🎯 أحسب العبارات التالية
A. $A = \dfrac{12}{63}\times\dfrac{45}{36}\times\dfrac{14}{35}\times\dfrac{49}{21}$
✅ الحل الكامل
$A = \dfrac{2}{9}$ ✅
بعد الاختزال: $A = \dfrac{2}{9}$ ✅
B. $B = \dfrac{\dfrac{12}{\dfrac{13}{\dfrac{7}{26}}}}{}$
✅ الحل الكامل
$B = \dfrac{42}{169}$ ✅
$\dfrac{13}{\dfrac{7}{26}}=13\times\dfrac{26}{7}=\dfrac{338}{7}$
M. $M = \dfrac{5}{3}-\left(\dfrac{3}{2}-\dfrac{1}{5}\right)\times\dfrac{5}{26}$
✅ الحل الكامل
$M = \dfrac{17}{12}$ ✅
$\dfrac{3}{2}-\dfrac{1}{5}=\dfrac{13}{10}$
N. $N = \dfrac{7}{3}+\dfrac{2}{3}\times\left(\dfrac{4}{5}+\dfrac{3}{2}\right)-1{,}3$
✅ الحل الكامل
$N = \dfrac{77}{30}$ ✅
$\dfrac{4}{5}+\dfrac{3}{2}=\dfrac{23}{10}$
C. $C = \dfrac{\dfrac{5}{4}+\dfrac{3}{2}}{\dfrac{7}{4}} + \dfrac{\dfrac{3}{4}+\dfrac{9}{2}}{\dfrac{7}{2}}$
✅ الحل الكامل
$C = \dfrac{43}{14}$ ✅
$\dfrac{11/4}{7/4}=\dfrac{11}{7}$ و $\dfrac{21/4}{7/2}=\dfrac{3}{2}$
D. $D = 3+\dfrac{7}{\dfrac{3}{2+\dfrac{1}{4}}+\dfrac{2}{3}}$
✅ الحل الكامل
$D = \dfrac{13}{2}$ ✅
$2+\dfrac{1}{4}=\dfrac{9}{4}$، $\dfrac{3}{9/4}=\dfrac{4}{3}$، $\dfrac{4}{3}+\dfrac{2}{3}=2$
E. أحسب بطريقتين العبارة $E = \dfrac{5}{3}\times\left(\dfrac{6}{5}+\dfrac{3}{20}\right)$
✅ الحل الكامل
$E = \dfrac{9}{4}$ ✅
**الطريقة الأولى:** $\dfrac{6}{5}+\dfrac{3}{20}=\dfrac{27}{20}$، $E=\dfrac{5}{3}\times\dfrac{27}{20}=\dfrac{9}{4}$ ✅