(\dfrac 73 - \dfrac 12\right) - \left(1 - \dfrac 35\right)$$
3. $$\dfrac{1 + \dfrac 32}3 - \left( 1 - \dfrac 32\right)$$
4. $$\dfrac{3 + \dfrac 12}{3 - \dfrac 12} : \dfrac 35$$
5. $$\dfrac 52 - \dfrac 35 : 3 - 2 \dfrac 13$$
6. $$\dfrac 32 - \dfrac 53 : \left(-1 + \dfrac 12\right)$$
7.  Opera y simplifica
1. $$\dfrac 52 : \dfrac 13 - \dfrac 35 \dfrac 73$$
2. $$\dfrac 12 - \left(\dfrac 13 - \dfrac 35 : 2\right)$$
3. $$\dfrac{1 - \dfrac 25 \left(1 - \dfrac 32\right)}{1 - \dfrac 72}$$
4. $$\dfrac{\dfrac 12 - \dfrac 23:\left(1-\dfrac 43\right)}{1 - \dfrac 25}$$
5. $$\dfrac{\dfrac 13 \dfrac 25 - \dfrac 13 - 1}{1 - \dfrac 53}$$
6. $$\dfrac{\dfrac 12-\dfrac 23 \left(1 - \dfrac 65\right)}{1 - \dfrac 72}$$
8. Opera y simplifica
1. $$\dfrac{\dfrac 13 - \left(1 + \dfrac 25\right)}{\dfrac 13} - \dfrac 12 : \dfrac 27$$
2. $$\dfrac{\dfrac 23 - \dfrac 15 \left(1 - \dfrac 23\right)}{-1 + \dfrac 15} - \dfrac 23$$
3. $$\dfrac 35 - \dfrac 23 \left(1 - \dfrac 72\right)$$
4. $$1 - \dfrac 13 : \left(1 - \dfrac 15\right)$$
5. $$\dfrac 13 - \dfrac 25 \left(1 - \dfrac 23\right)$$
6. $$\dfrac 12 - \dfrac 35 \left(2 - \dfrac 56\right)$$
9. Opera y simplifica
1. $$2 - \dfrac 23 \left(1 - \dfrac 15 : \dfrac 27\right) - \dfrac 27$$
2. $$2 - \dfrac 35 \left(\dfrac 23 - \dfrac 52\right)$$
3. $$\left(\dfrac 12 - \dfrac 23\right) : \dfrac 23 - \dfrac 12 \left(1 - \dfrac 52\right)$$
4. $$\left(\dfrac 12 - \dfrac 25 : \dfrac 23\right) \dfrac 53 - \dfrac 23 \left(-1 + \dfrac 25\right)$$
5. $$\dfrac{\dfrac 12 - \dfrac 72 \left(1 - \dfrac 52\right)}{\dfrac 23 - \dfrac 12} - 1$$
6. $$\dfrac{\dfrac 23 - \dfrac 15:\left(1 - \dfrac 53\right)}{-\dfrac 25 \dfrac 12} + \dfrac 32$$
10.  Opera y simplifica
1. $$\left(\dfrac 35 - \dfrac 23\right) : \dfrac 12 - \dfrac 53 \left(1 - \dfrac 72\right)$$
2. $$2 - \dfrac 23 \left(1 - \dfrac 15 : \dfrac 27\right) - \dfrac 13 : \dfrac 25$$
3. $$\left(\dfrac 13 - 2\right) \dfrac 12 - \dfrac 15 : \left(1 - \dfrac 23 : \dfrac 32\right)$$
4. $$\dfrac{1 - \dfrac 25 \left(1 - \dfrac 32\right)}{1 - \dfrac 72}$$
5. $$\dfrac{\dfrac 12 - \dfrac 23 : \left(1 - \dfrac 43\right)}{1 - \dfrac 25}$$
6. $$\dfrac{\dfrac 13 - \left(1 + \dfrac 25\right)}{\dfrac 13} -\dfrac 12 : \dfrac 27$$
11. Opera y simplifica
1. $$\dfrac{\dfrac 13 \dfrac 25 - \dfrac 13 - 1}{1 - \dfrac 53}$$
2. $$\dfrac{\left(2 - \dfrac 13\right) \left(6 + \dfrac 12\right)}{1 - \dfrac 12}$$
3. $$\dfrac{3 - \dfrac 34}{\left(2 + \dfrac 15\right)\left(1 - \dfrac 15\right)}$$
4. $$\left(\dfrac{16}3 - \dfrac 45 + \dfrac{11}{10}\right)\left(\dfrac 52 - \dfrac 54\right)^2$$
5. $$\dfrac{\dfrac 35 - \dfrac 7{10} + \dfrac 16}{\dfrac 43 - \dfrac 45 + \dfrac 1{12}} :\dfrac{\dfrac 72 + \dfrac 45}{\dfrac {11}5 - \dfrac 32}$$
6. $$\left(\dfrac {13}4 - \dfrac {13}3 + \dfrac{13}6\right) :\left(4 - \dfrac 73\right)^2$$
12.  Opera y simplifica
1. $$\left(\dfrac 53 - \dfrac 76 + \dfrac {11}{12}\right)\dfrac 4{\dfrac 72 - \dfrac 58 + \dfrac {13}{16}}$$
2. $$\left(\dfrac 23 + \dfrac 56 - \dfrac 7{12}\right)^2\left(\dfrac 52 - \dfrac{13}4\right)$$
3. $$\dfrac{\dfrac 73 - \dfrac 45 + \dfrac 7{10}}{3 + \dfrac 94 - \dfrac{11}{12}} :\left(1 + \dfrac 12 + \dfrac 13\right)$$
4. $$\left(1 - \dfrac 43\right) : \dfrac 12 - \dfrac 23 \left(1 - \dfrac 53 : 2\right)$$
5. $$\left(\dfrac 23 \dfrac 12 - 1\right) : \dfrac 23 -\dfrac 23 \left(1 - \dfrac 45\right)$$
6. $$\dfrac{1 - \dfrac 23 \left(1 - \dfrac 52\right)}{1 - \dfrac 23}- \dfrac 12$$

Ejercicios de fracciones: Operaciones con fracciones

1. Sumar las fracciones y después simplificar:
1. $\dfrac 47 + \dfrac 18 =$
2. $\dfrac 49 + \dfrac 16 =$
3. $\dfrac 49 + \dfrac 35 =$
4. $\dfrac 27 + \dfrac 16 =$
5. $\dfrac 25 + \dfrac 34 =$
2. Sumar por MCM y simplificar si es posible:
1. $\dfrac 35 + \dfrac 14 + \dfrac 16=$
2. $\dfrac 38 + 4 + \dfrac 45 =$
3. $\dfrac 45 + \dfrac 16 + \dfrac 67 =$
4. $3 + \dfrac 45 + \dfrac 16 =$
5. $\dfrac 67 + \dfrac 25 + \dfrac 29 =$
3. Restar las fracciones y después simplificar si es posible:
1. $\dfrac 49 - \dfrac 13=$
2. $\dfrac 49 - \dfrac 16 =$
3. $\dfrac 47 - \dfrac 16 =$
4. $\dfrac 67 - \dfrac 29 =$
5. $\dfrac 38 - \dfrac 29 =$
4. Resolver y simplificar:
1. $\frac{\frac 45 + \frac 16}7=$
2. $\dfrac{\left(\frac 15 + \frac 16\right)\frac 35}6 =$
3. $(8+4)\cdot \frac{4}{\frac 75 - \frac 13}=$
4. $\frac{\frac 47 \cdot \frac 57}{\frac 29 + \frac 45} =$
5. $\frac{13-\frac 18}{\frac 49 + 6} =$

Ejercicios de enteros: operaciones combinadas

1. Resolver las operaciones:
1. $[(6+1+3)-(-5+6)](-3)=$
2. $[(-7+5-2,5)+(-6+8)-(7,5-1)]=$
3. $\{[(-4+6)-(-1+6)]+[(3+1)]\}(-5)=$
4. $[(-4+6)-(-3(-4)][(-3+1)(-5)]=$
5. $[(-4+6)-(3)(-4)]:](-5+1,5)(-4)=$
6. $[(-6)+(-5)+(-2)]:(-8)=$
7. $[-6-(-12)+(-3)+(-5)]:(-2)=$
8. $[(-5+1)+(-5)]-[(-4+6+18)-(-7,5+6-2,5)]=$
9. $\{[(-5)(-3)(-2)]+[(-5+6-7)-(-8+9)]\}:(-8)=$
10. $[(-6+8-7+5)]+[(-5+2+1)(-3,5)]=$
2. Resolver la propiedad distributiva (en forma directa y  desarrollada)
1. $(-6+5-7+8)(-3)=$
2. $(-21+35-6+12)(-5)=$
3. $(-27+41-18+19)(-3)=$
4. $(-5+8-6+7+8)(-5)=$
5. $(-6+9-7+8)(-4)=$
6. $(-5+13-12)(-5)=$
7. $(-5-4+12)(-6)=$
8. $(-5-4+12)(-6)=$
9. $(-3+5-7+6)(-8)=$
10. $(-7+5+4+1)(-3)=$
3. Obtener un valor numérico:
1. $6^{-3}=$
2. $(-5)^{-4}=$
3. $(-2)^{-4}=$
4. $(-4)^{-3}=$
5. $(11)^{-3}=$
6. $\left(\frac 15\right)^{-3}=$
7. $\left(\frac{-3}7\right)^{-3}=$
8. $\left(\frac{5}{-7}\right)^{-3}=$
9. $\left(\frac{-4}7\right)^{-3}=$
10. $\left(\frac 6{11}\right)^{-4}=$
11. $6^{-3}\cdot 6^{-4}=$
12. $-5^{-3}\cdot (-5^6)=$
13. $11^3\cdot 11^{-3} \cdot 11^{-2}=$
14. $8^3\cdot 8^{-4}\cdot 8^2=$
15. $5^{-6}\cdot 5^6=$
16. $6^{-2} : 6^4=$
17. $7^{-3} \cdot 7^{-2}=$
18. $6^4\cdot 6^3 \cdot 6^{-5}=$
19. $13^{-4} \cdot 13^{-5} : 13^{-2}=$
20. $2^4: 2^{-3} \cdot 2^5=$