Ushtrime te zgjidhura - Radha e veprimeve ne nje shprehje

Ne baze te rregullave qe mesuam tek mesimi radha e veprimeve ne nje shprehje , zgjidhim ushtrimet me poshte:

Ushtrimi 1

Nisur nga radha e veprimeve që kemi mësuar, gjeni vlerat e shprehjeve:

a) $\displaystyle 5\cdot {{3}^{2}}+7+{{4}^{3}}:4-5\cdot 8+4\cdot {{2}^{3}}$

b) $\displaystyle 2\cdot 13+44:11+{{3}^{2}}\cdot 4-5\cdot {{2}^{2}}-8$

c) $\displaystyle {{5}^{3}}+{{4}^{2}}-{{2}^{2}}\cdot {{3}^{2}}+{{3}^{3}}:3-7-4\cdot 5$

Zgjidhje

$\displaystyle 5\cdot {{3}^{2}}+7+{{4}^{3}}:4-5\cdot 8+4\cdot {{2}^{3}}$

$\displaystyle =5\cdot 9+7+{{4}^{2}}-5\cdot 8+4\cdot 8$

$\displaystyle =5\cdot 9+7+15-5\cdot 8+4\cdot 8$

$\displaystyle =45+7+15-5\cdot 8+4\cdot 8$

$\displaystyle =45+7+15-40+4\cdot 8$

$\displaystyle =45+7+15-40+40$

$\displaystyle =52+15-40+40$

$\displaystyle =67-0$

$\displaystyle =67$

$\displaystyle 2\cdot 13+44:11+{{3}^{2}}\cdot 4-5\cdot {{2}^{2}}-8$

$\displaystyle =2\cdot 13+44:11+9\cdot 4-5\cdot 4-8$

$\displaystyle =26+4+36-20-8$

$\displaystyle =30+36-20-8$

$\displaystyle =66-20-8$

$\displaystyle =46-8$

$\displaystyle =38$

$\displaystyle {{5}^{3}}+{{4}^{2}}-{{2}^{2}}\cdot {{3}^{2}}+{{3}^{3}}:3-7-4\cdot 5$

$\displaystyle =125+16-4\cdot 9+9:3-7-4\cdot 5$

$\displaystyle =125+16-36+3-7-20$

$\displaystyle =141-36+3-7-20$

$\displaystyle =105+3-7-20$

$\displaystyle =101-20$

$\displaystyle =81$

Ushtrimi 2

Nisur nga radha e veprimeve që kemi mësuar, gjeni vlerat e shprehjeve:

a) $\displaystyle 3\cdot {{4}^{2}}+7+{{3}^{3}}:3-9\cdot 4+3\cdot {{2}^{3}}$

b) $\displaystyle {{3}^{2}}\cdot \left( 7\cdot {{2}^{2}}-8:4 \right)$

c) $\displaystyle \left( {{3}^{2}}-{{2}^{2}}:2+3 \right)+\left( {{5}^{2}}:5-{{2}^{2}} \right)$

d) $\displaystyle {{7}^{2}}\cdot 3-2\cdot {{3}^{2}}:6+5\cdot 3$

Zgjidhje

$\displaystyle 3\cdot {{4}^{2}}+7+{{3}^{3}}:3-9\cdot 4+3\cdot {{2}^{3}}$

$\displaystyle =3\cdot 16+7+27:3-9\cdot 4+3\cdot 8$

$\displaystyle =48+7+9-36+24$

$\displaystyle =55+9-60$

$\displaystyle =64-60$

$\displaystyle =4$

$\displaystyle {{3}^{2}}\cdot \left( 7\cdot {{2}^{2}}-8:4 \right)$

$\displaystyle =9\cdot \left( 7\cdot 4-4 \right)$

$\displaystyle =9\cdot \left( 28-4 \right)$

$\displaystyle =9\cdot 24$

$\displaystyle =216$

$\displaystyle \left( {{3}^{2}}-{{2}^{2}}:2+3 \right)+\left( {{5}^{2}}:5-{{2}^{2}} \right)$

$\displaystyle =\left( 9-4:2+3 \right)+\left( 25:5-4 \right)$

$\displaystyle =\left( 9-8+3 \right)+\left( 5-4 \right)$

$\displaystyle =4+1$

$\displaystyle =5$

$\displaystyle {{7}^{2}}\cdot 3-2\cdot {{3}^{2}}:6+5\cdot 3$

$\displaystyle =49\cdot 3-2\cdot 9:6+5\cdot 3$

$\displaystyle =147-2\cdot 9:6+5\cdot 3$

$\displaystyle =147-18:6+15$

$\displaystyle =147-3+15$

$\displaystyle =129$

Ushtrimi 3

Gjeni vlerat e shprehjeve:

a) $\displaystyle \left( 510:17+24 \right)\cdot {{3}^{2}}-80:4$

b) $\displaystyle 1+\left[ {{5}^{2}}-\left( {{2}^{4}}\cdot {{2}^{3}}+{{7}^{3}}\cdot 3-{{11}^{2}}\cdot 9 \right):4 \right]:2$

c) $\displaystyle {{3}^{2}}+\left\{ {{3}^{4}}+\left[ \left( 2\cdot {{2}^{3}}+{{3}^{2}}\cdot {{2}^{2}} \right):2-8:2 \right]+7 \right\}-2\cdot 5$

Zgjidhje

$\displaystyle \left( 510:17+24 \right)\cdot {{3}^{2}}-80:4$ $\displaystyle =\left( 30+24 \right)\cdot {{3}^{2}}-20$

$\displaystyle =54\cdot {{3}^{2}}-20$

$\displaystyle =54\cdot 9-20$

$\displaystyle =486-20$

$\displaystyle =466$

$\displaystyle 1+\left[ {{5}^{2}}-\left( {{2}^{4}}\cdot {{2}^{3}}+{{7}^{3}}\cdot 3-{{11}^{2}}\cdot 9 \right):4 \right]:2$

$\displaystyle =1+\left[ {{5}^{2}}-\left( 16\cdot 8+{{7}^{2}}\cdot 7\cdot 3-121\cdot 9 \right):4 \right]:2$

$\displaystyle =1+\left[ {{5}^{2}}-\left( 128+49\cdot 21-1089 \right):4 \right]:2$

$\displaystyle =1+\left[ {{5}^{2}}-\left( 128+1029-1089 \right):4 \right]:2$

$\displaystyle =1+\left[ {{5}^{2}}-\left( 128-60 \right):4 \right]:2$

$\displaystyle =1+\left[ {{5}^{2}}-68:4 \right]:2$

$\displaystyle =1+\left[ 25-17 \right]:2$

$\displaystyle =1+8:2$

$\displaystyle =1+4$

$\displaystyle =5$

$\displaystyle {{3}^{2}}+\left\{ {{3}^{4}}+\left[ \left( 2\cdot {{2}^{3}}+{{3}^{2}}\cdot {{2}^{2}} \right):2-8:2 \right]+7 \right\}-2\cdot 5$

$\displaystyle ={{3}^{2}}+\left\{ {{3}^{4}}+\left[ \left( 2\cdot 8+9\cdot 4 \right):2-8:2 \right]+7 \right\}-2\cdot 5$

$\displaystyle =9+\left\{ 9\cdot 9+\left[ \left( 16+36 \right):2-4 \right]+7 \right\}-10$

$\displaystyle =9+\left\{ 81+\left[ 52:2-4 \right]+7 \right\}-10$

$\displaystyle =9+\left\{ 81+\left[ 26-4 \right]+7 \right\}-10$

$\displaystyle =9+\left\{ 81+22+7 \right\}-10$

$\displaystyle =9+\left\{ 103+7 \right\}-10$

$\displaystyle =9+110-10$
$\displaystyle =9+100$
$\displaystyle =109$