Matemáticas 1 · Tema 1
Operaciones básicas
Videos
Video 1 — Ejemplos
Video 2 — Reglas de signos
Apuntes
Las operaciones básicas con números enteros incluyen sumas, restas, multiplicaciones, divisiones, raíces y potencias. La clave está en dominar las reglas de signos.
Sumas y restas
$+$ ganancia / $-$ deuda
Signos iguales se suman
Signos diferentes se restan
Predomina el signo del número más grande
Signos iguales se suman
Signos diferentes se restan
Predomina el signo del número más grande
Multiplicaciones y divisiones
Regla de signos:
$(+)(+) = (+)$ $(+)(-) = (-)$
$(-)(+) = (-)$ $(-)(-) = (+)$
$(+)(+) = (+)$ $(+)(-) = (-)$
$(-)(+) = (-)$ $(-)(-) = (+)$
Ejemplo
Resuelve las siguientes operaciones con enteros:
$-5+3-2+4-1 = 7-8 = $ $-1$
$2(-3)(4) = -6(4) = $ $-24$
$5(-3-8) = 5(-11) = $ $-55$
$\sqrt{36} = $ $\pm 6$
$(-2)^3 = (-2)(-2)(-2) = 4(-2) = $ $-8$
$4(-5)^2 = 4(-5)(-5) = 4(25) = $ $100$
$2(-3)(4) = -6(4) = $ $-24$
$5(-3-8) = 5(-11) = $ $-55$
$\sqrt{36} = $ $\pm 6$
$(-2)^3 = (-2)(-2)(-2) = 4(-2) = $ $-8$
$4(-5)^2 = 4(-5)(-5) = 4(25) = $ $100$
Ejercicios
Bloque 1
$-5+6-3+2-1=$
$3(-2)(-5)=$
$-2(-1-4)=$
$\sqrt{36}=$
$(-4)^3=$
$5(-2)^2=$
$3(-2)(-5)=$
$-2(-1-4)=$
$\sqrt{36}=$
$(-4)^3=$
$5(-2)^2=$
Bloque 2
$8-6+2-1-2=$
$-4(-1)(-5)=$
$-4(8-3)=$
$\sqrt{49}=$
$(5)^3=$
$2(-3)^3=$
$-4(-1)(-5)=$
$-4(8-3)=$
$\sqrt{49}=$
$(5)^3=$
$2(-3)^3=$
Bloque 3
$-9+1+3-2-4=$
$7(-2)(6)=$
$-3(-1+9)=$
$\sqrt{25}=$
$(-6)^2=$
$-4(1)^2=$
$7(-2)(6)=$
$-3(-1+9)=$
$\sqrt{25}=$
$(-6)^2=$
$-4(1)^2=$
Bloque 4
$-7-5+3-2-9=$
$9(1)(5)=$
$5(4+8)=$
$\sqrt{121}=$
$(-4)^4=$
$-6(5)^3=$
$9(1)(5)=$
$5(4+8)=$
$\sqrt{121}=$
$(-4)^4=$
$-6(5)^3=$
Bloque 5
$15+3-2+7-9=$
$8(3)(-2)=$
$-7(3-6)=$
$\sqrt{-21}=$
$(-2)^2=$
$-3(6)^2=$
$8(3)(-2)=$
$-7(3-6)=$
$\sqrt{-21}=$
$(-2)^2=$
$-3(6)^2=$
Bloque 6
$+3-5-2+7+6-8=$
$-2(5)(-7)=$
$-9(-1-6)=$
$\sqrt[3]{27}=$
$(-2)^5=$
$4(-8)^2=$
$-2(5)(-7)=$
$-9(-1-6)=$
$\sqrt[3]{27}=$
$(-2)^5=$
$4(-8)^2=$
Respuestas
▼Bloque 1
$-5+6-3+2-1 = 8-9 = $ $-1$
$3(-2)(-5) = -6(-5) = $ $30$
$-2(-1-4) = -2(-5) = $ $10$
$\sqrt{36} = $ $\pm 6$
$(-4)^3 = (-4)(-4)(-4) = 16(-4) = $ $-64$
$5(-2)^2 = 5(-2)(-2) = 5(4) = $ $20$
$3(-2)(-5) = -6(-5) = $ $30$
$-2(-1-4) = -2(-5) = $ $10$
$\sqrt{36} = $ $\pm 6$
$(-4)^3 = (-4)(-4)(-4) = 16(-4) = $ $-64$
$5(-2)^2 = 5(-2)(-2) = 5(4) = $ $20$
Bloque 2
$8-6+2-1-2 = 10-9 = $ $1$
$-4(-1)(-5) = 4(-5) = $ $-20$
$-4(8-3) = -4(5) = $ $-20$
$\sqrt{49} = $ $\pm 7$
$(5)^3 = (5)(5)(5) = 25(5) = $ $125$
$2(-3)^3 = 2(-3)(-3)(-3) = 2(-27) = $ $-54$
$-4(-1)(-5) = 4(-5) = $ $-20$
$-4(8-3) = -4(5) = $ $-20$
$\sqrt{49} = $ $\pm 7$
$(5)^3 = (5)(5)(5) = 25(5) = $ $125$
$2(-3)^3 = 2(-3)(-3)(-3) = 2(-27) = $ $-54$
Bloque 3
$-9+1+3-2-4 = 4-15 = $ $-11$
$7(-2)(6) = -14(6) = $ $-84$
$-3(-1+9) = -3(8) = $ $-24$
$\sqrt{25} = $ $\pm 5$
$(-6)^2 = (-6)(-6) = $ $36$
$-4(1)^2 = -4(1)(1) = -4(1) = $ $-4$
$7(-2)(6) = -14(6) = $ $-84$
$-3(-1+9) = -3(8) = $ $-24$
$\sqrt{25} = $ $\pm 5$
$(-6)^2 = (-6)(-6) = $ $36$
$-4(1)^2 = -4(1)(1) = -4(1) = $ $-4$
Bloque 4
$-7-5+3-2-9 = 3-23 = $ $-20$
$9(1)(5) = 9(5) = $ $45$
$5(4+8) = 5(12) = $ $60$
$\sqrt{121} = $ $\pm 11$
$(-4)^4 = (-4)(-4)(-4)(-4) = 16(16) = $ $256$
$-6(5)^3 = -6(5)(5)(5) = -6(125) = $ $-750$
$9(1)(5) = 9(5) = $ $45$
$5(4+8) = 5(12) = $ $60$
$\sqrt{121} = $ $\pm 11$
$(-4)^4 = (-4)(-4)(-4)(-4) = 16(16) = $ $256$
$-6(5)^3 = -6(5)(5)(5) = -6(125) = $ $-750$
Bloque 5
$15+3-2+7-9 = 25-11 = $ $14$
$8(3)(-2) = 24(-2) = $ $-48$
$-7(3-6) = -7(-3) = $ $21$
$\sqrt{-21} = $ No existe en $\mathbb{R}$
$(-2)^2 = (-2)(-2) = $ $4$
$-3(6)^2 = -3(6)(6) = -3(36) = $ $-108$
$8(3)(-2) = 24(-2) = $ $-48$
$-7(3-6) = -7(-3) = $ $21$
$\sqrt{-21} = $ No existe en $\mathbb{R}$
$(-2)^2 = (-2)(-2) = $ $4$
$-3(6)^2 = -3(6)(6) = -3(36) = $ $-108$
Bloque 6
$+3-5-2+7+6-8 = 16-15 = $ $1$
$-2(5)(-7) = -10(-7) = $ $70$
$-9(-1-6) = -9(-7) = $ $63$
$\sqrt[3]{27} = $ $3$
$(-2)^5 = (-2)(-2)(-2)(-2)(-2) = 16(-2) = $ $-32$
$4(-8)^2 = 4(-8)(-8) = 4(64) = $ $256$
$-2(5)(-7) = -10(-7) = $ $70$
$-9(-1-6) = -9(-7) = $ $63$
$\sqrt[3]{27} = $ $3$
$(-2)^5 = (-2)(-2)(-2)(-2)(-2) = 16(-2) = $ $-32$
$4(-8)^2 = 4(-8)(-8) = 4(64) = $ $256$
Ejercicios extra
▼Bloque 7
$-9+6-5+3-1=$
$3(-5)(-2)=$
$-1(-7-5)=$
$\sqrt{49}=$
$(-6)^3=$
$7(-2)^2=$
$3(-5)(-2)=$
$-1(-7-5)=$
$\sqrt{49}=$
$(-6)^3=$
$7(-2)^2=$
Bloque 8
$-6+7-4+3-1=$
$2(-3)(-6)=$
$-4(-5-3)=$
$\sqrt{81}=$
$(-9)^3=$
$8(-3)^2=$
$2(-3)(-6)=$
$-4(-5-3)=$
$\sqrt{81}=$
$(-9)^3=$
$8(-3)^2=$
Bloque 9
$-8+4-3+6-2=$
$6(-4)(-3)=$
$-2(-5-4)=$
$\sqrt{25}=$
$(-8)^3=$
$5(-1)^2=$
$6(-4)(-3)=$
$-2(-5-4)=$
$\sqrt{25}=$
$(-8)^3=$
$5(-1)^2=$
Bloque 10
$-7+6-5+4-1=$
$5(-3)(-2)=$
$-3(-4-2)=$
$\sqrt{36}=$
$(-7)^3=$
$6(-4)^2=$
$5(-3)(-2)=$
$-3(-4-2)=$
$\sqrt{36}=$
$(-7)^3=$
$6(-4)^2=$
Bloque 11
$-9+5-3+2-1=$
$4(-2)(-5)=$
$-1(-5-3)=$
$\sqrt{64}=$
$(-9)^3=$
$7(-3)^2=$
$4(-2)(-5)=$
$-1(-5-3)=$
$\sqrt{64}=$
$(-9)^3=$
$7(-3)^2=$
Bloque 12
$-8+6-4+2-1=$
$2(-3)(-6)=$
$-3(-4-2)=$
$\sqrt{49}=$
$(-8)^3=$
$5(-2)^2=$
$2(-3)(-6)=$
$-3(-4-2)=$
$\sqrt{49}=$
$(-8)^3=$
$5(-2)^2=$