Question

$\huge\pink{\fbox{\colorbox{yellow}{\color{blue}{Question}}}}$
Simplify :
$4 \frac{4}{5} ÷ \frac{3}{5} \: of \: 5 + \frac{4}{5} × \frac{3}{10} - \frac{1}{5}$
​

Answer 1

$\dag \: \sf{4 \frac{4}{5} ÷ \frac{3}{5} \: of \: 5 + \frac{4}{5} × \frac{3}{10} - \frac{1}{5}} \: \dag$

➩ Lets just simplify first.

$\star \sf{ \underline{1st \: simplification}}$

$\longmapsto \sf{4 \frac{4}{5} \div \frac{3}{5} } \\ \\ \longmapsto \sf{ \frac{4 \times 5 + 4}{5} \div \frac{3}{5} } \\ \\ \longmapsto \sf{ \frac{24}{5} \div \frac{3}{5} } \\ \\ \longmapsto \sf{ \frac{24}{5} \times \frac{5}{3} } \\ \\ \longmapsto \sf{ \frac{24 \times 5}{5 \times 3} } \\ \\ \longmapsto \sf{ \cancel \frac{120}{15} } \\ \\ \underline{ \boxed{ \sf{ \red{8}}}}$

$\therefore \underline{\boxed{\tt{8 \: of \: 5 + \frac{4}{5} \times \frac{3}{10} - \frac{1}{5} }}}$

$\star \: \sf{ \underline{2nd \: simplification}}$

$\longmapsto \sf{5 + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{5}{1 } + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{5 \times 5}{1 \times 5} + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{25}{5} + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{25 + 4}{5} } \\ \\ \longmapsto \sf{ \frac{29}{5} }$

$\therefore \underline{\boxed{\tt{8 \: of \: \frac{29}{5} \times \frac{3}{10} - \frac{1}{5} }}}$

$\star \: \sf{ \underline{3rd \: simplification}}$

$\longmapsto \sf{ \frac{29}{5} \times \frac{3}{10} } \\ \\ \longmapsto \sf{ \frac{29 \times 3}{5 \times 10} } \\ \\ \underline{ \boxed{ \sf{ \red{\frac{87}{50}}}}}$

$\therefore \underline{\boxed{\tt{8 \: of \: \frac{87}{50} - \frac{1}{5} }}}$

$\star \: \sf{ \underline{4th \: simplification}}$

$\longmapsto \sf{ \frac{87}{50} - \frac{1}{5} } \\ \\ \longmapsto \sf{ \frac{87}{50} - \frac{1 \times 10}{5 \times 10} } \\ \\ \longmapsto \sf{ \frac{87}{50} - \frac{10}{50} } \\ \\ \longmapsto \sf{ \frac{87 - 10}{50} } \\ \\ \longmapsto \underline{ \boxed{ \sf{ \red{\frac{77}{50} }}}}$

$\therefore \underline{\boxed{\tt{8 \: of \: \frac{77}{50} }}}$

___________________

Answer 2

Answer:

$\dag \: \sf{4 \frac{4}{5} ÷ \frac{3}{5} \: of \: 5 + \frac{4}{5} × \frac{3}{10} - \frac{1}{5}}$

†

➩ Lets just simplify first.

$\star \sf{ \underline{1st \: simplification}}⋆$

$\begin{gathered} \longmapsto \sf{4 \frac{4}{5} \div \frac{3}{5} } \\ \\ \longmapsto \sf{ \frac{4 \times 5 + 4}{5} \div \frac{3}{5} } \\ \\ \longmapsto \sf{ \frac{24}{5} \div \frac{3}{5} } \\ \\ \longmapsto \sf{ \frac{24}{5} \times \frac{5}{3} } \\ \\ \longmapsto \sf{ \frac{24 \times 5}{5 \times 3} } \\ \\ \longmapsto \sf{ \cancel \frac{120}{15} } \\ \\ \underline{ \boxed{ \sf{ \red{8}}}}\end{gathered}$

$\therefore \underline{\boxed{\tt{8 \: of \: 5 + \frac{4}{5} \times \frac{3}{10} - \frac{1}{5} }}}$

∴

$\star \: \sf{ \underline{2nd \: simplification}}⋆$

$\begin{gathered} \longmapsto \sf{5 + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{5}{1 } + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{5 \times 5}{1 \times 5} + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{25}{5} + \frac{4}{5} } \\ \\ \longmapsto \sf{ \frac{25 + 4}{5} } \\ \\ \longmapsto \sf{ \frac{29}{5} }\end{gathered}$

$\therefore \underline{\boxed{\tt{8 \: of \: \frac{29}{5} \times \frac{3}{10} - \frac{1}{5} }}}$

∴

$\star \: \sf{ \underline{3rd \: simplification}}⋆$

$\begin{gathered} \longmapsto \sf{ \frac{29}{5} \times \frac{3}{10} } \\ \\ \longmapsto \sf{ \frac{29 \times 3}{5 \times 10} } \\ \\ \underline{ \boxed{ \sf{ \red{\frac{87}{50}}}}}\end{gathered}$

$\therefore \underline{\boxed{\tt{8 \: of \: \frac{87}{50} - \frac{1}{5} }}}$

$\star \: \sf{ \underline{4th \: simplification}}$

⋆

$\begin{gathered} \longmapsto \sf{ \frac{87}{50} - \frac{1}{5} } \\ \\ \longmapsto \sf{ \frac{87}{50} - \frac{1 \times 10}{5 \times 10} } \\ \\ \longmapsto \sf{ \frac{87}{50} - \frac{10}{50} } \\ \\ \longmapsto \sf{ \frac{87 - 10}{50} } \\ \\ \longmapsto \underline{ \boxed{ \sf{ \red{\frac{77}{50} }}}}\end{gathered}$

$\therefore \underline{\boxed{\tt{8 \: of \: \frac{77}{50} }}}$

∴

Step-by-step explanation:

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