Inicio › Matemáticas 1 › Jerarquía de operaciones

Matemáticas 1 · Tema 2

Jerarquía de operaciones

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Ejemplo

Resuelve aplicando la jerarquía de operaciones:

−5+6(−3+8)−4(−3)(2)−5(−3)2=−5+6(5)+24−5(9)=−5+30+24−45=−50+54=4\begin{aligned} -5+6(-3+8)-4(-3)(2)-5(-3)^2 &= \\ -5+6(5)+24-5(9) &= \\ -5+30+24-45 &= \\ -50+54 &= \mathbf{4} \end{aligned}
2[−5(−3(−2+8))]=2[−5(−3(6))]=2[−5(−18)]=2[90]=180\begin{aligned} 2[-5(-3(-2+8))] &= \\ 2[-5(-3(6))] &= \\ 2[-5(-18)] &= \\ 2[90] &= \mathbf{180} \end{aligned}

Ejercicios

Bloque 1
4−2(−1)(−5)+6(−1+4)−3(−5)2=4-2(-1)(-5)+6(-1+4)-3(-5)^2=
5(−2)(3)+4(−1−5)−3+4(−1)2=5(-2)(3)+4(-1-5)-3+4(-1)^2=
8−6(3−4)−2(3)2+2(6)(−1)=8-6(3-4)-2(3)^2+2(6)(-1)=
3(−2)4+6−3(−4)(−1)+7(−3+10)=3(-2)^4+6-3(-4)(-1)+7(-3+10)=
−3+4(−2)(6)−5(3−8)+2(−4)2=-3+4(-2)(6)-5(3-8)+2(-4)^2=
7−3(2)(−4)+5(−6+2)−2(3)2=7-3(2)(-4)+5(-6+2)-2(3)^2=
Bloque 2
5[−3(4(−1−2))]=5[-3(4(-1-2))]=
−3[2(−5(−4+10))]=-3[2(-5(-4+10))]=
4[−3(2(−10+4))]=4[-3(2(-10+4))]=
−6[5(−4(3+7))]=-6[5(-4(3+7))]=
6[−4(3(−5+2))]=6[-4(3(-5+2))]=
−5[2(−6(4−9))]=-5[2(-6(4-9))]=

Respuestas

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Bloque 1
4−2(−1)(−5)+6(−1+4)−3(−5)2=4−10+6(3)−3(25)=4−10+18−75=22−85=−63\begin{aligned} 4-2(-1)(-5)+6(-1+4)-3(-5)^2 &= \\ 4-10+6(3)-3(25) &= \\ 4-10+18-75 &= \\ 22-85 &= \mathbf{-63} \end{aligned}
5(−2)(3)+4(−1−5)−3+4(−1)2=−30+4(−6)−3+4(1)=−30−24−3+4=−57+4=−53\begin{aligned} 5(-2)(3)+4(-1-5)-3+4(-1)^2 &= \\ -30+4(-6)-3+4(1) &= \\ -30-24-3+4 &= \\ -57+4 &= \mathbf{-53} \end{aligned}
8−6(3−4)−2(3)2+2(6)(−1)=8−6(−1)−2(9)−12=8+6−18−12=14−30=−16\begin{aligned} 8-6(3-4)-2(3)^2+2(6)(-1) &= \\ 8-6(-1)-2(9)-12 &= \\ 8+6-18-12 &= \\ 14-30 &= \mathbf{-16} \end{aligned}
3(−2)4+6−3(−4)(−1)+7(−3+10)=3(16)+6−12+7(7)=48+6−12+49=103−12=91\begin{aligned} 3(-2)^4+6-3(-4)(-1)+7(-3+10) &= \\ 3(16)+6-12+7(7) &= \\ 48+6-12+49 &= \\ 103-12 &= \mathbf{91} \end{aligned}
−3+4(−2)(6)−5(3−8)+2(−4)2=−3−48−5(−5)+2(16)=−3−48+25+32=−51+57=6\begin{aligned} -3+4(-2)(6)-5(3-8)+2(-4)^2 &= \\ -3-48-5(-5)+2(16) &= \\ -3-48+25+32 &= \\ -51+57 &= \mathbf{6} \end{aligned}
7−3(2)(−4)+5(−6+2)−2(3)2=7+24+5(−4)−2(9)=7+24−20−18=31−38=−7\begin{aligned} 7-3(2)(-4)+5(-6+2)-2(3)^2 &= \\ 7+24+5(-4)-2(9) &= \\ 7+24-20-18 &= \\ 31-38 &= \mathbf{-7} \end{aligned}
Bloque 2
5[−3(4(−1−2))]=5[−3(4(−3))]=5[−3(−12)]=5[36]=180\begin{aligned} 5[-3(4(-1-2))] &= \\ 5[-3(4(-3))] &= \\ 5[-3(-12)] &= \\ 5[36] &= \mathbf{180} \end{aligned}
−3[2(−5(−4+10))]=−3[2(−5(6))]=−3[2(−30)]=−3[−60]=180\begin{aligned} -3[2(-5(-4+10))] &= \\ -3[2(-5(6))] &= \\ -3[2(-30)] &= \\ -3[-60] &= \mathbf{180} \end{aligned}
4[−3(2(−10+4))]=4[−3(2(−6))]=4[−3(−12)]=4[36]=144\begin{aligned} 4[-3(2(-10+4))] &= \\ 4[-3(2(-6))] &= \\ 4[-3(-12)] &= \\ 4[36] &= \mathbf{144} \end{aligned}
−6[5(−4(3+7))]=−6[5(−4(10))]=−6[5(−40)]=−6[−200]=1200\begin{aligned} -6[5(-4(3+7))] &= \\ -6[5(-4(10))] &= \\ -6[5(-40)] &= \\ -6[-200] &= \mathbf{1200} \end{aligned}
6[−4(3(−5+2))]=6[−4(3(−3))]=6[−4(−9)]=6[36]=216\begin{aligned} 6[-4(3(-5+2))] &= \\ 6[-4(3(-3))] &= \\ 6[-4(-9)] &= \\ 6[36] &= \mathbf{216} \end{aligned}
−5[2(−6(4−9))]=−5[2(−6(−5))]=−5[2(30)]=−5[60]=−300\begin{aligned} -5[2(-6(4-9))] &= \\ -5[2(-6(-5))] &= \\ -5[2(30)] &= \\ -5[60] &= \mathbf{-300} \end{aligned}

Ejercicios extra 1

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Bloque A
−4(−3)(−2)−3(−2+6)+5−4(−3)2=-4(-3)(-2)-3(-2+6)+5-4(-3)^2=
6(2)(−5)+7(8−4)−3+5(2)3=6(2)(-5)+7(8-4)-3+5(2)^3=
4−3(5)(−2)+6(−9+7)−7(−4)2=4-3(5)(-2)+6(-9+7)-7(-4)^2=
−5(4)(3)+6(2−9)−2+8(5)3=-5(4)(3)+6(2-9)-2+8(5)^3=
7+5(3)(−6)−4(8−5)+9(2)2=7+5(3)(-6)-4(8-5)+9(2)^2=
−6(5)(−4)+7(2−6)−8+3(4)2=-6(5)(-4)+7(2-6)-8+3(4)^2=
Bloque B
−4[−5(−3(−2+8))]=-4[-5(-3(-2+8))]=
7[−3(4(5+1))]=7[-3(4(5+1))]=
−6[5(−2(3−7))]=-6[5(-2(3-7))]=
8[−6(2(4+3))]=8[-6(2(4+3))]=
−5[3(−7(6−2))]=-5[3(-7(6-2))]=
−7[−4(6(−2+9))]=-7[-4(6(-2+9))]=

Ejercicios extra 2

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Bloque C
9(3)(−2)−5(7)3+6(5−1)+2=9(3)(-2)-5(7)^3+6(5-1)+2=
−4+6(−8)2−3(2−7)+5(3)(−6)=-4+6(-8)^2-3(2-7)+5(3)(-6)=
8−7(4)(−3)+9(6−2)−5(2)3=8-7(4)(-3)+9(6-2)-5(2)^3=
−3(2)(5)+6+4(−9+3)−7(3)2=-3(2)(5)+6+4(-9+3)-7(3)^2=
Bloque D
6[−5(3(7+4))]=6[-5(3(7+4))]=
−8[3(−6(5−2))]=-8[3(-6(5-2))]=
5[−3(2(4+6))]=5[-3(2(4+6))]=
−4[6(−5(1+3))]=-4[6(-5(1+3))]=
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