Question

12 whole 1 upon 14 ÷13 whole13 upon 15×2 whole6upon27 +1upon 30

Answer 1

$\huge\bold{\color{aqua}{Solution :-}}$

$\quad\bold{12\frac{1}{14}÷13\frac{13}{15}×2\frac{6}{27}+\frac{1}{30}}$

$=\bold{\frac{(12×14)+1}{14}÷\frac{(13×15)+13}{15}×\frac{(2×27)+6}{27}+\frac{1}{30}}$

$=\bold{\frac{168+1}{14}÷\frac{195+13}{15}×\frac{54+6}{27}+\frac{1}{30}}$

$=\bold{\frac{169}{14}÷\frac{208}{15}×\frac{60}{27}+\frac{1}{30}}$

$=\bold{\frac{169}{14}×\frac{15}{208}×\frac{\red{\cancel{\blue{60}}}^{\green{\:20}}}{\red{\cancel{\blue{27}}}^{\green{\:9}}}+\frac{1}{30}}$

$=\bold{\frac{169}{\red{\cancel{\purple{14}}}^{\green{\:7}}}×\frac{\red{\cancel{\blue{15}}}^{\green{\:5}}}{208}×\frac{\red{\cancel{\purple{20}}}^{\green{\:10}}}{\red{\cancel{\blue{9}}}^{\green{\:3}}}+\frac{1}{30}}$

$=\bold{\frac{169}{7}×\frac{5}{208}×\frac{10}{3}+\frac{1}{30}}$

$=\bold{\frac{169}{7}×\frac{5}{\red{\cancel{\blue{208}}}^{\green{\:104}}}×\frac{\red{\cancel{\blue{10}}}^{\green{\:5}}}{3}+\frac{1}{30}}$

$=\bold{\frac{169}{7}×\frac{5}{104}×\frac{5}{3}+\frac{1}{30}}$

$=\bold{\frac{169}{7}×\frac{25}{312}+\frac{1}{30}}$

$=\bold{\frac{4225}{2184}+\frac{1}{30}}$

$=\bold{\frac{(4225×5)+364}{10920}}$

$=\bold{\frac{21125+364}{10920}}$

$=\green{\boxed{\bold{\pink{\frac{21489}{10920}}}}}$