Question

VA ROGGGGG E URGENT ​

Answer 1

$\displaystyle a)~\frac{^{4)}1}{2} +\frac{^{2)}1}{4} +\frac{1}{8} =\frac{4+2+1}{8} =\frac{7}{8} \\\\ b)~\frac{^{3)}1}4} +\frac{^{2)}1}{6} +\frac{1}{12}= \frac{3+2+1}{12} =\frac{6^{(6}}{12} =\frac{1}{2}\\\\c)~\frac{^{4)}2}{3} +\frac{^{2)}5}{6} +\frac{7}{12} =\frac{8+10+7}{12} =\frac{25}{12}$

$\displaystyle d)~\frac{^{6)}2}{5} +\frac{^{3)}7}{10} +\frac{^{2)}8}{15} =\frac{12+21+16}{30} =\frac{49}{30} \\\\ e)~\frac{1}{6} +\Bigg(\frac{^{4)}1}{3} +\frac{^{3)}5}{4} \Bigg)=\frac{1}{6} +\frac{4+15}{12} =\frac{^{2)}1}{6} +\frac{19}{12} =\frac{2+19}{12} =\frac{21^{(3}}{12} =\frac{7}{4}$

$\displaystyle f)~2\frac{7}{8} +\Bigg[1\frac{1}{4} +\Bigg(2\frac{1}{2}+\frac{1}{3} \Bigg)\Bigg]=\frac{2 \cdot 8+7}{8} +\Bigg[\frac{1 \cdot 4+1}{4}+ \Bigg(\frac{2\cdot 2+1}{2} +\frac{1}{3} \Bigg)\Bigg]=\\\\=\frac{16+7}{8} +\Bigg[\frac{4+1}{4} +\Bigg(\frac{4+1}{2} +\frac{1}{3} \Bigg)\Bigg]=\frac{23}{8} +\Bigg[\frac{5}{4} +\Bigg(\frac{^{3)}5}{2} +\frac{^{2)}1}{3} \Bigg)\Bigg]=$

$\displaystyle =\frac{23}{8} +\Bigg(\frac{5}{4} +\frac{15+2}{6} \Bigg)=\frac{23}{8} +\Bigg(\frac{^{3)}5}{4} +\frac{^{2)}17}{6} \Bigg)=\frac{23}{8} +\frac{15+34}{12} =\\\\=\frac{^{3)}23}{8} +\frac{^{2)}49}{12} =\frac{69+98}{24}= \frac{167}{24}$

$\displaystyle g)~\frac{3}{5} +\Bigg\{\frac{1}{2} +\Bigg[1\frac{1}{6} +\Bigg(\frac{2}{3} +1\frac{1}{10} \Bigg)\Bigg]\Bigg\}=\\\\=\frac{3}{5} +\Bigg\{\frac{1}{2} +\Bigg[\frac{1 \cdot 6+1}{6} +\Bigg(\frac{2}{3} +\frac{1 \cdot 10+1}{10} \Bigg)\Bigg]\Bigg\}=\\\\=\frac{3}{5} +\Bigg\{\frac{1}{2} +\Bigg[\frac{6+1}{6} +\Bigg(\frac{2}{3} +\frac{10+1}{10} \Bigg)\Bigg]\Bigg\}=$

$\displaystyle =\frac{3}{5} +\Bigg\{\frac{1}{2} +\Bigg[\frac{7}{6} +\Bigg(\frac{^{10)}2}{3} +\frac{^{3)}11}{10} \Bigg)\Bigg]\Bigg\}=\frac{3}{5} +\Bigg[\frac{1}{2} +\Bigg(\frac{7}{6} +\frac{20+33}{30} \Bigg)\Bigg]=\\\\=\frac{3}{5} +\Bigg[\frac{1}{2} +\Bigg(\frac{^{5)}7}{6} +\frac{53}{30} \Bigg)\Bigg]=\frac{3}{5} +\Bigg(\frac{1}{2} +\frac{35+53}{30} \Bigg)=\frac{3}{5} +\Bigg(\frac{^{15)}1}{2} +\frac{88}{30} \Bigg)=$

$\displaystyle =\frac{3}{5} +\frac{15+88}{30} =\frac{^{6)}3}{5} +\frac{103}{30} =\frac{18+103}{30} =\frac{121}{30}$

$\displaystyle h)~\frac{2}{5} +\frac{3}{5} +\frac{7}{5} +\frac{4}{5} =\frac{2+3+7+4}{5} =\frac{16}{5} \\\\ i)~\frac{3}{4} +\frac{5}{4} +\frac{1}{4} +\frac{7}{4} =\frac{3+5+1+7}{4} =\frac{16}{4} =4$

$\displaystyle j)~2\frac{1}{4} +3\frac{1}{3} +\frac{5}{6} =\frac{2 \cdot 4+1}{4} +\frac{3 \cdot 3+1}{3} +\frac{5}{6} =\frac{8+1}{4} +\frac{9+1}{3} +\frac{5}{6} =\\\\=\frac{^{3)}9}{4} +\frac{^{4)}10}{3} +\frac{^{2)}5}{6} =\frac{27+40+10}{12} =\frac{77}{12}$

$\displaystyle k)~3\frac{1}{2} +\frac{5}{3} +1\frac{2}{9} =\frac{3 \cdot 2+1}{2} +\frac{5}{3} +\frac{1\cdot9+2}{9} =\frac{6+1}{2} +\frac{5}{3} +\frac{9+2}{9} =\\\\=\frac{^{9)}7}{2} +\frac{^{6)}5}{3} +\frac{^{2)}11}{9} =\frac{63+30+22}{18} =\frac{115}{18}$